Modified Chebyshev Collocation Method for Solving Differential Equations
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M Ziaul Arif
2015-05-01
Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.
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 ...
A Chebyshev collocation method for solving two-phase flow stability problems
Boomkamp, P.A.M.; Boersma, B.J.; Miesen, R.H.M.; Beijnon, G.V.
1997-01-01
This paper describes a Chebyshev collocation method for solving the eigenvalue problem that governs the stability of parallel two-phase flow. The method is based on the expansion of the eigenfunctions in terms of Chebyshev polynomials, point collocation, and the subsequent solution of the resulting
MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method
Institute of Scientific and Technical Information of China (English)
S. ABBASBANDY; T. HAYAT; H. R. GHEHSAREH; A. ALSAEDI
2013-01-01
The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An eﬃcient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.
1994-01-01
Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential
Zhou, Rui-Rui; Li, Ben-Wen
2017-03-01
In this study, the Chebyshev collocation spectral method (CCSM) is developed to solve the radiative integro-differential transfer equation (RIDTE) for one-dimensional absorbing, emitting and linearly anisotropic-scattering cylindrical medium. The general form of quadrature formulas for Chebyshev collocation points is deduced. These formulas are proved to have the same accuracy as the Gauss-Legendre quadrature formula (GLQF) for the F-function (geometric function) in the RIDTE. The explicit expressions of the Lagrange basis polynomials and the differentiation matrices for Chebyshev collocation points are also given. These expressions are necessary for solving an integro-differential equation by the CCSM. Since the integrand in the RIDTE is continuous but non-smooth, it is treated by the segments integration method (SIM). The derivative terms in the RIDTE are carried out to improve the accuracy near the origin. In this way, a fourth order accuracy is achieved by the CCSM for the RIDTE, whereas it's only a second order one by the finite difference method (FDM). Several benchmark problems (BPs) with various combinations of optical thickness, medium temperature distribution, degree of anisotropy, and scattering albedo are solved. The results show that present CCSM is efficient to obtain high accurate results, especially for the optically thin medium. The solutions rounded to seven significant digits are given in tabular form, and show excellent agreement with the published data. Finally, the solutions of RIDTE are used as benchmarks for the solution of radiative integral transfer equations (RITEs) presented by Sutton and Chen (JQSRT 84 (2004) 65-103). A non-uniform grid refined near the wall is advised to improve the accuracy of RITEs solutions.
Nielsen, S A; Hesthaven, J S
2002-05-01
The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE.
Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.
2017-03-01
Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.
Indian Academy of Sciences (India)
Z AMERIAN; M K SALEM; A SALAR ELAHI; M GHORANNEVISS
2017-03-01
Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad–Shafranov equation (an axisymmetric,magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular crosssection of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.
Direct trajectory optimization based on a mapped Chebyshev pseudospectral method
Institute of Scientific and Technical Information of China (English)
Guo Xiao; Zhu Ming
2013-01-01
In view of generating optimal trajectories of Bolza problems,standard Chebyshev pseudospectral (PS) method makes the points' accumulation near the extremities and rarefaction of nodes close to the center of interval,which causes an ill-condition of differentiation matrix and an oscillation of the optimal solution.For improvement upon the difficulties,a mapped Chebyshev pseudospectral method is proposed.A conformal map is applied to Chebyshev points to move the points closer to equidistant nodes.Condition number and spectral radius of differentiation matrices from both methods are presented to show the improvement.Furthermore,the modification keeps the Chebyshev pseudospectral method's advantage,the spectral convergence rate.Based on three numerical examples,a comparison of the execution time,convergence and accuracy is presented among the standard Chebyshev pseudospectral method,other collocation methods and the proposed one.In one example,the error of results from mapped Chebyshev pseudospectral method is reduced to 5％ of that from standard Chebyshev pseudospectral method.
Chebyshev-Legendre method for discretizing optimal control problems
Institute of Scientific and Technical Information of China (English)
ZHANG Wen; MA He-ping
2009-01-01
In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
Chebyshev and Fourier spectral methods
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.
Chebyshev-Fourier Spectral Methods for Nonperiodic Boundary Value Problems
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Bojan Orel
2014-01-01
Full Text Available A new class of spectral methods for solving two-point boundary value problems for linear ordinary differential equations is presented in the paper. Although these methods are based on trigonometric functions, they can be used for solving periodic as well as nonperiodic problems. Instead of using basis functions periodic on a given interval −1,1, we use functions periodic on a wider interval. The numerical solution of the given problem is sought in terms of the half-range Chebyshev-Fourier (HCF series, a reorganization of the classical Fourier series using half-range Chebyshev polynomials of the first and second kind which were first introduced by Huybrechs (2010 and further analyzed by Orel and Perne (2012. The numerical solution is constructed as a HCF series via differentiation and multiplication matrices. Moreover, the construction of the method, error analysis, convergence results, and some numerical examples are presented in the paper. The decay of the maximal absolute error according to the truncation number N for the new class of Chebyshev-Fourier-collocation (CFC methods is compared to the decay of the error for the standard class of Chebyshev-collocation (CC methods.
Evaluation of Chebyshev pseudospectral methods for third order differential equations
Renaut, Rosemary; Su, Yi
1997-03-01
When the standard Chebyshev collocation method is used to solve a third order differential equation with one Neumann boundary condition and two Dirichlet boundary conditions, the resulting differentiation matrix has spurious positive eigenvalues and extreme eigenvalue already reaching O(N 5 for N = 64. Stable time-steps are therefore very small in this case. A matrix operator with better stability properties is obtained by using the modified Chebyshev collocation method, introduced by Kosloff and Tal Ezer [3]. By a correct choice of mapping and implementation of the Neumann boundary condition, the matrix operator has extreme eigenvalue less than O(N 4. The pseudospectral and modified pseudospectral methods are implemented for the solution of one-dimensional third-order partial differential equations and the accuracy of the solutions compared with those by finite difference techniques. The comparison verifies the stability analysis and the modified method allows larger time-steps. Moreover, to obtain the accuracy of the pseudospectral method the finite difference methods are substantially more expensive. Also, for the small N tested, N ? 16, the modified pseudospectral method cannot compete with the standard approach.
A fast Chebyshev method for simulating flexible-wing propulsion
Moore, M. Nicholas J.
2017-09-01
We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (Nlog N) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O (N2) cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, O (Nlog N) , allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.
A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method
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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.
Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method
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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.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
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Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
Chebyshev super spectral viscosity method for a fluidized bed model
Sarra, S 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.
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.
Short-time Chebyshev wave packet method for molecular photoionization
Sun, Zhaopeng; Zheng, Yujun
2016-08-01
In this letter we present the extended usage of short-time Chebyshev wave packet method in the laser induced molecular photoionization dynamics. In our extension, the polynomial expansion of the exponential in the time evolution operator, the Hamiltonian operator can act on the wave packet directly which neatly avoids the matrix diagonalization. This propagation scheme is of obvious advantages when the dynamical system has large Hamiltonian matrix. Computational simulations are performed for the calculation of photoelectronic distributions from intense short pulse ionization of K2 and NaI which represent the Born-Oppenheimer (BO) model and Non-BO one, respectively.
Schwarz and multilevel methods for quadratic spline collocation
Energy Technology Data Exchange (ETDEWEB)
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Mason, JC
2002-01-01
Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focused primarily on the theoretical aspects. A broad, up-to-date treatment is long overdue.Providing highly readable exposition on the subject''s state of the art, Chebyshev Polynomials is just such a treatment. It includes rigorous yet down-to-earth coverage of the theory along with an in-depth look at the properties of all four kinds of Chebyshev polynomials-properties that lead to a range of results in areas such as approximation, series expansions, interpolation, quadrature, and integral equations. Problems in each chapter, ranging in difficulty from elementary to quite advanced, reinforce the concepts and methods presented.Far from being an esoteric subject, Chebysh...
AN ACCURATE SOLUTION OF THE POISSON EQUATION BY THE FINITE DIFFERENCE-CHEBYSHEV-TAU METHOD
Institute of Scientific and Technical Information of China (English)
Hani I. Siyyam
2001-01-01
A new finite difference-Chebyshev-Tau method for the solution of the twodimensional Poisson equation is presented. Some of the numerical results are also presented which indicate that the method is satisfactory and compatible to other methods.
A modified orthogonal collocation method for reaction diffusion problems
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M. Soliman
2014-12-01
Full Text Available A low-order collocation method is often useful in revealing the main features such as concentration and temperature profiles and the effectiveness factor for porous catalyst particles. Two modifications are introduced in this paper to make the method more efficient. The first modification is to add an extra collocation point at the center of the particle. It is shown that such extra point introduces a single variable non-linear equation to be solved after obtaining the standard collocation method solution. In the second modification, the polynomial solution obtained from the application of the orthogonal collocation method is transformed to a rational function form. These two modifications are applied to specific examples and it is shown that they can improve the performance of collocation methods in general and the one-point collocation method in particular.
Time Collocation Method for Structural Dynamic Problems
Institute of Scientific and Technical Information of China (English)
TANG Chen; LUO Tao; YAN Haiqing; GU Xiaohui
2005-01-01
In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.
CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION
Institute of Scientific and Technical Information of China (English)
Benyu Guo; Songnian He; Heping Ma
2002-01-01
A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensionalunsteady Navier-Stokes equation. The generalized stability and convergence are proved.The numerical results show the advantages of this method.
Weighted Chebyshev distance classification method for hyperspectral imaging
Demirci, S.; Erer, I.; Ersoy, O.
2015-06-01
The main objective of classification is to partition the surface materials into non-overlapping regions by using some decision rules. For supervised classification, the hyperspectral imagery (HSI) is compared with the reflectance spectra of the material containing similar spectral characteristic. As being a spectral similarity based classification method, prediction of different level of upper and lower spectral boundaries of all classes spectral signatures across spectral bands constitutes the basic principles of the Multi-Scale Vector Tunnel Algorithm (MS-VTA) classification algorithm. The vector tunnel (VT) scaling parameters obtained from means and standard deviations of the class references are used. In this study, MS-VT method is improved and a spectral similarity based technique referred to as Weighted Chebyshev Distance (WCD) method for the supervised classification of HSI is introduced. This is also shown to be equivalent to the use of the WCD in which the weights are chosen as an inverse power of the standard deviation per spectral band. The use of WCD measures in terms of the inverse power of standard deviations and optimization of power parameter constitute the most important side of the study. The algorithms are trained with the same kinds of training sets, and their performances are calculated for the power of the standard deviation. During these studies, various levels of the power parameters are evaluated based on the efficiency of the algorithms for choosing the best values of the weights.
Parallel adaptive wavelet collocation method for PDEs
Energy Technology Data Exchange (ETDEWEB)
Nejadmalayeri, Alireza, E-mail: Alireza.Nejadmalayeri@gmail.com [FortiVenti Inc., Suite 404, 999 Canada Place, Vancouver, BC, V6C 3E2 (Canada); Vezolainen, Alexei, E-mail: Alexei.Vezolainen@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States); Brown-Dymkoski, Eric, E-mail: Eric.Browndymkoski@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States); Vasilyev, Oleg V., E-mail: Oleg.Vasilyev@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States)
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
Recent advances in radial basis function collocation methods
Chen, Wen; Chen, C S
2014-01-01
This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s ...
CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Sang Dong Kim; Byeong Chun Shin
2006-01-01
We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the L2w-and H-1w,- norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
A Collocation Method for Solving Fractional Riccati Differential Equation
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Yalçın Öztürk
2013-01-01
Full Text Available We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.
THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper applies the singular integral operators,singular quadrature operators and discretization matrices associated withsingular integral equations with Cauchy kernels, which are established in [1],to give a unified framework for various collocation methods of numericalsolutions of singular integral equations with Cauchy kernels. Under theframework, the coincidence of the direct quadrature method and the indirectquadrature method is very simple and obvious.
The energy balance to nonlinear oscillations via Jacobi collocation method
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M.K. Yazdi
2015-06-01
Full Text Available This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)
2016-05-15
The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.
A COLLOCATION METHOD FOR THE CONDUCTIVITY PROBLEM WITH DISCONTINUOUS COEFFICIENT
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the γ is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.
Wang, Zhiheng
2015-01-01
A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.
Meshfree local radial basis function collocation method with image nodes
Baek, Seung Ki; Kim, Minjae
2017-07-01
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.
APPLICATION OF NEWTON'S AND CHEBYSHEV'S METHODS TO PARALLEL FACTORIZATION OF POLYNOMIALS
Institute of Scientific and Technical Information of China (English)
Shi-ming Zheng
2001-01-01
In this paper it is shown in two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.
Numerical simulation of GEW equation using RBF collocation method
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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.
3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
Zhou, D.; Lo, S. H.; Cheung, Y. K.
2009-02-01
The three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time.
FRACTURE CALCULATION OF BENDING PLATES BY BOUNDARY COLLOCATION METHOD
Institute of Scientific and Technical Information of China (English)
王元汉; 伍佑伦; 余飞
2003-01-01
Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it ts only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time This is an effective semi-analytical and semi-numerical method.
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
Error Control Strategies for Numerical Integrations in Fast Collocation Methods
Institute of Scientific and Technical Information of China (English)
陈仲英; 巫斌; 许跃生
2005-01-01
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
A variational sinc collocation method for strong-coupling problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)
2006-06-02
We have devised a variational sinc collocation method (VSCM) which can be used to obtain accurate numerical solutions to many strong-coupling problems. Sinc functions with an optimal grid spacing are used to solve the linear and nonlinear Schroedinger equations and a lattice {phi}{sup 4} model in (1 + 1). Our results indicate that errors decrease exponentially with the number of grid points and that a limited numerical effort is needed to reach high precision. (letter to the editor)
Directory of Open Access Journals (Sweden)
Zahra Masouri
2014-04-01
Full Text Available The focus of this paper is on the numerical solution of linear systems of Fredhlom integral equations of the second kind. For this purpose, the Chebyshev cardinal functions with Gauss-Lobatto points are used. By combination of properties of these functions and the effective Clenshaw-Curtis quadrature rule, an applicable numerical method for solving the mentioned systems is formulated. Some error bounds for the method are computed and its convergence rate is estimated. The method is numerically evaluated by solving some test problems caught from the literature by which the accuracy and computational efficiency of the method will be demonstrated.
A Collocation Method for Numerical Solutions of Coupled Burgers' Equations
Mittal, R. C.; Tripathi, A.
2014-09-01
In this paper, we propose a collocation-based numerical scheme to obtain approximate solutions of coupled Burgers' equations. The scheme employs collocation of modified cubic B-spline functions. We have used modified cubic B-spline functions for unknown dependent variables u, v, and their derivatives w.r.t. space variable x. Collocation forms of the partial differential equations result in systems of first-order ordinary differential equations (ODEs). In this scheme, we did not use any transformation or linearization method to handle nonlinearity. The obtained system of ODEs has been solved by strong stability preserving the Runge-Kutta method. The proposed scheme needs less storage space and execution time. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. The scheme is simple as well as easy to implement. The scheme provides approximate solutions not only at the grid points, but also at any point in the solution range.
DEFF Research Database (Denmark)
Nielsen, S.A.; Hesthaven, J.S.
2002-01-01
The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applica......The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model...... such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral...... solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. (C) 2002 Elsevier Science B.V. All rights reserved....
Euler-Chebyshev methods for integro-differential equations
Houwen, P.J. van der; Sommeijer, B.P.
1996-01-01
We construct and analyse explicit methods for solving initial value problems for systems of differential equations with expensive righthand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Such equations arise after spatial discretization of parabolic integro-differen
COLLOCATION DICTIONARY OF ADJECTIVES IN TEACHING TURKISH: METHOD AND PRACTICE
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Yrd.Doç.Dr.Bülent ÖZKAN
2010-09-01
Full Text Available To collect the main vocabulary of a language is the major aims of lexicology works. Lexicology looks after to prepare not only for general purpose lexicon for mother tongue users but also particular purpose lexicons for special aims (e.g. proverbs and idioms dictionary, terms dictionary, synonym words dictionary, antonym words dictionary, collocation dictionary etc.. Today, when the studies are considered about the vocabulary of Turkey Turkish, general purpose lexicon works, and particular purpose lexicons for special aim works are insufficient and limited. In lexicology, collocation dictionary is one of the main products of lexicology, seen as a non mentioned subject at the study of Turkey Turkish vocabulary. On the other hand, in lexicology, collocation has been taken place in literature as an important applying method, especially in the corpus linguistics applications and defining the stage of preferences in language teaching.This study’s object is to investigate the collocations in a corpus-based approach, is defined as adjective and lexicalized 11.320 lexemes as headword in Türkçe Sözlük (Turkish Dictionary which is including the vocabulary of Turkey Turkish. This study has speciality is being the first, about purpose, content and method also executing by experienced researchers at similar studies. The anticipated outcomes of this study are as follows: 1.It will be defined the adjectives’s syntactic features which have intense usage in generally language and especially in Turkey Turkish. 2.It will be made semantic and syntactic corpus-control of adjectives in Türkçe Sözlük (Turkish Dictionary which is including the vocabulary of Turkey Turkish. 3.It will be defined the concept domains of adjectives-noun and noun-adjectives relationship in Turkish. 4.It will be defined the adjective-noun usages based by frequency appearance relationships about mother tongue and second language teaching for Turkish. 5.It will be collected main
Simplex-stochastic collocation method with improved scalability
Energy Technology Data Exchange (ETDEWEB)
Edeling, W.N., E-mail: W.N.Edeling@tudelft.nl [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hopital, 75013 Paris (France); Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands); Dwight, R.P., E-mail: R.P.Dwight@tudelft.nl [Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands); Cinnella, P., E-mail: P.Cinnella@ensam.eu [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hopital, 75013 Paris (France)
2016-04-01
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.
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Javidi, M. [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: mo_javidi@yahoo.com; Golbabai, A. [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: golbabai@iust.ac.ir
2009-01-30
In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge-Kutta method for time integration to solve the generalized Burger's-Huxley equation (GBHE). To reduce round-off error in spectral collocation (pseudospectral) method we use preconditioning. Firstly, theory of application of Chebyshev spectral collocation method with preconditioning (CSCMP) and domain decomposition on the generalized Burger's-Huxley equation presented. This method yields a system of ordinary differential algebric equations (DAEs). Secondly, we use fourth order Runge-Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.
Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan
2016-01-01
We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text] (d denotes the space dimensions) as the collocation points. The error analysis in [Formula: see text]-norm and [Formula: see text]-norm theoretically justifies the exponential convergence of spectral collocation method in multidimensional space. We give two numerical examples in order to illustrate the validity of the proposed Jacobi spectral collocation method.
De Raedt, H; Michielsen, K; Kole, JS; Figge, MT
2003-01-01
We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.
A Newton-Picard collocation method for periodic solutions of delay differential equations
Verheyden, Koen; Lust, Kurt
This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We exploit the equivalence of the linearized collocation system and the discretization of the linearized periodic boundary
Che, Cheng-Xuan; Wang, Xiu-Ming; Lin, Wei-Jun
2010-06-01
Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method (SEM) using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient (PCG)-element by element (EBE) method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method (FDM) for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.
An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations
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Lee Ken Yap
2014-01-01
Full Text Available The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
Block Hybrid Collocation Method with Application to Fourth Order Differential Equations
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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.
Directory of Open Access Journals (Sweden)
Xiaoyong Xu
2015-01-01
Full Text Available A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs and initial value problems (IVPs in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. Accuracy and efficiency of the suggested method are established through comparing with the existing quintic B-spline collocation method, homotopy asymptotic method, and modified decomposition method. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literatures.
Evaluating the uncertainty of Darcy velocity with sparse grid collocation method
Institute of Scientific and Technical Information of China (English)
SHI LiangSheng; YANG JinZhong; ZHANG DongXiao
2009-01-01
Spatial variability of Darcy velocity is presented due to the heterogeneity of aquifer parameters.The uncertainty qualification of velocity suffers great challenge in the complex porous media.This work focuses on the use of sparse grid collocation method in velocity simulation.Since the sparse grid col-location method provides a non-intrusive way to incorporate any existing deterministic solver, the mixed finite element method is combined as the deterministic solver to retain the local continuity of Darcy velocity.We decompose the error of the velocity into three components, and illustrate that the Karhunen-Loeve truncation brings more error into velocity approximation than into head.The conver-gence properties of velocity moments restrict the application of sparse grid collocation method in the problems with small correlation lengths.This work provides insights towards the application of sparse grid collocation method to velocity modeling.It is demonstrated that for which problems the sparse grid collocation method is expected to be competitive with the Monte Carlo simulation.Further work about the anisotropic sparse grid collocation method should be extended to circumvent the obstacle of dimensionality.
Evaluating the uncertainty of Darcy velocity with sparse grid collocation method
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Spatial variability of Darcy velocity is presented due to the heterogeneity of aquifer parameters. The uncertainty qualification of velocity suffers great challenge in the complex porous media. This work focuses on the use of sparse grid collocation method in velocity simulation. Since the sparse grid collocation method provides a non-intrusive way to incorporate any existing deterministic solver, the mixed finite element method is combined as the deterministic solver to retain the local continuity of Darcy velocity. We decompose the error of the velocity into three components, and illustrate that the Karhunen-Loeve truncation brings more error into velocity approximation than into head. The convergence properties of velocity moments restrict the application of sparse grid collocation method in the problems with small correlation lengths. This work provides insights towards the application of sparse grid collocation method to velocity modeling. It is demonstrated that for which problems the sparse grid collocation method is expected to be competitive with the Monte Carlo simulation. Further work about the anisotropic sparse grid collocation method should be extended to circumvent the obstacle of dimensionality.
Directory of Open Access Journals (Sweden)
Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
A two-level stochastic collocation method for semilinear elliptic equations with random coefficients
Energy Technology Data Exchange (ETDEWEB)
Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos
2017-05-01
In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse mesh $\\mathcal{T}_H$ with a low level stochastic collocation (corresponding to the polynomial space $\\mathcal{P}_{P}$) and solve linearized equations on a fine mesh $\\mathcal{T}_h$ using high level stochastic collocation (corresponding to the polynomial space $\\mathcal{P}_p$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $\\mathcal{T}_h$ and $\\mathcal{P}_p$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.
Ellahi, Rahmat; Wang, Xinil; Hameed, Muhammad
2014-02-01
This article is concerned with the study of heat transfer and nonlinear slip effects on the Couette flow of a third-grade fluid. Numerical solutions are obtained by solving nonlinear differential equations using the higher-order Chebyshev spectral method. The results for no slip and no thermal slip become special cases of this study. Moreover, the results for Poiseuille flow can be obtained as a special case from the generalized Couette flow analysis by setting the plate velocity to zero. Graphical results for involved pertinent parameters are sketched and examined.
Directory of Open Access Journals (Sweden)
Somayeh Nemati
2016-11-01
Full Text Available In this paper, we consider the second-kind Chebyshev polynomials (SKCPs for the numerical solution of the fractional optimal control problems (FOCPs. Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.
Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
Skvortsov, L. M.
2012-10-01
Stiffly accurate Runge-Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge-Kutta methods.
Directory of Open Access Journals (Sweden)
Bashar Zogheib
2017-01-01
Full Text Available A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients. By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points, equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the efficiency and spectral (exponential accuracy of the proposed method.
A Collocation Method for Numerical Solution of the Generalized Burgers-Huxley Equation
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Mohammad ZAREBNIA
2014-08-01
Full Text Available In this paper, we use a collocation method to solve the Burgers-Huxley equation. To achieve this aim, we use mesh free technique based on sinc functions. The stability analysis is discussed. Some numerical examples are provided to illustrate the accuracy and fluency of the method.
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).
A stochastic collocation method for the second order wave equation with a discontinuous random speed
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.
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Morel, J.E.
1981-01-01
A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field. The method is easily extended to other geometries and higher dimensions. Applications exist in the areas of neutron transport with highly anisotropic scattering (such as that associated with hydrogenous media), charged-particle transport, and particle transport in controlled-fusion plasmas. 23 figures, 6 tables.
A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
Govindarajan, N.; De Visser, C.C.; Krishnakumar, K.
2014-01-01
This paper presents a sparse collocation method for solving the time-dependent Hamilton–Jacobi–Bellman (HJB) equation associated with the continuous-time optimal control problem on a fixed, finite timehorizon with integral cost functional. Through casting the problem in a recursive framework using t
A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE IMMISCIBLE PROBLEMS
Institute of Scientific and Technical Information of China (English)
Ma Ning
2007-01-01
Two-phase, incompressible, immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations. The pressure equation is elliptic,whereas the concentration equation is parabolic, and both are treated by the collocation scheme. Existence and uniqueness of solutions of the algorithm are proved. A optimal convergence analysis is given for the method.
The Application of the Probabilistic Collocation Method to a Transonic Axial Flow Compressor
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.
A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
Govindarajan, N.; De Visser, C.C.; Krishnakumar, K.
2014-01-01
This paper presents a sparse collocation method for solving the time-dependent Hamilton–Jacobi–Bellman (HJB) equation associated with the continuous-time optimal control problem on a fixed, finite timehorizon with integral cost functional. Through casting the problem in a recursive framework using
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
Babuška, Ivo
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.
Banerjee, Amartya S; Hu, Wei; Yang, Chao; Pask, John E
2016-01-01
The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis set to solve the equations of density functional theory in a discontinuous Galerkin framework. The methodology is implemented in the Discontinuous Galerkin Density Functional Theory (DGDFT) code for large-scale parallel electronic structure calculations. In DGDFT, the basis is generated on-the-fly to capture the local material physics, and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. Hence, DGDFT combines the key advantage of planewave basis sets in terms of systematic improvability with that of localized basis sets in reducing basis size. A central issue for large-scale calculations, however, is the computation of the electron density from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials si...
Numerical Solution of One-dimensional Telegraph Equation using Cubic B-spline Collocation Method
Directory of Open Access Journals (Sweden)
J. Rashidinia
2014-02-01
Full Text Available In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained by some existing methods to verify the accurate nature of our method.
Directory of Open Access Journals (Sweden)
Sohrab Bazm
2016-11-01
Full Text Available Alternative Legendre polynomials (ALPs are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
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.
Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations
Li, Haojun; Rieder, Andreas; Freude, Wolfgang
2012-01-01
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices.
ELASTO－PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD
Institute of Scientific and Technical Information of China (English)
SongKangzu; ZhangXiong; LuMiugwau
2003-01-01
A meshless approach based on the moving least square method is developed for elasto-plasticity analysis, in which the incremental formulation is used. In this approach, the displacement shape functions are constructed by using the moving least square approximation, and the discrete governing equations for elasto-plastic material are constructed with the direct collocation method. The boundary conditions are also imposed by collocation. The method established is a truly meshless one, as it does not need any mesh, either for the purpose of interpolation of the solution variables, or for the purpose of construction of the discrete equations. It is simply formulated and very efficient, and no post-processing procedure is required to compute the derivatives of the unknown variables, since the solution from this method based on the moving least square approximation is already smooth enough. Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-rdasticity analysis.
Institute of Scientific and Technical Information of China (English)
Emiko ISHIWATA; Yoshiaki MUROYA
2009-01-01
To compute long term integrations for the pantograph differential equation with proportional delay qt,0 ＜ q ≤1:y'(t) = ay(t) + by(qt) +f(t),y(0) = Yo,we offer two kinds of numerical methods using special mesh distributions,that is,a rational approximant with 'quasi-uniform meshes'(see E.Ishiwata and Y.Muroya [Appl.Math.Comput.,2007,187:741-747]) and a Gauss collocation method with 'quasi-constrained meshes'.If we apply these meshes to rational approximant and Gauss collocation method,respectively,then we obtain useful numerical methods of order p* = 2m for computing long term integrations. Numerical investigations for these methods are also presented.
Energy Technology Data Exchange (ETDEWEB)
Menz, J. [Technische Univ. Freiburg (Germany). Inst. fuer Markscheidewesen und Geodaesie; Bian Shaofeng [Technical Univ. of Surveying and Mapping, Wuhan (China)
1998-10-01
The contribution shows that Hardy`s multisquare method leads to results that are similar in their structure to the predictions by collocation. On the basis of geostatistical model assumptions, equations for calculating the prediction error are presented, and the multisquare method is compared with the collocation method on this basis. Equivalences between collocation and kriging are gone into, and information is presented on how predictions can be improved in the Bayesian sense. [Deutsch] In der folgenden Arbeit soll zuerst gezeigt werden, dass die Multiquadratische Methode nach HARDY zu Vorhersagen fuehrt, die in ihrer Struktur den Vorhersagen durch Kollokation entsprechen. Unter geostatistischen Modellannahmen werden nach dem Fehlerfortpflanzungsgesetz Formeln fuer die Berechnung der Vorhersagefehler angegeben. Auf der Grundlage dieser Formeln wird die Multiquadratische Methode mit der Kollokation verglichen. Es wird auf die Aequivalenzen zwischen Kollokation und Kriging verwiesen und angegeben, wie sich die Vorhersagen im BAYESschen Sinne verbessern lassen. (orig./MSK)
Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems
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A. H. Bhrawy
2011-01-01
Full Text Available We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs. An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.
Collocation method with quintic b-spline method for solving hirota-satsuma coupled KDV equation
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K. R. Raslan
2016-05-01
Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled system of KdV (CKdV equation with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms, are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors
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Musil T.
2007-11-01
Full Text Available A parallel algorithm of a numeric procedure based on a method of trigonometric collocation is presented for investigating an unbalance response of a rotor supported by journal bearings. After a condensation process the trigonometric collocation method results in a set of nonlinear algebraic equations which is solved by the Newton-Raphson method. The order of the set is proportional to the number of nonlinear bearing coordinates and terms of the finite Fourier series. The algorithm, realized in the MATLAB parallel computing environment (DCT/DCE, uses message passing technique for interacting among processes on nodes of a parallel computer. This technique enables portability of the source code both on parallel computers with distributed and shared memory. Tests, made on a Beowulf cluster and a symmetric multiprocessor, have revealed very good speed-up and scalability of this algorithm.
A novel stochastic collocation method for uncertainty propagation in complex mechanical systems
Qi, WuChao; Tian, SuMei; Qiu, ZhiPing
2015-02-01
This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.
An adaptive multi-element probabilistic collocation method for statistical EMC/EMI characterization
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.
Subich, Christopher J.
2015-08-01
This work extends the machinery of the moving mesh partial differential equation (MMPDE) method to the spectral collocation discretization of time-dependent partial differential equations. Unlike previous approaches which bootstrap the moving grid from a lower-order, finite-difference discretization, this work uses a consistent spectral collocation discretization for both the grid movement problem and the underlying, physical partial differential equation. Additionally, this work develops an error monitor function based on filtering in the spectral domain, which concentrates grid points in areas of locally poor resolution without relying on an assumption of locally steep gradients. This makes the MMPDE method more robust in the presence of rarefaction waves which feature rapid change in higher-order derivatives.
Milling Stability Analysis Based on Chebyshev Segmentation
HUANG, Jianwei; LI, He; HAN, Ping; Wen, Bangchun
2016-09-01
Chebyshev segmentation method was used to discretize the time period contained in delay differential equation, then the Newton second-order difference quotient method was used to calculate the cutter motion vector at each time endpoint, and the Floquet theory was used to determine the stability of the milling system after getting the transfer matrix of milling system. Using the above methods, a two degree of freedom milling system stability issues were investigated, and system stability lobe diagrams were got. The results showed that the proposed methods have the following advantages. Firstly, with the same calculation accuracy, the points needed to represent the time period are less by the Chebyshev Segmentation than those of the average segmentation, and the computational efficiency of the Chebyshev Segmentation is higher. Secondly, if the time period is divided into the same parts, the stability lobe diagrams got by Chebyshev segmentation method are more accurate than those of the average segmentation.
A pseudospectral collocation time-domain method for diffractive optics
DEFF Research Database (Denmark)
Dinesen, P.G.; Hesthaven, J.S.; Lynov, Jens-Peter
2000-01-01
We present a pseudospectral method for the analysis of diffractive optical elements. The method computes a direct time-domain solution of Maxwell's equations and is applied to solving wave propagation in 2D diffractive optical elements. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights...
Adaptive-Anisotropic Wavelet Collocation Method on general curvilinear coordinate systems
Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2017-03-01
A new general framework for an Adaptive-Anisotropic Wavelet Collocation Method (A-AWCM) for the solution of partial differential equations is developed. This proposed framework addresses two major shortcomings of existing wavelet-based adaptive numerical methodologies, namely the reliance on a rectangular domain and the "curse of anisotropy", i.e. drastic over-resolution of sheet- and filament-like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution. The A-AWCM addresses both of these challenges by incorporating coordinate transforms into the Adaptive Wavelet Collocation Method for the solution of PDEs. The resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet-based adaptive refinement in a complimentary fashion, resulting in greatly reduced cost of resolution for anisotropic features. The proposed Adaptive-Anisotropic Wavelet Collocation Method retains the a priori error control of the solution and fully automated mesh refinement, while offering new abilities through the flexible mesh geometry, including body-fitting. The new A-AWCM is demonstrated for a variety of cases, including parabolic diffusion, acoustic scattering, and unsteady external flow.
An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients
Directory of Open Access Journals (Sweden)
Wei Guo
2016-05-01
Full Text Available The stochastic collocation method for solving differential equations with random inputs has gained lots of popularity in many applications, since such a scheme exhibits exponential convergence with smooth solutions in the random space. However, in some circumstance the solutions do not fulfill the smoothness requirement; thus a direct application of the method will cause poor performance and slow convergence rate due to the well known Gibbs phenomenon. To address the issue, we propose an adaptive high-order multi-element stochastic collocation scheme by incorporating a WENO (Weighted Essentially non-oscillatory interpolation procedure and an adaptive mesh refinement (AMR strategy. The proposed multi-element stochastic collocation scheme requires only repetitive runs of an existing deterministic solver at each interpolation point, similar to the Monte Carlo method. Furthermore, the scheme takes advantage of robustness and the high-order nature of the WENO interpolation procedure, and efficacy and efficiency of the AMR strategy. When the proposed scheme is applied to stochastic problems with non-smooth solutions, the Gibbs phenomenon is mitigated by the WENO methodology in the random space, and the errors around discontinuities in the stochastic space are significantly reduced by the AMR strategy. The numerical experiments for some benchmark stochastic problems, such as the Kraichnan-Orszag problem and Burgers’ equation with random initial conditions, demonstrate the reliability, efficiency and efficacy of the proposed scheme.
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2009-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape and topology optimization of fluid flows. Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid in complex geometries (where grid resolution varies both in space and time time), while Brinkman volume penalization allows easy variation of flow geometry without using body-fitted meshes by simply changing the shape of the penalization region. The use of Brinkman volume penalization approach allow seamless transition from shape to topology optimization by combining it with level set approach and increasing the size of the optimization space. The approach is demonstrated for shape optimization of a variety of fluid flows by optimizing single cost function (time averaged Drag coefficient) using covariance matrix adaptation (CMA) evolutionary algorithm.
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.
Institute of Scientific and Technical Information of China (English)
曲庆国; 徐大举
2012-01-01
研究了计算大型稀疏对称矩阵的若干个最大或最小特征值的问题,首先引入了求解大型对称特征值问题的预处理子空间迭代法和Chebyshev迭代法,并对其作了理论分析.为了加速顶处理子空间迭代法的收敛性,笔者采用组合Chebyshev迭代法和预处理子空间选代法,提出了计算大型对称稀疏矩阵的几个最大或最小特征值的Chebyshev预处理子空间迭代法.数值结果表明,该方法比预处理子空间方法优越.%The problem of computing a few of the largest (or smallest) eigenvalues of a large symmetric sparse matrix is dealt with. This paper considers the preconditioning subspace iteration method and the Chebyshev iteration, and analyzes them. In order to accelerate the convergence rate of the preconditioning subspace iteration method,a new method, i. e. Chebyshev -PSI(the preconditioning subspace iteration) method, is presented for computing the extreme eigenvalues of a large symmetric sparse matrix. The new method combines the Chebyshev iteration with the PSI method. Numerical experiments show that the Chebyshev - PS1 metod is very effective for computing the extreme eigenvalues of a large symmetric sparse matrix.
Directory of Open Access Journals (Sweden)
S. China Venkateswarlu
2013-07-01
Full Text Available This paper investigates the effect of Dolph-Chebyshev window frequency response Side lobe Attenuation on the improvement of Speech quality in terms of six objective quality measures. In Speech Enhancement process, signal corrupted by noise is segmented into frames and each segment is Windowed using Dolph-Chebyshev Window with variation in the side lobe attenuation parameter α. The Windowed Speech segments are applied to the Weiner Filter Speech Enhancement algorithm and the Enhanced Speech signal is reconstructed in its time domain. The focus is to study the effect of Dolph-Chebyshev Window spectral side lobe attenuation on the Speech Enhancement process. For different side lobe attenuations of the Dolph-Chebyshev Window frequency response, speech quality objective measures have been computed. From this study, it is observed that the Side lobe Attenuation parameter α plays an important role on the Speech enhancement process in terms of six objective quality measures. The results are compared with the measures of Hanning window and an optimum side lobe attenuation parameter in dB for the Dolph-Chebyshev Window is proposed for better speech quality
DEFF Research Database (Denmark)
E. Fischer, Joel; Porcheron, Martin; Lucero, Andrés
2016-01-01
In the 25 years since Ellis, Gibbs, and Rein proposed the time-space taxonomy, research in the ‘same time, same place’ quadrant has diversified, perhaps even fragmented. This one-day workshop will bring together researchers with diverse, yet convergent interests in tabletop, surface, mobile......, and wearable technologies, spaces and spatial interaction, and those interested in the social aspects of interaction, such as conversation analysis and ethnomethodology. These communities have matured considerably, and produced significant exemplars of systems, methods, and studies concerned with collocated...
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
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.
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.
Cvitaš, Marko T.; Althorpe, Stuart C.
2013-08-01
We extend a recently developed wave packet method for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions [M. T. Cvitaš and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)], 10.1021/jp8111974 to include the Chebyshev propagator. The method uses the further partitioned approach to reactant-product decoupling, which uses artificial decoupling potentials to partition the coordinate space of the reaction into separate reactant, product, and transition-state regions. Separate coordinates and basis sets can then be used that are best adapted to each region. We derive improved Chebyshev partitioning formulas which include Mandelshtam-and-Taylor-type decoupling potentials, and which are essential for the non-unitary discrete variable representations that must be used in 4-atom reactive scattering calculations. Numerical tests on the fully dimensional OH + H2 → H2O + H reaction for J = 0 show that the new version of the method is as efficient as the previously developed split-operator version. The advantages of the Chebyshev propagator (most notably the ease of parallelization for J > 0) can now be fully exploited in state-to-state reactive scattering calculations on 4-atom reactions.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Directory of Open Access Journals (Sweden)
Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Institute of Scientific and Technical Information of China (English)
GAO Wei; DUAN Ya-li; LIU Ru-xun
2009-01-01
In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows.
Kumar, Y Satish; Talarico, Claudio; Wang, Janet; 10.1109/DATE.2005.31
2011-01-01
Since the advent of new nanotechnologies, the variability of gate delay due to process variations has become a major concern. This paper proposes a new gate delay model that includes impact from both process variations and multiple input switching. The proposed model uses orthogonal polynomial based probabilistic collocation method to construct a delay analytical equation from circuit timing performance. From the experimental results, our approach has less that 0.2% error on the mean delay of gates and less than 3% error on the standard deviation.
Orthogonal grid generation of an irregular region using a local polynomial collocation method
Wu, Nan-Jing; Tsay, Ting-Kuei; Yang, Tun-Chi; Chang, Hung-Yuan
2013-06-01
In this study, a 2-D orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares (MLS) approach. This method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied, so it is more robust and accurate than conventional collocation methods. Though the method used to solve the coordinate transforming equations is meshless, it does not deteriorate the value of present work, because most numerical models in modern use are grid-dependent, and grid generation of service to these models is still strongly desired, particularly for finite difference models in irregular domains. Before applying to grid generation problems, the performance of present method is tested by a bench mark potential flow problem. Additional to two basic grid generation problems, a bottleneck problem of previous works, which contains zero-degree corners in the domain, is carried out. Finally, the model is applied to the orthogonal grid generation in a multi-connected domain. The correctness is testified by checking the orthogonality of the generated results.
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.
Banerjee, Amartya S.; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E.
2016-10-01
The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.
Radial point collocation method (RPCM) for solving convection-diffusion problems
Institute of Scientific and Technical Information of China (English)
LIU Xin
2006-01-01
In this paper, Radial point collocation method (RPCM), a kind ofmeshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the present method is very attractive in solving computational fluid problems.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis
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.
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 fast collocation method for a variable-coefficient nonlocal diffusion model
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.
DEFF Research Database (Denmark)
Kolmogorov, Dmitry
appearing in the immediate vicinity of a wind turbine rotor makes them invaluable tools in the field of wind energy. Since direct computations of a fully resolved flow around a wind turbine are computationally expensive, a typical requirement for a good CFD method is that it is able to predict the flow...... field efficiently without jeopardizing the accuracy. In this thesis, some fundamental developments of direct CFD methods are presented to provide a platform for the development of sliding grid method for wind turbine computations. As one of the most prospective CFD methods for incompressible wind...... 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...
Directory of Open Access Journals (Sweden)
Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Directory of Open Access Journals (Sweden)
Wei Sun
2013-01-01
problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.
The application of the Chebyshev-spectral method in transport phenomena
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...
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
Chebyshev type lattice path weight polynomials by a constant term method
Brak, R
2009-01-01
We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary `decorated' weights as well as an arbitrary `background' weight. Our CT theorem, like Viennot's lattice path theorem from which it is derived primarily by a change of variable lemma, is expressed in terms of orthogonal polynomials which in our applications of interest often turn out to be non-classical. Hence we also present an efficient method for finding explicit closed form polynomial expressions for these non-classical orthogonal polynomials. Our method for finding the closed form polynomial expressions relies on simple combinatorial manipulations of Viennot's diagrammatic representation for orthogonal polynomials. In the course of the paper we also provide a new proof of Viennot's original orthogonal polynomial lattice path theorem. The new proof is of interest because it uses diagonalization of the transfer matrix, but gets around difficulties that have ari...
ON A FAMILY OF CHEBYSHEV-HALLEY TYPE METHODS IN BANACH SPACE UNDER WEAKER SMALE CONDITION
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, we discuss local convergence of a family of Chebychev-Halley type methods with a parameter θ∈[0,1] in Banach space using Smale-type δ criterion under 2-th γ-condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.
Spectral methods for partial differential equations
Hussaini, M. Y.; Streett, C. L.; Zang, T. A.
1984-01-01
Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid-dynamical applications are emphasized.
Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
B. A. Jacobs
2014-01-01
Full Text Available A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.
A study of the radiative transfer equation using a spherical harmonics-nodal collocation method
Capilla, M. T.; Talavera, C. F.; Ginestar, D.; Verdú, G.
2017-03-01
Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.
Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere
Layton, Anita T.
2002-07-01
Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finite-element methods. The spectral transform method, which yields high-order approximations, requires Legendre transforms, which have a computational complexity of O(N3), where N is the number of subintervals in one dimension. Thus, high-order finite-element methods may be a viable alternative to spectral methods. In this study, we present a new numerical method for solving the shallow water equations (SWE) in spherical coordinates. In this implementation, the SWE are discretized in time with the semi-implicit leapfrog method, and in space with the cubic spline collocation method on a skipped latitude-longitude grid. Numerical results for the Williamson et al. SWE test cases [D. L. Williamson, J. B. Blake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, J. Comput. Phys.102, 211 (1992)] are presented to demonstrate the stability and accuracy of the method. Results are also shown for an efficiency comparison between this method and a similar method in which spatial discretization is done on a uniform latitude-longitude grid.
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.
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2014-01-01
Full Text Available We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral collocation method. The spatial approximation is based on shifted Jacobi polynomials Jn(α,β(r with α,β∈(-1,∞, r∈(0,1 and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes for the spectral method. After deriving the method for a rather general class of equations, we apply it to several specific examples. One natural example is a nonlinear boundary value problem related to the Yamabe problem which arises in mathematical physics and geometry. A number of specific numerical experiments demonstrate the accuracy and the efficiency of the spectral method. We discuss the extension of the method to account for more complicated forms of nonlinearity.
Quartic B-spline collocation method applied to Korteweg de Vries equation
Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md
2014-07-01
The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+ɛuux+μuxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L∞-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L∞-norm are also increase.
Baran, Anthony J.; Groth, Samuel P.
2017-09-01
The measurement of the shape and size distributions of small atmospheric ice particles (i.e. less than about 100 μm in size) is still an unresolved problem in atmospheric physics. This paper is composed of two parts, each addressing one of these measurements. In the first part, we report on an application of a new open-source electromagnetic boundary element method (BEM) called ;BEM++; to characterise the shape of small ice particles through the simulation of the two-dimensional (2D) light scattering patterns of extreme Chebyshev ice particles. Previous electromagnetic studies of Chebyshev particles have concentrated upon high Chebyshev orders, but with low Chebyshev deformation parameters. Here, we extend such studies by concentrating on the 2D light scattering properties of Chebyshev particles with extreme deformation parameters, up to 0.5, and with Chebyshev orders up to 16, at a size parameter of 15, in a fixed orientation. The results demonstrate the applicability of BEM++ to the study of the electromagnetic scattering properties of extreme particles and the usefulness of measuring the light scattering patterns of particles in 2D to mimic the scattering behaviours of highly irregular particles, such as dendritic atmospheric ice or hazardous biological and/or aerosol particles. In the second part, we demonstrate the potential application of remotely sensed very-high-resolution brightness temperature measurements of optically thin cirrus between wavelengths of about 8.0 and 12.0 μm to resolve the current atmospheric physics issue of determining the number concentration of small ice particles with size less than about 100 μm.
Directory of Open Access Journals (Sweden)
Xiaojia Xiang
2015-01-01
Full Text Available The collocation method is extended to the special orthogonal group SO(3 with application to optimal attitude control (OAC of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3 is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3, referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation in so(3 of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3. The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
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.
Energy Technology Data Exchange (ETDEWEB)
Webster, Clayton; Tempone, Raul (Florida State University, Tallahassee, FL); Nobile, Fabio (Politecnico di Milano, Italy)
2007-12-01
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
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...
Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi
2017-02-01
A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod-Patterson-Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.
Xue, L.; Dai, C.; Zhang, D.; Guadagnini, A.
2015-12-01
It is critical to predict contaminant plume in an aquifer under uncertainty, which can help assess environmental risk and design rational management strategies. An accurate prediction of contaminant plume requires the collection of data to help characterize the system. Due to the limitation of financial resources, ones should estimate the expectative value of data collected from each optional monitoring scheme before carried out. Data-worth analysis is believed to be an effective approach to identify the value of the data in some problems, which quantifies the uncertainty reduction assuming that the plausible data has been collected. However, it is difficult to apply the data-worth analysis to a dynamic simulation of contaminant transportation model owning to its requirement of large number of inverse-modeling. In this study, a novel efficient data-worth analysis framework is proposed by developing the Probabilistic Collocation Method based Ensemble Kalman Filter (PCKF). The PCKF constructs polynomial chaos expansion surrogate model to replace the original complex numerical model. Consequently, the inverse modeling can perform on the proxy rather than the original model. An illustrative example, considering the dynamic change of the contaminant concentration, is employed to demonstrate the proposed approach. The Results reveal that schemes with different sampling frequencies, monitoring networks location, prior data content will have significant impact on the uncertainty reduction of the estimation of contaminant plume. Our proposition is validated to provide the reasonable value of data from various schemes.
2013-02-06
least C2 at all interior collocation points and at least C1 on the Neumann boundary. We note that there are many forms and instantiations of...form still requires at least C1 -continuous basis functions or additional terms that handle the jumps in the derivatives of C0-continuous basis functions...Ω Ni ( a · ∇Nj ) dΩ + ∫ Ω ∇Ni · ( D∇Nj ) dΩ (22) Fi = ∫ Ω Nif dΩ + ∫ ΓN Nih dΓ (23) A comparison with the corresponding terms of the collocation
Energy Technology Data Exchange (ETDEWEB)
Castillo, Victor Manuel [Univ. of California, Davis, CA (United States)
1999-01-01
A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number
Energy Technology Data Exchange (ETDEWEB)
Castillo, V M
2005-01-12
A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number
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
Multi-Index Monte Carlo and stochastic collocation methods for random PDEs
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.
Collocation methods for uncertainty quanti cation in PDE models with random data
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.
A Chebyshev-collation approach for a continuous formulation of ...
African Journals Online (AJOL)
A Chebyshev-collation approach for a continuous formulation of hybrid methods for initial value problems in ordinary differential ... Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT ...
CSIR Research Space (South Africa)
Napier, JAL
2002-09-01
Full Text Available intensity factors to be solved directly at the crack edges. This is achieved by employing an enhanced edge collocation procedure. The limiting interpretation of the governing integral equations is discussed and two simple examples are presented to illustrate...
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2010-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape optimization for drag reduction in flows past linked bodies. This optimization relies on Adaptive Wavelet Collocation Method along with the Brinkman penalization technique and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid, while a level set approach is used to describe the body shape and the Brinkman volume penalization allows for an easy variation of flow geometry without requiring body-fitted meshes. We perform 2D simulations of linked bodies in order to investigate whether flat geometries are optimal for drag reduction. In order to accelerate the costly cost function evaluations we exploit the inherent parallelism of ES and we extend the CMA-ES implementation to a multi-host framework. This framework allows for an easy distribution of the cost function evaluations across several parallel architectures and it is not limited to only one computing facility. The resulting optimal shapes are geometrically consistent with the shapes that have been obtained in the pioneering wind tunnel experiments for drag reduction using Evolution Strategies by Ingo Rechenberg.
Geostationary satellites collocation
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.
Senses, Begum
A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush-Kuhn-Tucker matrices that arise from the discretization of optimal control problems via a Legendre-Gauss-Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush-Kuhn-Tucker matrix that arises from the orthogonal collocation method. The state-defect constraint pairing graph coarsening method pairs each component of the state with its corresponding defect constraint and forces paired rows to be adjacent in the reordered Karush-Kuhn-Tucker matrix. Aggregate state-defect constraint pairing results are presented using a wide variety of benchmark optimal control problems where it is found that the proposed state-defect constraint pairing graph coarsening method significantly reduces both the number of delayed pivots and the number of floating point operations and increases the computational efficiency by performing more floating point operations per unit time. It is then shown that the state-defect constraint pairing graph coarsening method is less effective on Karush-Kuhn-Tucker matrices arising from Legendre-Gauss-Radau collocation when the optimal control problem contains state and control equality path constraints because such matrices may have delayed pivots that correspond to both defect and path constraints. An unweighted alternate graph coarsening method that employs maximal matching and a weighted alternate graph coarsening method that employs Hungarian algorithm on a weighting matrix are then used to attempt to further reduce the number of delayed pivots. It is found, however, that these alternate graph coarsening methods provide no further advantage over the state-defect constraint pairing graph coarsening method.
A nodal collocation method for the calculation of the lambda modes of the P {sub L} equations
Energy Technology Data Exchange (ETDEWEB)
Capilla, M. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: tcapilla@mat.upv.es; Talavera, C.F. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: talavera@mat.upv.es; Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: dginesta@mat.upv.es; Verdu, G. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: gverdu@iqn.upv.es
2005-11-15
P {sub 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 {sub 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.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, H.D.; Paik, S. (EG and G Idaho, Inc., Idaho Falls, ID (United States)); Chung, J.N. (Washington State Univ., Pullman, WA (United States). Dept. of Mechanical and Materials Engineering)
1992-01-01
A spectral model, based on the stream function and vorticity, is developed in order to calculate the time-dependent solution of flow past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the stream fiinction and vorticity in the radial and angular directions, respectively, along with the backward Euler approximation to advance in time. Consistent treatment of boundary conditions is made to resolve the lack of vorticity boundary conditions by means of the influence matrix technique. The computed flow field, the drag coefficient, and the interfacial velocity are presented for Reynolds numbers in the range from 0.5 to 50 for both continuous and dispersed phases with viscosity ratios of 1 and 3. Comparison of the present results to those found in the literature indicate that the model is capable of predicting the correct nature of the flow associated with a droplet.
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.
A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations
Bhrawy, Ali H.; Al-Shomrani, M. M.
2012-01-01
The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel. The scheme consists of Jacobi dual-Petrov Galerkin-Jacobi collocation method in space combined with Crank-Nicholson-leap-frog method in time such that at each time step only a sparse banded linear algebraic system needs to be solved. Numerical results are presented to show that the proposed...
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 force...... in a cell is spread on neighboring cells by applying equivalent pressure jumps at the cell faces. The method shows excellent results when applied for simulating the flow through an actuator disk, which is relevant for wind turbine wake simulations. (c) 2015 Elsevier Ltd. All rights reserved....
扩展型动网格的Chebyshev有限谱方法%Chebyshev Finite Spectral Method With Extended Moving Grids
Institute of Scientific and Technical Information of China (English)
詹杰民; 李毓湘; 董志
2011-01-01
A Chebyshev finite spectral method on non-uniform mesh was proposed. An equidis tribution scheme for two types of extended moving grids was proposed for grid generation. One type of grid was designed to provide better resolution for wave surface. The other type was for highly variable gradients. The method was of high-order accuracy because of the use of Chebyshev polynomial as the basis function. The polynomial was used to interpolate values between the two non-uniform meshes from the previous time step to the current time step. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, a numerical technique on non-uniform mesh was introduced to improve the numerical stability. The proposed numerical scheme was validated by applications to the Burgers equation ( nonlinear convection-diffusion problem) and KdV equation( single solitary and 2-soiltary wave problems), where analytical solutions were awilable for comparison. Numerical resuits agree very well with the corresponding analytical solutions in all cases.%给出了基于非均匀网格的Chebyshev有限谱方法.提出了可生成两种类型扩展型动网格的均布格式一种类型的网格被用来提高波面附近的分辨率,另一种类型则用在梯度较大的流动区域.由于采用Chebyshev多项式作为基函数,该方法具有高阶精度.从上个时间步到当前时间步,两套不均匀网格间的物理量采用Chebyshev多项式插值.为使方法在时间离散方面保持高精度,采用了Adams-Bashforth预报格式和Adams-Moulton校正格式.为了避免由Korteweg-de Vries(KdV)方程的弥散项引起的数值振荡,给出了一种非均匀网格下的数值稳定器.给出的方法与具有分析解的Burgers方程的非线性对流扩散问题和KdV方程的单孤独波和双孤独波传播问题进行了比较,结果非常吻合.
The problem of convexity of Chebyshev sets
Balaganskii, V. S.; Vlasov, L. P.
1996-12-01
Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography
Spectral-collocation variational integrators
Li, Yiqun; Wu, Boying; Leok, Melvin
2017-03-01
Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and have a relatively small memory footprint. In this paper, we introduce a general framework to convert a spectral-collocation method into a shooting-based variational integrator for Hamiltonian systems. We also compare the proposed spectral-collocation variational integrators to spectral-collocation methods and Galerkin spectral variational integrators in terms of their ability to reproduce accurate trajectories in configuration and phase space, their ability to conserve momentum and energy, as well as the relative computational efficiency of these methods when applied to some classical Hamiltonian systems. In particular, we note that spectrally-accurate variational integrators, such as the Galerkin spectral variational integrators and the spectral-collocation variational integrators, combine the computational efficiency of spectral methods together with the geometric structure-preserving and long-time structural stability properties of symplectic integrators.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Trajectory planning based on collocation methods for multiple aerial and ground autonomous vehicles
Vera Rendón, Santiago
2015-01-01
Esta tesis doctorar presenta una serie de contribuciones en los métodos de coordinación y generación de trayectorias de grupos de vehículos, concretamente de vehículos autónomos. Los métodos de colocación, más conocidos por su nombre en inglés “Collocation methods”, han despertado un creciente interés en los últimos años, entre los distintos métodos numéricos para resolver cualquier tipo de problema dentro del campo de la ingeniería. Esta tesis en concreto, presenta un nuevo punto de vista de...
Isogeometric Collocation for Elastostatics and Explicit Dynamics
2012-01-25
collocation methods within the framework of Isogeometric Analysis (IGA) to multi-patch NURBS con gurations, various boundary and patch interface conditions...development of collocation methods within the framework of Iso- geometric Analysis (IGA) to multi-patch NURBS configurations, various boundary and patch...finite element analysis. Key words: Isogeometric analysis; collocation methods; B-splines; NURBS ; explicit dynamics. 1 Introduction There are many
Kattelans, Thorsten; Heinrichs, Wilhelm
2009-09-01
For Stokes problems least-squares schemes have the big advantage that they require no stabilization and equal order interpolation can be used. The disadvantage of Least-Squares Finite Element Method (LSFEM) and of Least-Squares Spectral Element Method (LSSEM) is that they perform poorly with respect to conservation of mass for internal flow problems, where the LSSEM compensates this by a superior conservation of momentum. In the literature it has been shown that Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the steady Stokes. Here, we extend the study to the time-dependent Stokes equations for an internal flow problem, where the domain is decomposed into different elements using the transfinite mapping of Gordon and Hall. Minimizing the influence of round-off errors we use QR decomposition for solving the resulting overdetermined algebraic systems instead of forming normal equations.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
A Stochastic Collocation Algorithm for Uncertainty Analysis
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
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.
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.
Ni, Ming-Jiu
2009-10-01
Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier-Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Mittal, R. C.; Jain, R. K.
2012-12-01
In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.
Application of Chebyshev Polynomial to simulated modeling
Institute of Scientific and Technical Information of China (English)
CHI Hai-hong; LI Dian-pu
2006-01-01
Chebyshev polynomial is widely used in many fields, and used usually as function approximation in numerical calculation. In this paper, Chebyshev polynomial expression of the propeller properties across four quadrants is given at first, then the expression of Chebyshev polynomial is transformed to ordinary polynomial for the need of simulation of propeller dynamics. On the basis of it,the dynamical models of propeller across four quadrants are given. The simulation results show the efficiency of mathematical model.
An Automatic Collocation Extraction from Arabic Corpus
Directory of Open Access Journals (Sweden)
Abdulgabbar M. Saif
2011-01-01
Full Text Available Problem statement: The identification of collocations is very important part in natural language processing applications that require some degree of semantic interpretation such as, machine translation, information retrieval and text summarization. Because of the complexities of Arabic, the collocations undergo some variations such as, morphological, graphical, syntactic variation that constitutes the difficulties of identifying the collocation. Approach: We used the hybrid method for extracting the collocations from Arabic corpus that is based on linguistic information and association measures. Results: This method extracted the bi-gram candidates of Arabic collocation from corpus and evaluated the association measures by using the n-best evaluation method. We reported the precision values for each association measure in each n-best list. Conclusion: The experimental results showed that the log-likelihood ratio is the best association measure that achieved highest precision.
Krypiak-Gregorczyk, Anna; Wielgosz, Paweł; Jarmołowski, Wojciech
2017-04-01
The ionosphere plays a crucial role in space weather that affects satellite navigation as the ionospheric delay is one of the major errors in GNSS. On the other hand, GNSS observations are widely used to determine the amount of ionospheric total electron content (TEC). An important aspect in the electron content estimation at regional and global scale is adopting the appropriate interpolation strategy. In this paper we propose and validate a new method for regional TEC modeling based on least squares collocation (LSC) with noise variance estimation. This method allows for providing accurate TEC maps with high spatial and temporal resolution. Such maps may be used to support precise GNSS positioning and navigation, e.g. in RTK mode and also in the ionosphere studies. To test applicability of new TEC maps to positioning, double-difference ionospheric corrections were derived from the maps and their accuracy was analyzed. In addition, the corrections were applied to GNSS positioning and validated in ambiguity resolution domain. The tests were carried out during a strong ionospheric storm when the ionosphere is particularly difficult to model. The performance of the new approach was compared to IGS and UPC global, and CODE regional TEC maps. The results showed an advantage of our solution with resulting accuracy of the relative ionospheric corrections usually better than 10 cm, even during the ionospheric disturbances. This proves suitability of our regional TEC maps for, e.g. supporting fast ambiguity resolution in kinematic GNSS positioning.
Hu, Zhang-Mao; Tian, Hong; Li, Ben-Wen; Zhang, Wei; Yin, Yan-Shan; Ruan, Min; Chen, Dong-Lin
2017-10-01
The ray-effect is a major discretization error in the approximate solution method for the radiative transfer equation (RTE). To overcome this problem, the incident energy transfer equation (IETE) is proposed. The incident energy, instead of radiation intensity, is obtained by directly solving this new equation. Good numerical properties are found for the incident energy transfer equation. To show the properties of numerical solution, the collocation spectral method (CSM) is employed to solve the incident energy transfer equation. Three test cases are taken into account to verify the performance of the incident energy transfer equation. The result shows that the radiative heat flux obtained based on IETE is much more accurate than that based on RTE, which means that the IETE is very effective in eliminating the impacts of ray-effect on the heat flux. However, on the contrary, the radiative intensity obtained based on IETE is less accurate than that based on RTE due to the ray-effect. So, this equation is more suitable for those radiative heat transfer problems, in which the radiation heat flux and incident energy are needed rather than the radiation intensity.
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.
Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming
2017-05-01
The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.
Directory of Open Access Journals (Sweden)
Suleiman Banihani
2013-01-01
Full Text Available The point collocation method of finite spheres (PCMFS is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD model order reduction (MOR technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.
Rectangular spectral collocation
Driscoll, Tobin A.
2015-02-06
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.
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....
Digital terrain modeling with the Chebyshev polynomials
Florinsky, I V
2015-01-01
Mathematical problems of digital terrain analysis include interpolation of digital elevation models (DEMs), DEM generalization and denoising, and computation of morphometric variables by calculation of partial derivatives of elevation. Traditionally, these procedures are based on numerical treatments of two-variable discrete functions of elevation. We developed a spectral analytical method and algorithm based on high-order orthogonal expansions using the Chebyshev polynomials of the first kind with the subsequent Fejer summation. The method and algorithm are intended for DEM analytical treatment, such as, DEM global approximation, denoising, and generalization as well as computation of morphometric variables by analytical calculation of partial derivatives. To test the method and algorithm, we used a DEM of the Northern Andes including 230,880 points (the elevation matrix 480 $\\times$ 481). DEMs were reconstructed with 480, 240, 120, 60, and 30 expansion coefficients. The first and second partial derivatives ...
Error Control Strategies for Numerical Integrations in Fast Collocation Methods%快速配置法中数值积分的误差控制策略
Institute of Scientific and Technical Information of China (English)
陈仲英; 巫斌; 许跃生
2005-01-01
We propose two error control techniques for numerical integrations infast multiscale collocation methods for solving Fredholm integral equations of thesecond kind with weakly singular kernels. Both techniques utilize quadratures forsingular integrals using graded points. One has a polynomial order of accuracy ifthe integrand has a polynomial order of smoothness except at the singular point andthe other has exponential order of accuracy if the integrand has an infinite orderof smoothness except at the singular point. We estimate the order of convergenceand computational complexity of the corresponding approximate solutions of theequation. We prove that the second technique preserves the order of convergence andcomputational complexity of the original collocation method. Numerical experimentsare presented to illustrate the theoretical estimates.
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.
Multi-fidelity stochastic collocation method for computation of statistical moments
Energy Technology Data Exchange (ETDEWEB)
Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu [Department of Mathematics, University of Iowa, Iowa City, IA 52242 (United States); Linebarger, Erin M., E-mail: aerinline@sci.utah.edu [Department of Mathematics, University of Utah, Salt Lake City, UT 84112 (United States); Xiu, Dongbin, E-mail: xiu.16@osu.edu [Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)
2017-07-15
We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.
IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.
Romero, M; de Madrid, A P; Mañoso, C; Vinagre, B M
2013-07-01
This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies.
Seyrich, Jonathan
2013-01-01
In this work, we present the hitherto most efficient and accurate method for the numerical integration of post-Newtonian equations of motion. We first transform the Poisson system as given by the post-Newtonian approximation to canonically symplectic form. Then we apply Gauss Runge-Kutta schemes to numerically integrate the resulting equations. This yields a convenient method for the structure preserving long-time integration of post-Newtonian equations of motion. In extensive numerical experiments, this approach turns out to be faster and more accurate i) than previously proposed structure preserving splitting schemes and ii) than standard explicit Runge-Kutta methods.
A collocation method for surface tension calculations with the density gradient theory
DEFF Research Database (Denmark)
Larsen, Peter Mahler; Maribo-Mogensen, Bjørn; Kontogeorgis, Georgios M.
2016-01-01
Surface tension calculations are important in many industrial applications and over a wide range of temperatures, pressures and compositions. Empirical parachor methods are not suitable over a wide condition range and the combined use of density gradient theory with equations of state has been...... proposed in literature. Often, many millions of calculations are required in the gradient theory methods, which is computationally very intensive. In this work, we have developed an algorithm to calculate surface tensions an order of magnitude faster than the existing methods, with no loss of accuracy...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
A Collocation Method by Moving Least Squares Applicable to European Option Pricing
Directory of Open Access Journals (Sweden)
M. Amirfakhrian
2016-05-01
Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.
Incidental Learning of Collocation
Webb, Stuart; Newton, Jonathan; Chang, Anna
2013-01-01
This study investigated the effects of repetition on the learning of collocation. Taiwanese university students learning English as a foreign language simultaneously read and listened to one of four versions of a modified graded reader that included different numbers of encounters (1, 5, 10, and 15 encounters) with a set of 18 target collocations.…
Collocations in Business English
Directory of Open Access Journals (Sweden)
Matjaž Martič
2009-12-01
Full Text Available The article starts with a brief theoretical overview that defines the term ‚collocation.‛ It then presents a corpus study designed to determine the most frequent lexical collocations in Business English using the concordance program WordSmith Tools. This study is based on the assumption that English mainly consists of various (changeable phraseological units and that both free combinations as well as completely ‚frozen‛ word combinations account for only a small share of the language. English is therefore a language of collocations and one can assume that this is valid not only for general English, but also for ESP and thus for Business English as well. In addition, the study investigated whether the most frequent collocations in this corpus could be found in major dictionaries of collocations, which would then establish their suitability for Business English purposes.
Walsh, Raymond P
2016-01-01
The fundamental interaction between tropical cyclones was investigated through a series of water tank experiements by Fujiwhara [20, 21, 22]. However, a complete understanding of tropical cyclones remains an open research challenge although there have been numerous investigations through measurments with aircrafts/satellites, as well as with numerical simulations. This article presents a computational model for simulating the interaction between cyclones. The proposed numerical method is presented briefly, where the time integration is performed by projecting the discrete system onto a Krylov subspace. The method filters the large scale fluid dynamics using a multiresolution approximation, and the unresolved dynamics is modeled with a Smagorinsky type subgrid scale parameterization scheme. Numerical experiments with Fujiwhara interactions are considered to verify modeling accuracy. An excellent agreement between the present simulation and a reference simulation at Re = 5000 has been demonstrated. At Re = 3744...
Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems
2003-04-01
solving optimal control problems for trajectory optimization, spacecraft attitude control, jet thruster control, missile guidance and many other... optimal control problems using a pseudospectral direct transcription method. These problems are stated here so that they may be referred to elsewhere...e.g., [7]. 2.3 Prototypical Examples Throughout this thesis two example problems are used to demonstrate various prop- erties associated with solving
CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM
Directory of Open Access Journals (Sweden)
S.H. Nasseri
2009-10-01
Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
LUPOD: Collocation in POD via LU decomposition
Rapún, M.-L.; Terragni, F.; Vega, J. M.
2017-04-01
A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent with the essence of POD, collocation points are computed via the LU decomposition with pivoting of the snapshot matrix. The new method is illustrated in simple applications in which POD is used as a data-processing method. The performance of the method is tested in the computationally efficient construction of reduced order models based on POD plus Galerkin projection for the complex Ginzburg-Landau equation in one and two space dimensions.
Indian Academy of Sciences (India)
Mategaonkar Meenal; T I Eldho
2012-06-01
Remediation of the groundwater contamination problem is a tedious, time consuming and expensive process. Pump and treat (PAT) is one of the commonly used techniques for groundwater remediation in which the contaminated groundwater is pumped, treated and put back to the aquifer system or other sources. Developing simulation-optimization (S/O) model proved to be very useful in the design process of an effective PAT system. Simulation models help in predicting the spatial and temporal variation of the contamination plume while optimization models help in minimizing the cost of pumping. Generally, grid or mesh based models such as Finite Difference Method (FDM) or Finite Element Methods (FEM) is used for the groundwater ﬂow and transport simulation. But it is found that grid/mesh generation is a time consuming process. Therefore, recently Meshfree (MFree) based numerical models are developed to avoid this difﬁculty of meshing and remeshing. MFree Point Collocation Method (PCM) is a simple meshfree method used for the simulation of coupled groundwater ﬂow and contaminant transport. For groundwater optimization problems, even though number of methods such as linear programming, nonlinear programming, etc. are available, evolutionary algorithm based techniques such as genetic algorithm (GA) and particle swarm optimization (PSO) are found to be very effective. In this paper, a simulation model using MFree PCM for conﬁned groundwater ﬂow and transport and a PSO based single objective optimization model are developed and coupled to get an effective S/O model for groundwater remediation using PAT. The S/O model based on PCM and PSO is applied for a polluted hypothetical conﬁned aquifer and its performance is compared with Finite Element Method–Binary Coded Genetic Algorithm (FEM–GA) model. It is found that both the models are in good agreement with each other showing the applicability of the present approach. The PCM–PSO based S/O model is simple and more
Directory of Open Access Journals (Sweden)
Vasily P. Shapeev
2017-01-01
Full Text Available In the work, we consider the problem of accelerating the iteration process of the numerical solution of boundary-value problems for partial differential equations (PDE by the method of collocations and least residuals (CLR. To solve this problem, it is proposed to combine simultaneously three techniques of the iteration process acceleration: the preconditioner, the multigrid algorithm, and the correction of the PDE solution at the intermediate iterations in the Krylov subspace. The influence of all three techniques of the iteration acceleration was investigated both individually for each technique and at their combination. Each of the above techniques is shown to make its contribution to the quantitative figure of iteration process speed-up. The algorithm which employs the Krylov subspaces makes the most significant contribution. The joint simultaneous application of all three techniques for accelerating the iterative solution of specific boundary-value problems enabled a reduction of the CPU time of their solution on computer by a factor of up to 230 in comparison with the case when no acceleration techniques were applied. A two-parameter preconditioner was investigated. It is proposed to find the optimal values of its parameters by the numerical solution of a computationally inexpensive problem of minimizing the condition number of the system of linear algebraic equations. The problem is solved by the CLR method and it is modified by the preconditioner. It is shown that it is sufficient to restrict oneself in the multigrid version of the CLR method only to a simple solution prolongation operation on the multigrid complex to reduce substantially the CPU time of the boundary-value problem solution.Numerous computational examples are presented, which demonstrate the efficiency of the approaches proposed for accelerating the iterative processes of the numerical solution of the boundary-value problems for the two-dimensional Navier
A note on the rate of convergence for Chebyshev-Lobatto and Radau systems
Directory of Open Access Journals (Sweden)
Berriochoa Elías
2016-01-01
Full Text Available This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
Application research of the MLPG mixed collocation method in shape optimization%MLPG混合配点法在形状优化中的应用研究
Institute of Scientific and Technical Information of China (English)
赵亮; 李书; 鲁大伟
2011-01-01
建立了无网格MLPG(Meshless Local Petrov-Galerkin)混合配点法求解二维弹性体位移、应力的数学模型,使用罚函数法添加本质边界条件,并将其应用到结构形状优化,结合遗传算法提出了一种新的连续体结构优化设计方法.对于节点支持域半径的选取进行了重点探讨,提出一种动态支持域选择方法,建立了基于MLPG混合配点法的优化模型,对两个实际工程算例进行了形状优化,并与现有结果比较,验证了该方法的有效性.%The mathematics model of the MLPG (the Meshless Local Petrov-Galerkin) mixed collocation method is built for solving the displacement and stress of 2-D elasticity, and the essential boundary condition is imposed by penalty function method, which is applied in structure shape optimization.A new design method of continuum structure is proposed with MLPG mixed collocation method and Genetic Algorithm.The select of node's support domain radius is mainly discussed and a dynamic support domain radius chosen method is given.An optimization model is presented based on MLPG mixed collocation method.Numerical examples show that the proposed method is effective.
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....
Blind Signature Scheme Based on Chebyshev Polynomials
Directory of Open Access Journals (Sweden)
Maheswara Rao Valluri
2011-12-01
Full Text Available A blind signature scheme is a cryptographic protocol to obtain a valid signature for a message from a signer such that signer’s view of the protocol can’t be linked to the resulting message signature pair. This paper presents blind signature scheme using Chebyshev polynomials. The security of the given scheme depends upon the intractability of the integer factorization problem and discrete logarithms ofChebyshev polynomials.
Blind Signature Scheme Based on Chebyshev Polynomials
Maheswara Rao Valluri
2011-01-01
A blind signature scheme is a cryptographic protocol to obtain a valid signature for a message from a signer such that signer’s view of the protocol can’t be linked to the resulting message signature pair. This paper presents blind signature scheme using Chebyshev polynomials. The security of the given scheme depends upon the intractability of the integer factorization problem and discrete logarithms ofChebyshev polynomials.
Collocations in Business English
Matjaž Martič
2009-01-01
The article starts with a brief theoretical overview that defines the term ‚collocation.‛ It then presents a corpus study designed to determine the most frequent lexical collocations in Business English using the concordance program WordSmith Tools. This study is based on the assumption that English mainly consists of various (changeable) phraseological units and that both free combinations as well as completely ‚frozen‛ word combinations account for only a small share of the language. Englis...
Simulasi Perancangan Filter Analog dengan Respon Chebyshev
Directory of Open Access Journals (Sweden)
RUSTAMAJI RUSTAMAJI
2016-02-01
Full Text Available Abstrak Dalam suatu sistem komunikasi penggunaan rangkaian filter sangat penting. Salah satu cara untuk memudahkan dalam perancangan sebuah filter dilakukanlah teknik simulasi. Penelitian ini bertujuan untuk merancang simulasi yang menghasilkan respon filter jenis chebyshev serta menghasilkan nilai komponen induktor (L dan kapasitor (C yang dibutuhkan untuk merangkai filter. Simulasi yang dirancang pada penelitian ini menggunakan Graphical User Interface (GUI. Dari simulasi yang dilakukan, didapatkan respon Chebyshev pada low pass filter, high pass filter, band pass filter, dan band stop filter sudah sesuai dengan input yang dimasukkan ke dalam parameter program dan sesuai dengan teori respon filter Chebyshev. Hasil Simulasi dari rangkaian band pass filter dan band stop filter dengan menggunakan Electronic Workbench (EWB, menunjukkan respon dengan pergeseran frekuensi sebesar 0,1 kHz lebih tinggi dari frekuensi yang diharapkan. Kata Kunci :filter, Chebyshev, band, respon frekuensi. Abstract On communication system using filter is very important. One way to simplify the design of filter undertaken a simulation technique. This research aims to design a simulation that generates the filter response of chebyshev and generate the value component of the inductor (L and capacitor (C that needed for constructing the filter. This Simulation using Graphical User Interface (GUI. From result simulation, response in low pass filter, high pass filter, band pass filter, band stop filter and is in compliance with the input entered into the program and in accordance with the theory of Chebyshev filter response. The simulation of the band pass filter and bands stop filter by using electronic workbench ( EWB , show a response with shifts frequency of 0.1 khz higher than frequency expected. Keywords: filter, Chebyshev, band, frequency respons
Parsani, Matteo
2016-10-04
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Institute of Scientific and Technical Information of China (English)
梁文娟; 郑逢斌; 杜莹
2009-01-01
In order to improve the intelligence of the input method, collocation repositories are studied. Firstly the Chinese intelligent input method based on grammar and semantics and its improved functions are introduced briefly. Then based on the analysis of the collocation in the Corpus and combined the application of the collocation in the input method, some statistics language models are improved and the key structures of the collocation repository, the grammatical collocation repository and the semantic collocation repository are presented. Based on these improved statistics language models and grammatical and semantic knowledge, these collocation repositories are realized. Last some experimental results are presented and analyzed.%为提高输入法的智能性,对供输入法使用的搭配知识库进行了研究.介绍了汉字语法语义智能输入法及其改进的功能,在对语料库中搭配知识分析的基础上,结合输入法中搭配知识的使用,对现有的统计语言模型进行了改进,并给出了词语搭配知识库,语法搭配知识库和语义搭配知识库的关键结构,利用改进后的统计语言模型和语法语义搭配知识,对各搭配知识库进行了算法实现,最后给出了各个搭配知识库的部分实验结果并对其进行了分析.
The Application of Fuzzy Logic to Collocation Extraction
Bisht, Raj Kishor
2008-01-01
Collocations are important for many tasks of Natural language processing such as information retrieval, machine translation, computational lexicography etc. So far many statistical methods have been used for collocation extraction. Almost all the methods form a classical crisp set of collocation. We propose a fuzzy logic approach of collocation extraction to form a fuzzy set of collocations in which each word combination has a certain grade of membership for being collocation. Fuzzy logic provides an easy way to express natural language into fuzzy logic rules. Two existing methods; Mutual information and t-test have been utilized for the input of the fuzzy inference system. The resulting membership function could be easily seen and demonstrated. To show the utility of the fuzzy logic some word pairs have been examined as an example. The working data has been based on a corpus of about one million words contained in different novels constituting project Gutenberg available on www.gutenberg.org. The proposed me...
Almost Chebyshev set with respect to bounded subsets
Institute of Scientific and Technical Information of China (English)
李冲; 王兴华
1997-01-01
The uniqueness and existence of restricted Chebyshev center with respect to arbitrary subset are investigated. The concept of almost Chebyshev sets with respect to bounded subsets is introduced. It is proved that each closed subset in a reflexive locally uniformly convex (uniformly convex, respectively) Banach space is an almost Chebyshev subset with respect to compact convex subsets (bounded convex subsets and bounded subsets, respectively).
Pantokratoras, A
2007-01-01
In the paper [Chaos, Solitons & Fractals, 2006, vol. 30, pp. 851-858]the authors treat the boundary layer flow of a micropolar fluid along a horizontal flat plate with blowing or suction. The fluid viscosity and thermal conductivity are assumed functions of temperature. The boundary layer equations are transformed into ordinary ones and subsequently are solved using the Chebyshev finite difference method. However, there are some deficiencies and errors in this paper.
Terminological collocations in medical latin and english: a comparative study.
Bieliaieva, Olena M; Lysanets, Yuliia V; Znamenska, Ivanna V; Rozhenko, Inesa V; Nikolaieva, Nataliia M
The present paper examines the linguistic status of terminological collocations in medical Latin and English, discusses the most productive term-formation models and ways of Latin-English translation. The authors aim to provide the comparative analysis of Latin and English terminological collocations and suggest their classification in terms of the idiomaticity level and semantic valency. The research is based on the corpus of terminological collocations in Latin and English medical discourse using structural, etymological, typological, comparative methods, as well as the method of semantic analysis and conceptual metaphor theory. The research has resulted in the delineation of the following groups of terminological collocations in medical Latin and English: (1) terminological collocations with lower degree of idiomaticity - analytical units whose semantics correlates with the amount of free meanings of the components; (2) terminological collocations with semantic cohesion of the components due to metaphorical nature of the terminological element with active / passive valency; (3) clinical idioms - terminological collocations with higher degree of idiomaticity. Within the latter group, we suggest to discern eponymic, toponymic, zoomorphic, botanic and mythonimic subtypes of terminological collocations. A promising area of future research is the development of bilingual explanatory dictionaries with Latin and English equivalents of terminological collocations, as well as the information about the semantics of their components.
Collocations in Marine Engineering English
Directory of Open Access Journals (Sweden)
Mirjana Borucinsky
2016-05-01
Full Text Available Collocations are very frequent in the English language (Hill, 2000, and they are probably the most common and most representative of English multi-word expressions (Lewis, 2000. Furthermore, as a subset of formulaic sequences, collocations are considered to be a central aspect of communicative competence (Nation, 2001. Hence, the importance of teaching collocations in General English (GE as well as in English for Specific Purposes (ESP is undeniable. Understanding and determining the relevant collocations and their mastery are of “utmost importance to a ME instructor” (Cole et al., 2007, p. 137, and collocations are one of the most productive ways of enriching vocabulary and terminology in modern ME. Vişan & Georgescu (2011 have undertaken a relevant study on collocations and “collocational competence” on board ships, including mostly nautical terminology. However, no substantial work on collocations in Marine Engineering English as a sub-register of ME has been carried out. Hence, this paper tries to determine the most important collocations in Marine Engineering English, based on a small corpus of collected e-mails. After determining the most relevant collocations, we suggest how to implement these in the language classroom and how to improve the collocational competence of marine engineering students.
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.…
Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas; Galgon, Martin; Fehske, Holger; Hager, Georg; Lang, Bruno; Wellein, Gerhard
2016-11-01
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 102 innermost eigenpairs of a topological insulator matrix with dimension 109 derived from quantum physics applications.
Institute of Scientific and Technical Information of China (English)
彭丽
2002-01-01
The finite element solution of two points boundary value problem for nonlinear ordinary differential equation is studied by using the collocation-Galerkin method.The Jacobi points are introduced to establish high orders of accuracy for the approximate solution.Numerical results are presented for a sample problem.
Charoenkwan, Phasit; Shoombuatong, Watshara; Lee, Hua-Chin; Chaijaruwanich, Jeerayut; Huang, Hui-Ling; Ho, Shinn-Ying
2013-01-01
Existing methods for predicting protein crystallization obtain high accuracy using various types of complemented features and complex ensemble classifiers, such as support vector machine (SVM) and Random Forest classifiers. It is desirable to develop a simple and easily interpretable prediction method with informative sequence features to provide insights into protein crystallization. This study proposes an ensemble method, SCMCRYS, to predict protein crystallization, for which each classifier is built by using a scoring card method (SCM) with estimating propensity scores of p-collocated amino acid (AA) pairs (p=0 for a dipeptide). The SCM classifier determines the crystallization of a sequence according to a weighted-sum score. The weights are the composition of the p-collocated AA pairs, and the propensity scores of these AA pairs are estimated using a statistic with optimization approach. SCMCRYS predicts the crystallization using a simple voting method from a number of SCM classifiers. The experimental results show that the single SCM classifier utilizing dipeptide composition with accuracy of 73.90% is comparable to the best previously-developed SVM-based classifier, SVM_POLY (74.6%), and our proposed SVM-based classifier utilizing the same dipeptide composition (77.55%). The SCMCRYS method with accuracy of 76.1% is comparable to the state-of-the-art ensemble methods PPCpred (76.8%) and RFCRYS (80.0%), which used the SVM and Random Forest classifiers, respectively. This study also investigates mutagenesis analysis based on SCM and the result reveals the hypothesis that the mutagenesis of surface residues Ala and Cys has large and small probabilities of enhancing protein crystallizability considering the estimated scores of crystallizability and solubility, melting point, molecular weight and conformational entropy of amino acids in a generalized condition. The propensity scores of amino acids and dipeptides for estimating the protein crystallizability can aid
TEACH SCIENCE STUDENTS COLLOCATION —— MAKE IT A PRACTICE
Institute of Scientific and Technical Information of China (English)
WangXiuwen; ZhengShutang
2004-01-01
In recent years collocation has emerged as an important category of lexical patterning and it is fast becoming an established unit of description in language teaching courses and materials. Teachers should teach students collocation. Scientific students in particular should learn collocation and chunks, because technical language has a greater tendency ( than creative writing, for example ) to use fixed chunks. This paper makes an initiative analysis as to the content (particularly) and method relating to teaching science students collocation in class.
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...
Mobile Collocated Interactions With Wearables
DEFF Research Database (Denmark)
Lucero, Andrés; Wilde, Danielle; Robinson, Simon
2015-01-01
powerful, and closer to our bodies. Therefore, mobile collocated interactions research, which originally looked at smartphones and tablets, will inevitably move towards fully integrated wearable technologies. 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 from, through and around the body using wearable technologies.......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...
Efficient Prime Counting and the Chebyshev Primes
Directory of Open Access Journals (Sweden)
Michel Planat
2013-01-01
Full Text Available The function where is the logarithm integral and the number of primes up to is well known to be positive up to the (very large Skewes' number. Likewise, according to Robin's work, the functions and , where and are Chebyshev summatory functions, are positive if and only if Riemann hypothesis (RH holds. One introduces the jump function at primes and one investigates , , and . In particular, , and for . Besides, for any odd , an infinite set of the so-called Chebyshev primes. In the context of RH, we introduce the so-called Riemann primes as champions of the function (or of the function . Finally, we find a good prime counting function , that is found to be much better than the standard Riemann prime counting function.
On the convexity of N-Chebyshev sets
Borodin, Petr A.
2011-10-01
We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N\\ge 3 is odd and X is smooth uniformly convex.
A comparison of numerical methods for the Rayleigh equation in unbounded domains
Liou, W. W.; Morris, P. J.
1991-01-01
A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.
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.
The Chebyshev-polynomials-based unified model neural networks for function approximation.
Lee, T T; Jeng, J T
1998-01-01
In this paper, we propose the approximate transformable technique, which includes the direct transformation and indirect transformation, to obtain a Chebyshev-Polynomials-Based (CPB) unified model neural networks for feedforward/recurrent neural networks via Chebyshev polynomials approximation. Based on this approximate transformable technique, we have derived the relationship between the single-layer neural networks and multilayer perceptron neural networks. It is shown that the CPB unified model neural networks can be represented as a functional link networks that are based on Chebyshev polynomials, and those networks use the recursive least square method with forgetting factor as learning algorithm. It turns out that the CPB unified model neural networks not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural networks. Furthermore, we have also derived the condition such that the unified model generating by Chebyshev polynomials is optimal in the sense of error least square approximation in the single variable ease. Computer simulations show that the proposed method does have the capability of universal approximator in some functional approximation with considerable reduction in learning time.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
On Chebyshev polynomials and torus knots
Gavrilik, A. M.; Pavlyuk, A. M.
2009-01-01
In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, wit...
On Chebyshev-Markov rational functions over several intervals
Lukashov, AL
1998-01-01
Chebyshev-Markov rational functions are the solutions of the following extremal problem [GRAPHICS] with K being a compact subset of R and omega(n)(x) being a fixed real polynomial of degree less than n, positive on K. A parametric representation of Chebyshev-Markov rational functions is found for K
Institute of Scientific and Technical Information of China (English)
刘蕴贤
2003-01-01
Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.
Analysis of Japanese Compound Nouns using Collocational Information
Kobayashi, Y; Tanaka, H; Kobayasi, Yosiyuki; Takunaga, Takenobu; Tanaka, Hozumi
1994-01-01
Analyzing compound nouns is one of the crucial issues for natural language processing systems, in particular for those systems that aim at a wide coverage of domains. In this paper, we propose a method to analyze structures of Japanese compound nouns by using both word collocations statistics and a thesaurus. An experiment is conducted with 160,000 word collocations to analyze compound nouns of with an average length of 4.9 characters. The accuracy of this method is about 80%.
Institute of Scientific and Technical Information of China (English)
2010-01-01
On the basis of introducing the fundamental principles of the least square methods, the Chebyshev polynomial data fitting method is given, by using this method, the grain yield of Jilin Province from 1952 to 2008 is analyzed. The results show that when analyzing the research data of agricultural economy, the least square method of the Chebyshev polynomials is a good choice; by establishing the prediction model of the least square method of Chebyshev polynomials, we get the results that the grain yield in Jilin Province from 2009 to 2015 is 29.004 millon, 29.836 million, 30.681 million, 31.540 million, 32.412 million, 33.298 million, 34.197 million ton ; the annual average growth rate of grain yield from 2009 to 2015 is 2.78%, lower than the annual growth rate of 7.12% from 2000 to 2008.
Efficient prime counting and the Chebyshev primes
Planat, Michel
2011-01-01
The function $\\epsilon(x)=li(x)-\\pi(x)$ is known to be positive up to the (very large) Skewes' number. Besides, according to Robin's work, the functions $\\epsilon_{\\theta}(x)=li[\\theta(x)]-\\pi(x)$ and $\\epsilon_{\\psi}(x)=li[\\psi(x)]-\\pi(x)$ are positive if and only if Riemann hypothesis (RH) holds (the first and the second Chebyshev function are $\\theta(x)=\\sum_{p \\le x} \\log p$ and $\\psi(x)=\\sum_{n=1}^x \\Lambda(n)$, respectively, $li(x)$ is the logarithmic integral, $\\mu(n)$ and $\\Lambda(n)$ are the M\\"obius and the Von Mangoldt functions). Negative jumps in the above functions $\\epsilon$, $\\epsilon_{\\theta}$ and $\\epsilon_{\\psi}$ may potentially occur only at $x+1 \\in \\mathcal{P}$ (the set of primes). One denotes $j_p=li(p)-li(p-1)$ and one investigates the jumps $j_p$, $j_{\\theta(p)}$ and $j_{\\psi(p)}$. In particular, $j_p1$ for $p<10^{11}$. Besides, $j_{\\psi(p)}<1$ for any odd $p \\in \\mathcal{Ch}$, an infinite set of so-called {\\it Chebyshev primes} with partial list ${109, 113, 139, 181, 197, 199, ...
A Novel Learning Scheme for Chebyshev Functional Link Neural Networks
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Satchidananda Dehuri
2011-01-01
dimensional-space where linear separability is possible. Moreover, the proposed HCFLNN combines the best attribute of particle swarm optimization (PSO, back propagation learning (BP learning, and functional link neural networks (FLNNs. The proposed method eliminates the need of hidden layer by expanding the input patterns using Chebyshev orthogonal polynomials. We have shown its effectiveness of classifying the unknown pattern using the publicly available datasets obtained from UCI repository. The computational results are then compared with functional link neural network (FLNN with a generic basis functions, PSO-based FLNN, and EFLN. From the comparative study, we observed that the performance of the HCFLNN outperforms FLNN, PSO-based FLNN, and EFLN in terms of classification accuracy.
On Chebyshev polynomials and torus knots
Gavrilik, A M
2009-01-01
In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q,p-numbers, the generalized two-variable Alexander polynomials, and prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.
Directory of Open Access Journals (Sweden)
Kaustubh Gaikwad
2016-06-01
Full Text Available ASIC Chips and Digital Signal Processors are generally used for implementing digital filters. Now days the advanced technologies lead to use of field programmable Gate Array (FPGA for the implementation of Digital Filters.The present paper deals with Design and Implementation of Digital IIR Chebyshev type II filter using Xilinx System Generator. The Quantization and Overflow are main crucial parameters while designing the filter on FPGA and that need to be consider for getting the stability of the filter. As compare to the conventional DSP the speed of the system is increased by implementation on FPGA. Digital Chebyshev type II filter is initially designed analytically for the desired Specifications and simulated using Simulink in Matlab environment. This paper also proposes the method to implement Digital IIR Chebyshev type II Filter by using XSG platform. The filter has shown good performance for noise removal in ECG
A spectral element method for fluid dynamics - Laminar flow in a channel expansion
Patera, A. T.
1984-01-01
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
Dencker, Peter; Erb, Wolfgang
2015-01-01
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes linked to these curves, we derive a discrete orthogonality structure on these node sets. Using this orthogonality structure, we obtain unique polynomial interpolation in appropriately defined spaces of multivariate Chebyshev polynomials. Our results g...
Rational Chebyshev Spectral Transform for the dynamics of high-power laser diodes
Javaloyes, J
2014-01-01
This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of high-power laser diodes, either broad area lasers, index guided lasers or monolithic master oscillator power amplifier devices. This spectral method can be used in combination with the delay algebraic equation approach developed in \\cite{JB-OE-12}, which allows to substantially reduce the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in \\cite{PJB-JSTQE-13} as a particular case. It is also extended to the consideration of index guiding with an arbitrary profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev Rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of th...
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Fakhrodin Mohammadi
2017-10-01
Full Text Available Stochastic fractional differential equations (SFDEs have been used for modeling many physical problems in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, an efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs. In this approach, operational matrices of the second kind Chebyshev wavelets are used for reducing SFDEs to a linear system of algebraic equations that can be solved easily. Convergence and error analysis of the proposed method is considered. Some numerical examples are performed to confirm the applicability and efficiency of the proposed method.
The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator
Energy Technology Data Exchange (ETDEWEB)
Borzov, V. V., E-mail: borzov.vadim@yandex.ru [Department of Mathematics, St. Petersburg State University of Telecommunications, 191186, Moika 61, St. Petersburg (Russian Federation); Damaskinsky, E. V., E-mail: evd@pdmi.ras.ru [Department of Natural Sciences, Institute of Defense Technical Engineering (VITI), 191123, Zacharievskaya 22, St. Petersburg (Russian Federation)
2014-10-15
In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.
Webb, Stuart; Kagimoto, Eve
2011-01-01
This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates…
State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration
Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.
2015-06-01
The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.
Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs
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.
Multi-Index Stochastic Collocation for random PDEs
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.
Xie, Jiaquan; Huang, Qingxue; Yang, Xia
2016-01-01
In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.
Institute of Scientific and Technical Information of China (English)
叶长遷; 邢鼎生; 王中来
2001-01-01
建立的固定床吸附模型以固体表面扩散为基础，同时考虑吸附剂颗粒内外扩散阻力、床层轴向弥散、非线性吸附平衡和吸附剂形状的影响.应用非矩阵法构造了权函数分别为W(x)=1和W(x)=1-x，最大配置点数为20，适用于非对称性问题的正交配置表.应用正交配置法求解吸附数学模型，并利用文献数值解和文献实验数据检验数值模拟结果.%A mathematical model of fixed bed adsorber is presented, whichdescribes the solid diffusion mechanism considering both internal and external mass transfer resistance. The model accounts for the concentration dependence of intraparticle surface diffusion coefficient，and for the axial diffusion. The nonlinear isotherms, i.e. Langmuir's or Freundlich's isotherms, are used to describe the adsorption equilibrium. The orthogonal collocation tables for unsymmetric geometry based on weighting functions W(x)=1 and W(x)=1-x are constructed by the non-matrix method, with different numbers of collocation pointing from 1 to 20. Numerical solutions are obtained by using the orthogonal collocation method and tested by comparing numerical solutions with experimental data in the literature.
A Corpus-based Study on Collocation and Colligation of "Soil" in Agricultural English
Institute of Scientific and Technical Information of China (English)
Hu Jia-ying; Sun Yuan-yuan
2014-01-01
This paper was based on the corpus built by the writers on agricultural science and technology English. Through corpus-based research and statistical tools AntConc 3.2.1 and BFSU Collocator 1.0 (Beijing Foreign Studies University Collocator 1.0), this paper tried to make an analysis of the collocation and colligation of the word "soil". The result revealed the colligation between "soil"and its collocates in agricultural academic papers, which was instructive to academic writing and the research method was a practical reference of building a corpus on agricultural science and technology English.
Chebyshev's bias and generalized Riemann hypothesis
Alamadhi, Adel; Solé, Patrick
2011-01-01
It is well known that $li(x)>\\pi(x)$ (i) up to the (very large) Skewes' number $x_1 \\sim 1.40 \\times 10^{316}$ \\cite{Bays00}. But, according to a Littlewood's theorem, there exist infinitely many $x$ that violate the inequality, due to the specific distribution of non-trivial zeros $\\gamma$ of the Riemann zeta function $\\zeta(s)$, encoded by the equation $li(x)-\\pi(x)\\approx \\frac{\\sqrt{x}}{\\log x}[1+2 \\sum_{\\gamma}\\frac{\\sin (\\gamma \\log x)}{\\gamma}]$ (1). If Riemann hypothesis (RH) holds, (i) may be replaced by the equivalent statement $li[\\psi(x)]>\\pi(x)$ (ii) due to Robin \\cite{Robin84}. A statement similar to (i) was found by Chebyshev that $\\pi(x;4,3)-\\pi(x;4,1)>0$ (iii) holds for any $x0$ (iv), where $B(x;k,l)=li[\\phi(k)*\\psi(x;k,l)]-\\phi(k)*\\pi(x;k,l)$ is a counting function introduced in Robin's paper \\cite{Robin84} and $R$ resp. $N$) is a quadratic residue modulo $q$ (resp. a non-quadratic residue). We investigate numerically the case $q=4$ and a few prime moduli $p$. Then, we proove that (iv) is eq...
RADIAL BASIS COLLOCATION METHOD FOR BENDING PROBLEMS OF BEAM AND PLATE%基于径向基函数配点法的梁板弯曲问题分析
Institute of Scientific and Technical Information of China (English)
王莉华; 仲政
2012-01-01
采用径向基函数配点法分析考虑剪切效应的梁板弯曲问题,该方法利用径向基函数作为近似函数,基于配点法离散方程,通过最小二乘法求解.径向基函数配点法在离散和计算过程中不需要划分任何形式的网格,是一种真正的无网格法；径向基函数可以用一元函数来描述多元函数,存在明显的储存和运算简单的特点；而基于配点法求解不需要积分,提高了计算效率.分析考虑剪切效应的薄梁板问题时,传统的有限元法或无网格法求解均会存在剪切锁闭问题,而径向基函数在全域内存在无限连续性,能够准确地满足Kirchhoff约束条件,因此径向基函数配点法能够消除剪切锁闭现象,而且不会出现应力波动.该方法的优势在于,其不仅易于离散、精度高,而且具有指数收敛率,计算效率高.数值算例验证了上述结论和该方法的稳定性.%Radial basis collocation method is introduced to analyze the bending problems of Timoshen-ko beam and Reissner-Mindlin plate. The radial basis functions are employed for approximation,the collocation method is utilized for discretization,and the least squares approach is adopted to solve the discretized equations. No mesh will be required in the discretization and resolution and so radial basis collocation method is a truly meshfree method. 1-D radial basis functions can represent all the 2-D or 3-D radial functions which greatly reduce the memory space. No integration will be used in collocation method which improves the computational efficiency. For resolving the problems of thin Timoshenko beam and Reissner-Mindlin plate,analysis demonstrates that radial basis collocation method is free of locking since the shape functions with infinite continuity can satisfy the Kirchhoff constraint conditions, and no stress oscillation is observed, while conventional finite element method and conventional meshfree methods suffer locking problems. The
Spectral functions and time evolution from the Chebyshev recursion
Wolf, F. Alexander; Justiniano, Jorge A.; McCulloch, Ian P.; Schollwöck, Ulrich
2015-03-01
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of T =0 many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor ˜1/6 . We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time-evolution algorithm that instead of the group operator e-i H t only involves the action of the generator H . For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within the dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from H than time evolution algorithms when fixing a given amount of created entanglement.
Computing the Ball Size of Frequency Permutations under Chebyshev Distance
Shieh, Min-Zheng
2011-01-01
Let $S_n^\\lambda$ be the set of all permutations over the multiset $\\{\\overbrace{1,...,1}^{\\lambda},...,\\overbrace{m,...,m}^\\lambda\\}$ where $n=m\\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of $S_n^\\lambda$ in which every two elements have distance $d$. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in $O\\left({2d\\lambda \\choose d\\lambda}^{2.376}\\log n\\right)$ time and $O\\left({2d\\lambda \\choose d\\lambda}^{2}\\right)$ space. The second one runs in $O\\left({2d\\lambda \\choose d\\lambda}{d\\lambda+\\lambda\\choose \\lambda}\\frac{n}{\\lambda}\\right)$ time and $O\\left({2d\\lambda \\choose d\\lambda}\\right)$ space. For small constants $\\lambda$ and $d$, both are efficient ...
A Note on The Convexity of Chebyshev Sets
Directory of Open Access Journals (Sweden)
Sangeeta
2009-07-01
Full Text Available Perhaps one of the major unsolved problem in Approximation Theoryis: Whether or not every Chebyshev subset of a Hilbert space must be convex. Many partial answers to this problem are available in the literature. R.R. Phelps[Proc. Amer. Math. Soc. 8 (1957, 790-797] showed that a Chebyshev set in an inner product space (or in a strictly convex normed linear space is convex if the associated metric projection is non-expansive. We extend this result to metricspaces.
Institute of Scientific and Technical Information of China (English)
范文玎; 孙光耀; 张彬航; 陈锐; 郝丽娟
2016-01-01
燃耗计算在反应堆设计、分析研究中起着重要作用.相比于传统点燃耗算法,切比雪夫有理逼近方法(Chebyshev rational approximation method,CRAM)具有计算速度快、精度高的优点.基于超级蒙特卡罗核计算仿真软件系统SuperMC(Super Monte Carlo Simulation Program for Nuclear and Radiation Process),采用切比雪夫有理逼近方法和桶排序能量查找方法,进行了蒙特卡罗燃耗计算的初步研究与验证.通过燃料棒燃耗例题以及IAEA-ADS(International Atomic Energy Agency-Accelerator Driven Systems)国际基准题,初步验证了该燃耗计算方法的正确性,且IAEA-ADS基准题测试表明,与统一能量网格方法相比,桶排序能量查找方法在保证了计算效率的同时减少了内存开销.%Background:Burnup calculation is the key point of reactor design and analysis. It's significant to calculate the burnup situation and isotopic atom density accurately while a reactor is being designed.Purpose:Based on the Monte Carlo particle simulation code SuperMC (Super Monte Carlo Simulation Program for Nuclear and Radiation Process), this paper aimed to conduct preliminary study and verification on Monte Carlo burnup calculations. Methods:For the characteristics of accuracy, this paper adopted Chebyshev rational approximation method (CRAM) as the point-burnup algorithm. Moreover, instead of the union energy grids method, this paper adopted an energy searching method based on bucket sort algorithm, which reduced the memory overhead on the condition that the calculation efficiency is ensured.Results:By calculating the fuel rod burnup problem and the IAEA-ADS (International Atomic Energy Agency - Accelerator Driven Systems) international benchmark, the simulation results were basically consistent with Serpent and other counties' results, respectively. In addition, the bucket sort energy searching method reduced about 95% storage space compared with union energy grids method for IAEA
Bosse-Andrieu, J.; Mareschal, G.
1998-01-01
Discusses the definition of collocation, demonstrates that associative word combinations do form a continuum, and proposes some parameters to help delimit the scope of collocations in everyday contemporary French. (Author/VWL)
Measuring receptive collocational competence across proficiency levels
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Déogratias Nizonkiza
2015-12-01
Full Text Available The present study investigates, (i English as Foreign Language (EFL learners’ receptive collocational knowledge growth in relation to their linguistic proficiency level; (ii how much receptive collocational knowledge is acquired as proficiency develops; and (iii the extent to which receptive knowledge of collocations of EFL learners varies across word frequency bands. A proficiency measure and a collocation test were administered to English majors at the University of Burundi. Results of the study suggest that receptive collocational competence develops alongside EFL learners’ linguistic proficiency; which lends empirical support to Gyllstad (2007, 2009 and Author (2011 among others, who reported similar findings. Furthermore, EFL learners’ collocations growth seems to be quantifiable wherein both linguistic proficiency level and word frequency occupy a crucial role. While more gains in terms of collocations that EFL learners could potentially add as a result of change in proficiency are found at lower levels of proficiency; collocations of words from more frequent word bands seem to be mastered first, and more gains are found at more frequent word bands. These results confirm earlier findings on the non-linearity nature of vocabulary growth (cf. Meara 1996 and the fundamental role played by frequency in word knowledge for vocabulary in general (Nation 1983, 1990, Nation and Beglar 2007, which are extended here to collocations knowledge.
Probe, A.; Macomber, B.; Kim, D.; Woollands, R.; Junkins, J.
2014-09-01
Modified Chebyshev Picard Iteration (MCPI) is a numerical method for approximating solutions of Ordinary Differential Equations (ODEs). MCPI uses Picard Iteration with Orthogonal Chebyshev Polynomial basis functions to recursively update approximate time histories of system states. Unlike stepping numerical integrators, such as explicit Runge-Kutta methods, MCPI approximates large segments of the trajectory by evaluating the forcing function at multiple nodes along the current approximation during each iteration. Importantly, the Picard sequence theoretically converges to the solution over large time intervals if the forces are continuous and once differentiable. Orthogonality of the basis functions and a vector-matrix formulation allow for low overhead cost, efficient iterations, and parallel evaluation of the forcing function. Despite these advantages MCPI only achieves a geometric rate of convergence. Depending on the quality of the starting approximation, MCPI sometimes requires more function evaluations than competing methods; for parallel applications, this is not a serious drawback, but may be for some serial applications. To improve efficiency, the Terminal Convergence Approximation Modified Chebyshev Picard Iteration (TCA-MCPI) was developed. TCA-MCPI takes advantage of the property that once moderate accuracy of the approximating trajectory has been achieved, the subsequent displacement of nodes asymptotically approaches zero. Applying judicious approximation methods to the force function at each node in the terminal convergence iterations is shown to dramatically reduce the computational cost to achieve accurate convergence. To illustrate this approach we consider high-order spherical-harmonic gravity for high accuracy orbital propagation. When combined with a starting approximation from the 2-body solution TCA-MCPI, is shown to outperform 2 current state-of-practice integration methods for astrodynamics. This paper presents the development of TCA
τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES
Institute of Scientific and Technical Information of China (English)
H. Mazaheri
2006-01-01
The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], and as a counterpart to best approximation in normed linear spaces, best coapproximation was introduced by Franchetti and Furi[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.
Lexical richness and collocational competence in second-language writing
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
Radon transforms and Gegenbauer-Chebyshev integrals, I
Rubin, Boris
2017-06-01
We suggest new modifications of the Helgason's support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer-Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line.
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Evaluating a new test of whole English collocations
DEFF Research Database (Denmark)
Revier, Robert Lee
2009-01-01
The research reported in this chapter explores an alternative approach to the study of L2 collocation knowledge. This approach is characterized by four underlying assumptions. First, collocation knowledge can viewed as an independent construct. Second, collocations constitute lexical items...
Supporting Collocation Learning with a Digital Library
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…
ON NEWMAN-TYPE RATIONAL INTERPOLATION TO |x| AT THE CHEBYSHEV NODES OF THE SECOND KIND
Institute of Scientific and Technical Information of China (English)
Laiyi Zhu; Zhaolin Dong
2006-01-01
Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [-1, 1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O (1/nlnn).
Efficient generation of correlated random numbers using Chebyshev-optimal magnitude-only IIR filters
Rodríguez, A; Johnson, Steven G.; Rodriguez, Alejandro
2007-01-01
We compare several methods for the efficient generation of correlated random sequences (colored noise) by filtering white noise to achieve a desired correlation spectrum. We argue that a class of IIR filter-design techniques developed in the 1970s, which obtain the global Chebyshev-optimum minimum-phase filter with a desired magnitude and arbitrary phase, are uniquely suited for this problem but have seldom been used. The short filters that result from such techniques are crucial for applications of colored noise in physical simulations involving random processes, for which many long random sequences must be generated and computational time and memory are at a premium.
CONSTRUCTION OF THE ENCRYPTION MATRIX BASED ON CHEBYSHEV CHAOTIC NEURAL NETWORKS
Institute of Scientific and Technical Information of China (English)
Zou Ajin; Wu Wei; Li Renfa; Li Yongjiang
2012-01-01
The paper proposes a novel algorithm to get the encryption matrix.Firstly,a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected.Then,a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices.The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and autocorrelation with the natural frequency of the plaintext being hidden and homogenized.
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Minimum Phase Property of Chebyshev-Sharpened Cosine Filters
Directory of Open Access Journals (Sweden)
Miriam Guadalupe Cruz Jiménez
2015-01-01
Full Text Available We prove that the Chebyshev sharpening technique, recently introduced in literature, provides filters with a Minimum Phase (MP characteristic when it is applied to cosine filters. Additionally, we demonstrate that cascaded expanded Chebyshev-Sharpened Cosine Filters (CSCFs are also MP filters, and we show that they achieve a lower group delay for similar magnitude characteristics in comparison with traditional cascaded expanded cosine filters. The importance of the characteristics of cascaded expanded CSCFs is also elaborated. The developed examples show improvements in the group delay ranged from 23% to 47% at the cost of a slight increase of usage of hardware resources. For an application of a low-delay decimation filter, the proposed scheme exhibits a 24% lower group delay, with 35% less computational complexity (estimated in Additions per Output Sample and slightly less usage of hardware elements.
The parabolic trigonometric functions and the Chebyshev radicals
Dattoli, G.; Migliorati, M.; Ricci, P. E.
2011-01-01
The parabolic trigonometric functions have recently been introduced as an intermediate step between circular and hyperbolic functions. They have been shown to be expressible in terms of irrational functions, linked to the solution of third degree algebraic equations. We show the link of the parabolic trigonometric functions with the Chebyshev radicals and also prove that further generalized forms of trigonometric functions, providing the natural solutions of the quintic algebraic equation, ca...
SINGULAR INTEGRAL OPERATORS IN L2 SPACE WITH CHEBYSHEV WEIGHTS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper defines a class of singular integral operators Iwj on L2wj space,where wights wj(j=1-4) are four kinds of Chebyshev weights.The authors prove that Iwj is an unique linear extension of classic singular integral operator Iwj on Holder space,some important properties of Iwj and some results of singular integral equation in L2wj space.
1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind
Dragoljub Pavlović, Vlastimir; Stanojko Dončov, Nebojša; Gradimir Ćirić, Dejan
2013-11-01
Christoffel-Darboux formula for Chebyshev continual orthogonal polynomials of the first kind is proposed to find a mathematical solution of approximation problem of a one-dimensional (1D) filter function in the z domain. Such an approach allows for the generation of a linear phase selective 1D low-pass digital finite impulse response (FIR) filter function in compact explicit form by using an analytical method. A new difference equation and structure of corresponding linear phase 1D low-pass digital FIR filter are given here. As an example, one extremely economic 1D FIR filter (with four adders and without multipliers) is designed by the proposed technique and its characteristics are presented. Global Christoffel-Darboux formula for orthonormal Chebyshev polynomials of the first kind and for two independent variables for generating linear phase symmetric two-dimensional (2D) FIR digital filter functions in a compact explicit representative form, by using an analytical method, is proposed in this paper. The formula can be most directly applied for mathematically solving the approximation problem of a filter function of even and odd order. Examples of a new class of extremely economic linear phase symmetric selective 2D FIR digital filters obtained by the proposed approximation technique are presented.
Mining visual collocation patterns via self-supervised subspace learning.
Yuan, Junsong; Wu, Ying
2012-04-01
Traditional text data mining techniques are not directly applicable to image data which contain spatial information and are characterized by high-dimensional visual features. It is not a trivial task to discover meaningful visual patterns from images because the content variations and spatial dependence in visual data greatly challenge most existing data mining methods. This paper presents a novel approach to coping with these difficulties for mining visual collocation patterns. Specifically, the novelty of this work lies in the following new contributions: 1) a principled solution to the discovery of visual collocation patterns based on frequent itemset mining and 2) a self-supervised subspace learning method to refine the visual codebook by feeding back discovered patterns via subspace learning. The experimental results show that our method can discover semantically meaningful patterns efficiently and effectively.
Study on solar properties of approaching compact Chebyshev sets%逼近紧 Chebyshev 集的太阳性
Institute of Scientific and Technical Information of China (English)
崔云安; 赵振兴
2014-01-01
Let X be a local uniformly convex space , G be an approaching compact Chebyshe set.This paper proved that the equivalence of G being an approaching compact Chebyshev set was that G was a sun set .%设X是局部一致凸空间，G是逼近紧Chebyshev集。证明了G是逼近紧Chebyshev集的充分必要条件是G是太阳集。
Measuring receptive collocational competence across proficiency ...
African Journals Online (AJOL)
Kate H
These limitations range from testing collocational knowledge and another aspect of vocabulary knowledge in the same test battery (e.g. Mochizuki 2002 and Nizonkiza. 2011) to .... with overall proficiency, depth, and vocabulary size tests.
Chebyshev and Modified Wavelet Algorithm Based Sleep Arousals Detection Using EEG Sensor Database
Directory of Open Access Journals (Sweden)
Mahalaxmi U. S. B. K.
2017-04-01
Full Text Available Electroencephalographic (EEG arousals are generally observed in EEG recordings as an awakening response of the human brain. Sleep apnea is a major sleep disorder. The patients, with Severe Sleep Apnea (SAS suffers from frequent interruptions in their sleep which brings about EEG arousals. In this paper, a new method for Segmentation and Filtering process of EEG sensor database signals for finding sleep arousals using Chebyshev and Modified Wavelet Algorithm is proposed. The Segmentation Algorithm appears as various features extracted from EEG Data’s and PSG Recordings. The Chebyshev Equiripple Filter is used in Filtering algorithm and then MSVM [M-Support Vector Machine] was utilized as Classification Tool. Algorithms are performed and different features are extracted and the ROC characteristics are performed. The extracted features are Delta, Gama, Beta, Alpha, Sigma of the EEG signal, EEG Signal Mean, EEG Signal Standard Deviation, EEG Signal Peak Signal to Noise Ratio [PSNR], and EEG Signal Normalization. MSVM tool showing EEG signals results.
Directory of Open Access Journals (Sweden)
Chih-Hong Lin
2016-06-01
Full Text Available A permanent magnet (PM synchronous generator system driven by wind turbine (WT, connected with smart grid via AC-DC converter and DC-AC converter, are controlled by the novel recurrent Chebyshev neural network (NN and amended particle swarm optimization (PSO to regulate output power and output voltage in two power converters in this study. Because a PM synchronous generator system driven by WT is an unknown non-linear and time-varying dynamic system, the on-line training novel recurrent Chebyshev NN control system is developed to regulate DC voltage of the AC-DC converter and AC voltage of the DC-AC converter connected with smart grid. Furthermore, the variable learning rate of the novel recurrent Chebyshev NN is regulated according to discrete-type Lyapunov function for improving the control performance and enhancing convergent speed. Finally, some experimental results are shown to verify the effectiveness of the proposed control method for a WT driving a PM synchronous generator system in smart grid.
High-frequency collocations of nouns in research articles across eight disciplines
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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.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A method to estimate the probabilistic density function (PDF) of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial(SCOP) combined with sample moments (the originmoments)was used to approximate the PDF of parameters. χ2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme value Ⅰ , gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.
Locating CVBEM collocation points for steady state heat transfer problems
Hromadka, T.V.
1985-01-01
The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
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.
Discrete Fourier Analysis and Chebyshev Polynomials with G2 Group
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Huiyuan Li
2012-10-01
Full Text Available The discrete Fourier analysis on the 30°-60°-90° triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2, which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type.
Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.
2014-09-01
Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the
Institute of Scientific and Technical Information of China (English)
姜剑; 王兆清; 庄美玲
2015-01-01
The nonlinear vibration of multi-degree-of-freedom systems can be modeled by initial value problem of nonlinear differential equation,this paper mainly studied the application of barycentric rational interpolation iterative collocation method to solve nonlinear vibration of multi-degree-of-freedom systems. A linear iterative scheme is constructed for approximating nonlinear differential equations. The linear differential equations are discretized into algebraic equations by applying Barycentric rational interpolation differential matrixes. Then, the numerical results of nonlinear vibration problem can be obtained by solving the algebraic equations with iteration method. The examples of nonlinear vibration of coupled systems demonstrated the proposed method is simple, effective and excellent stability and can accurately simulate various physical quantities of the nonlinear vibration.%多自由度非线性振动的数学模型为非线性微分方程组的初值问题。文章运用重心有理插值迭代配点法研究了求解多自由度非线性振动的问题；通过构造一个逼近非线性微分方程组的线性化迭代格式，采用重心有理插值微分矩阵离散线性化微分方程组，由线性化迭代计算最终得到非线性方程组的数值解。结果表明：依据算例的解析解和数值解比较，重心有理插值迭代配点法能够高精度计算模拟多自由度非线性振动的各项物理量，并且简单有效，具有优异的计算稳定性。
Spatial optimum collocation model of urban land and its algorithm
Kong, Xiangqiang; Li, Xinyun
2007-06-01
Optimizing the allocation of urban land is that layout and fix position the various types of land-use in space, maximize the overall benefits of urban space (including economic, social, environment) using a certain method and technique. There is two problems need to deal with in optimizing the allocation of urban land in the technique: one is the quantitative structure, the other is the space structure. In allusion to these problems, according to the principle of spatial coordination, a kind of new optimum collocation model about urban land was put forward in this text. In the model, we give a target function and a set of "soft" constraint conditions, and the area proportions of various types of land-use are restricted to the corresponding allowed scope. Spatial genetic algorithm is used to manipulate and calculate the space of urban land, the optimum spatial collocation scheme can be gradually approached, in which the three basic operations of reproduction, crossover and mutation are all operated on the space. Taking the built-up areas of Jinan as an example, we did the spatial optimum collocation experiment of urban land, the spatial aggregation of various types is better, and an approving result was got.
LEXICAL APPROACH IN TEACHING TURKISH: A COLLOCATIONAL STUDY MODEL
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Eser ÖRDEM
2013-06-01
Full Text Available Abstract This study intends to propose Lexical Approach (Lewis, 1998, 2002; Harwood, 2002 and a model for teaching Turkish as a foreign language so that this model can be used in classroom settings. This model was created by the researcher as a result of the studies carried out in applied linguistics (Hill, 20009 and memory (Murphy, 2004. Since one of the main problems of foreign language learners is to retrieve what they have learnt, Lewis (1998 and Wray (2008 assume that lexical approach is an alternative explanation to solve this problem.Unlike grammar translation method, this approach supports the idea that language is not composed of general grammar but strings of word and word combinations.In addition, lexical approach posits the idea that each word has tiw gramamtical properties, and therefore each dictionary is a potential grammar book. Foreign language learners can learn to use collocations, a basic principle of Lexical approach. Thus, learners can increase the level of retention.The concept of retrieval clue (Murphy, 2004 is considered the main element in this collocational study model because the main purpose of this model is boost fluency and help learners gain native-like accuracy while producing the target language. Keywords: Foreign language teaching, lexical approach, collocations, retrieval clue
Mars Mission Optimization Based on Collocation of Resources
Chamitoff, G. E.; James, G. H.; Barker, D. C.; Dershowitz, A. L.
2003-01-01
This paper presents a powerful approach for analyzing Martian data and for optimizing mission site selection based on resource collocation. This approach is implemented in a program called PROMT (Planetary Resource Optimization and Mapping Tool), which provides a wide range of analysis and display functions that can be applied to raw data or imagery. Thresholds, contours, custom algorithms, and graphical editing are some of the various methods that can be used to process data. Output maps can be created to identify surface regions on Mars that meet any specific criteria. The use of this tool for analyzing data, generating maps, and collocating features is demonstrated using data from the Mars Global Surveyor and the Odyssey spacecraft. The overall mission design objective is to maximize a combination of scientific return and self-sufficiency based on utilization of local materials. Landing site optimization involves maximizing accessibility to collocated science and resource features within a given mission radius. Mission types are categorized according to duration, energy resources, and in-situ resource utilization. Optimization results are shown for a number of mission scenarios.
A class of high-order Runge-Kutta-Chebyshev stability polynomials
O'Sullivan, Stephen
2015-01-01
The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order $N$ is presented. Roots of FRKC stability polynomials of degree $L = MN$ are used to construct explicit schemes comprising $L$ forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to $\\sim L^2$. The associated stability domain scales as $M^2$ along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear problems at orders above 2, complex splitting or Butcher group composition methods are required. Linear order conditions of the FRKC stability polynomials are verified at orders 2, 4, and 6 in numerical experiments. Comparative studies with existing methods show the second-order unsplit FRKC2 scheme and higher order (4 and 6) split FRKC schemes are efficient ...
Energy Technology Data Exchange (ETDEWEB)
Abdulle, Assyr, E-mail: Assyr.Abdulle@epfl.ch [Mathematics Section, École Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne (Switzerland); Vilmart, Gilles, E-mail: Gilles.Vilmart@bretagne.ens-cachan.fr [École Normale Supérieure de Cachan, Antenne de Bretagne, INRIA Rennes, IRMAR, CNRS, UEB, Av. Robert Schuman, F-35170 Bruz (France)
2013-06-01
A partitioned implicit–explicit orthogonal Runge–Kutta method (PIROCK) is proposed for the time integration of diffusion–advection–reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.
Abdulle, Assyr; Vilmart, Gilles
2013-06-01
A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.
Kopeliovich, Vladimir B
2016-01-01
The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables $J_N^2(z_N^\\theta)$, where $\\theta$ is the polar angle defining the momentum of the final (cumulative) particle, $z_N^\\theta = cos (\\theta/N)$, the integer $N$ being the multiplicity of the process (the number of interactions). Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials $J_N^2[cos(\\pi/N)]=0$. The recurrent relations between polynomials with different $N$ are obtained, and their connection with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result of this equality, differential cross section of the cumulative particle production has characteristic behaviour $d\\sigma \\sim 1/ \\sqrt {\\pi - \\theta}$ at $\\theta \\sim \\pi$ (the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, begin...
On the Functions of Lexical Collocation in English Texts
Institute of Scientific and Technical Information of China (English)
XIAO Fuliang
2016-01-01
Lexical collocation , as a cohesive device of an English text, is helpful to make up a cohesive and coherent text. Therefore, to better comprehend English text, different patterns and functions of lexical collocation should be guided in detail.
Khader, M. M.
2015-10-01
In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge-Kutta method is given.
On the Content of Prepositions in Prepositional Collocations
Directory of Open Access Journals (Sweden)
Eva Sicherl
2004-12-01
Full Text Available The article aims to shed some light on the problems faced by non-native speakers in the formation of so-called prepositional collocations (i.e. typical, recurrent combinations of verbal, nominal or adjectival bases with prepositional collocators. The reasons for frequent mistakes mainly lie in the meaning of the preposition used as part of collocation, which tends to be even more dispersed, abstract and difficult to define than that of the preposition used in a free combination. However, the preposition when used as a collocator seems to act, at least to some extent, as a carrier of some content; this can be proven by valency patterns: meaning-related content words (collocational bases tend to regularly combine with identical prepositions. The fact that prepositions used in collocations also have their semantic part to contribute to the whole unit should also be considered in the classification of collocations into grammatical and lexical ones.
Evaluating a new test of whole English collocations
DEFF Research Database (Denmark)
Revier, Robert Lee
2009-01-01
collocations of the verb-object-noun syntactic type (e.g. make a complaint). It is also designed to explore whether test takers' ability to generate targetd English word combinations is influenced by the semantic properties of such items. The chapter consists of two parts. In the first part, I address a number...... of theoretical and practical issues informing the experimental study. Once I have desribed how collocations are defined and classified, I go on to explain how collocation knowledge is conceptualized and operationalized in the present research and how the collocation test was designed and developed. In the second......The research reported in this chapter explores an alternative approach to the study of L2 collocation knowledge. This approach is characterized by four underlying assumptions. First, collocation knowledge can viewed as an independent construct. Second, collocations constitute lexical items...
Institute of Scientific and Technical Information of China (English)
梅成才; 潘修强; 陈军杰
2013-01-01
Robotic manipulators have long been applied to industrial welding in the past decades. This study pays an emphasis on coaching the manipulator not to slew its five joints into the weldment of two orthogonally intersecting cylinders. Direct Collocation with Nonlinear Programming (DCNLP) is the key numerical method adopted in this study which discretizes the time history of the mo-tion into N segments and approximates the solutions in each segment by cubic polynomials. The constraint functions are comprised of the inequality constraints and defect equations. As soon as the constraint functions converge, the optimal solution is found.% 为了实现相贯线接缝的自动焊接，提出了一种基于直接配置非线性规划方法（DCNLP）的焊道轨迹运动控制方法。以两圆柱相贯自动焊接接管为例，通过将相贯线接缝曲线焊接时间离散化为N个时间区间，在每个区间内用三次多项式代表状态变量随时间变化的关系，使用Hermite-Simpson插值定义多项式，计算逼近的多项式和实际运动方程之间的差值。为使机器手臂各关节不掠入相贯圆柱体，研究亦设下额外的不等式限制方程，以确保关节不触及圆柱体，其中不等式限制方程加上缺陷方程构成所有的限制方程，当所有限制方程均满足时，迭代的结果就收敛，同时找到最优解。仿真结果表明DCNLP在处理焊接轨迹控制问题时具有较强的鲁棒性。
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas
2014-02-06
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.
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....
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
Designing mobile experiences for collocated interaction
Lundgren, Sus; Fischer, Joel; Reeves, Stuart; Torgersson, Olof
2015-01-01
Many of our everyday social interactions involve mobile devices. Yet, these tend to only provide good support for distributed social interactions. Although much HCI and CSCW research has explored how we might support collocated, face-to-face situations using mobile devices, much of this work exists as isolated exemplars of technical systems and / or interaction designs. This paper draws on a range of such exemplars to develop a practical design framework intended for guiding the design of new...
Corpus-based collocation research targeted at Japanese language learners
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Irena SRDANOVIĆ
2014-07-01
Full Text Available This paper discusses corpus-based research on collocations, introduces various tools for querying and extracting Japanese collocations and presents an analysis of Japanese collocations using language corpora and related tools. First, major corpus query tools such as Sketch Engine, NINJAL-NLP, Natsume, Chunagon, which can be used by learners and teachers of Japanese language, are briefly described. Focus then shifts to adjectival and nominal collocates and the resource "Collocation data of adjectives and nouns" which consists of adjective headwords and their nominal collocates extracted from two large corpora, BCCWJ and JpTenTen: 500 adjectives and 9,218 collocate nouns, and 500 adjectives and 23,220 collocate nouns from each corpus respectively. Finally, it is shown that corpus-based resources can be used in the creation of reference materials for learners of the Japanese language. The benefits of empirical research into collocations are also shown by comparing the obtained results with collocations in textbooks for Japanese as foreign language.
Chakraborty, Debananda
2011-01-01
We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potential term yields a critical phenomenon--that is, the solution behavior around the critical parameter value bifurcates into two extreme cases. Pinpointing the critical value with arbitrary accuracy is even more challenging. In this work, we adopt the generalized polynomial chaos (gPC) method to determine the critical values and the mean solutions around such values. First, we consider the critical value associated with the strength of the singular potential for the Klein-Gordon equation. We expand the solution in the random variable associated with the parameter. The obtained partial differential equations are solved using the Chebyshev collocation method. Due to the existence of the singularity, the Gibbs phenomenon appears in the solution, yielding a slow convergence of the numerically computed critical value. To deal with the singul...
Semantic Analysis of Verbal Collocations with Lexical Functions
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,...
On Collocations and Their Interaction with Parsing and Translation
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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.
Verb-Noun Collocation Proficiency and Academic Years
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Fatemeh Ebrahimi-Bazzaz
2014-01-01
Full Text Available Generally vocabulary and collocations in particular have significant roles in language proficiency. A collocation includes two words that are frequently joined concurrently in the memory of native speakers. There have been many linguistic studies trying to define, to describe, and to categorise English collocations. It contains grammatical collocations and lexical collocations which include nouns, adjectives, verbs, and adverb. In the context of a foreign language environment such as Iran, collocational proficiency can be useful because it helps the students improve their language proficiency. This paper investigates the possible relationship between verb-noun collocation proficiency among students from one academic year to the next. To reach this goal, a test of verb-noun collocations was administered to Iranian learners. The participants in the study were 212 Iranian students in an Iranian university. They were selected from the second term of freshman, sophomore, junior, and senior years. The students’ age ranged from 18 to 35.The results of ANOVA showed there was variability in the verb-noun collocations proficiency within each academic year and between the four academic years. The results of a post hoc multiple comparison tests demonstrated that the means are significantly different between the first year and the third and fourth years, and between the third and the fourth academic year; however, students require at least two years to show significant development in verb-noun collocation proficiency. These findings provided a vital implication that lexical collocations are learnt and developed through four academic years of university, but requires at least two years showing significant development in the language proficiency. Keywords: Language proficiency, Collocation, Communicative Competence, academic year, Iranian EFL learners
Chatpunnarangsee, Kwanjira
2013-01-01
The purpose of this study is to explore ways of incorporating web-based concordancers for the purpose of teaching English collocations. A mixed-methods design utilizing a case study strategy was employed to uncover four specific dimensions of corpus use by twenty-four students in two classroom sections of a writing course at a university in…
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
2010-10-01
... that each of the following conditions is met: (i) Either legitimate security concerns, or operational... met: (i) Construction of a separate entrance is technically feasible; (ii) Either legitimate security... and maintenance requirements. The incumbent must provide power and physical collocation services...
Optimization of Low-Thrust Spiral Trajectories by Collocation
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.
Lai, Hong; Orgun, Mehmet A.; Pieprzyk, Josef; Li, Jing; Luo, Mingxing; Xiao, Jinghua; Xiao, Fuyuan
2016-08-01
We propose an approach that achieves high-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding. In particular, we encode a key with the Chebyshev-map values corresponding to Lucas numbers and then use k-Chebyshev maps to achieve consecutive and flexible key expansion and apply the pre-shared classical information between Alice and Bob and fountain codes for privacy amplification to solve the security of the exchange of classical information via the classical channel. Consequently, our high-capacity protocol does not have the limitations imposed by orbital angular momentum and down-conversion bandwidths, and it meets the requirements for longer distances and lower error rates simultaneously.
Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams
Ait-Haddou, Rachid
2013-08-01
The notion of a blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Müntz spaces with integer exponents, the notion of a Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Müntz spaces in terms of Schur functions. We derive an explicit expression for the Chebyshev-Bernstein basis via an inductive argument on nested Müntz spaces. We also reveal a simple algorithm for dimension elevation. Free-form design schemes in Müntz spaces with Young diagrams as shape parameters are discussed. © 2013 Elsevier Ltd. All rights reserved.
Lai, Hong; Orgun, Mehmet A.; Pieprzyk, Josef; Li, Jing; Luo, Mingxing; Xiao, Jinghua; Xiao, Fuyuan
2016-11-01
We propose an approach that achieves high-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding. In particular, we encode a key with the Chebyshev-map values corresponding to Lucas numbers and then use k-Chebyshev maps to achieve consecutive and flexible key expansion and apply the pre-shared classical information between Alice and Bob and fountain codes for privacy amplification to solve the security of the exchange of classical information via the classical channel. Consequently, our high-capacity protocol does not have the limitations imposed by orbital angular momentum and down-conversion bandwidths, and it meets the requirements for longer distances and lower error rates simultaneously.
Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks
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…
Vyas, Bhargav Y; Das, Biswarup; Maheshwari, Rudra Prakash
2016-08-01
This paper presents the Chebyshev neural network (ChNN) as an improved artificial intelligence technique for power system protection studies and examines the performances of two ChNN learning algorithms for fault classification of series compensated transmission line. The training algorithms are least-square Levenberg-Marquardt (LSLM) and recursive least-square algorithm with forgetting factor (RLSFF). The performances of these algorithms are assessed based on their generalization capability in relating the fault current parameters with an event of fault in the transmission line. The proposed algorithm is fast in response as it utilizes postfault samples of three phase currents measured at the relaying end corresponding to half-cycle duration only. After being trained with only a small part of the generated fault data, the algorithms have been tested over a large number of fault cases with wide variation of system and fault parameters. Based on the studies carried out in this paper, it has been found that although the RLSFF algorithm is faster for training the ChNN in the fault classification application for series compensated transmission lines, the LSLM algorithm has the best accuracy in testing. The results prove that the proposed ChNN-based method is accurate, fast, easy to design, and immune to the level of compensations. Thus, it is suitable for digital relaying applications.
Directory of Open Access Journals (Sweden)
Jong-Seung Park
2016-11-01
Full Text Available Collocations in Japanese and Korean have been studied extensively based on statistical tools. The criteria for collocations in these languages, however, have not been fully established in the literature, and it is not obvious whether all statistically significant combinations of words could be regarded as collocations. In this article, we point out empirical problems in extracting collocations in Japanese and Korean, and provide a standard for identifying collocations (to be separated from “free combination” and “idiom” in these languages. We concentrate on the discussion of empirical aspects of collocation research, rather than the statistical analyses of collocational patterns. As a preliminary to developing a database for Japanese-Korean contrastive work on collocations, the present study focuses on ten “Chinese-words” (漢語. We show that (i the co-occurring verbs for eight Chinese-words in Korean all carry over to Japanese (but not vice versa; (ii in the other two cases, Korean exhibits co-occurring verbs not found in Japanese; (iii language-specific patterns of verb co-occurring are also observed in some instances. Overall, it is indicated that a much wider variety of co-occurring verbs are found in Japanese than in Korean.
Directory of Open Access Journals (Sweden)
Likun Wang
2016-01-01
Full Text Available Given the fact that Cross-track Infrared Sounder (CrIS and the Visible Infrared Imaging Radiometer Suite (VIIRS are currently onboard the Suomi National Polar-orbiting Partnership (Suomi NPP satellite and will continue to be carried on the same platform as future Joint Polar Satellite System (JPSS satellites for the next decade, it is desirable to develop a fast and accurate collocation scheme to collocate VIIRS products and measurements with CrIS for applications that rely on combining measurements from two sensors such as inter-calibration, geolocation assessment, and cloud detection. In this study, an accurate and fast collocation method to collocate VIIRS measurements within CrIS instantaneous field of view (IFOV directly based on line-of-sight (LOS pointing vectors is developed and discussed in detail. We demonstrate that this method is not only accurate and precise from a mathematical perspective, but also easy to implement computationally. More importantly, with optimization, this method is very fast and efficient and thus can meet operational requirements. Finally, this collocation method can be extended to a wide variety of sensors on different satellite platforms.
Jiménez-Teja, Y; Molino, A; Fernandes, C A C
2015-01-01
Photometric redshifts, which have become the cornerstone of several of the largest astronomical surveys like PanStarrs, DES, J-PAS or the LSST, require precise measurements of galaxy photometry in different bands using a consistent physical aperture. This is not trivial, due to the variation in the shape and width of the Point Spread Function (PSF) introduced by wavelength differences, instrument positions and atmospheric conditions. Current methods to correct for this effect rely on a detailed knowledge of the PSF characteristics as a function of the survey coordinates, which can be difficult due to the relative paucity of stars tracking the PSF behaviour. Here we show that it is possible to measure accurate, consistent multicolour photometry without knowing the shape of PSF. The Chebyshev-Fourier Functions (CHEFs) can fit the observed profile of each object and produce high signal-to-noise integrated flux measurements unaffected by the PSF. These total fluxes, which encompass all the galaxy populations, are...
Institute of Scientific and Technical Information of China (English)
Ma Shao-Juan; Xu Wei; Li Wei; Fang Tong
2006-01-01
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter.Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
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.
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M. R.Odekunle
2014-08-01
Full Text Available Tau method which is an economized polynomial technique for solving ordinary and partial differential equations with smooth solutions is modified in this paper for easy computation, accuracy and speed. The modification is based on the systematic use of „Catalan polynomial‟ in collocation tau method and the linearizing the nonlinear part by the use of Adomian‟s polynomial to approximate the solution of 2-dimentional Nonlinear Partial differential equation. The method involves the direct use of Catalan Polynomial in the solution of linearizedPartial differential Equation without first rewriting them in terms of other known functions as commonly practiced. The linearization process was done through adopting the Adomian Polynomial technique. The results obtained are quite comparable with the standard collocation tau methods for nonlinear partial differential equations.
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)
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Tony Berber Sardinha
2016-06-01
Full Text Available This article presents the results from a corpus-based multidimensional analysis of the language of the Brazilian economy, building on a previous study that determined the major dimensions underlying the statistical collocations of the +8,000 most frequent words in Brazilian Portuguese (Berber Sardinha et al., submitted. The corpus used was the Corpus Brasileiro (Brazilian Corpus (LAEL, CEPRIL, PUCSP, Fapesp, CNPq, a multi-register corpus with 1 billion tokens. Dimensions of collocation are the communicative parameters that underlie collocational choice, and the method for identifying them is based on the Multidimensional Analysis framework developed by Biber (1988. This study focused on dimension 6, which reflects the language used to talk about the economy in Brazilian Portuguese; this dimension was broken down into five other (sub- dimensions, which further specify the nuances of the language of the economy. These five (sub-dimensions were then analyzed for metaphor by hand, and the analysis revealed that metaphors account for almost 30% of the collocations. Furthermore, metaphors are not distributed evenly across the (sub-dimensions of the language of the economy. This study is part of a larger project whose ultimate goal is to produce a corpus-based dictionary of Brazilian Portuguese collocations.
Extraction of V-N-Collocations from Text Corpora A Feasibility Study for German
Breidt, E
1996-01-01
The usefulness of a statistical approach suggested by Church et al. (1991) is evaluated for the extraction of verb-noun (V-N) collocations from German text corpora. Some problematic issues of that method arising from properties of the German language are discussed and various modifications of the method are considered that might improve extraction results for German. The precision and recall of all variant methods is evaluated for V-N collocations containing support verbs, and the consequences for further work on the extraction of collocations from German corpora are discussed. With a sufficiently large corpus (>= 6 mio. word-tokens), the average error rate of wrong extractions can be reduced to 2.2% (97.8% precision) with the most restrictive method, however with a loss in data of almost 50% compared to a less restrictive method with still 87.6% precision. Depending on the goal to be achieved, emphasis can be put on a high recall for lexicographic purposes or on high precision for automatic lexical acquisiti...
Automated Abnormal Mass Detection in the Mammogram Images Using Chebyshev Moments
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Alireza Talebpour
2013-01-01
Full Text Available Breast cancer is the second leading cause of cancer mortality among women after lung cancer. Early diagnosis of this disease has a major role in its treatment. Thus the use of computer systems as a detection tool could be viewed as essential to helping with this disease. In this study a new system for automated mass detection in mammography images is presented as being more accurate and valid. After optimization of the image and extracting a better picture of the breast tissue from the image and applying log-polar transformation, Chebyshev moments can be calculated in all areas of breast tissue. Then after extracting effective features in the diagnosis of mammography images, abnormal masses, which are important for the physician and specialists, can be determined with applying the appropriate threshold. To check the system performance, images in the MIAS (Mammographic Image Analysis Society mammogram database have been used and the results allowed us to draw a FROC (Free Response Receiver Operating Characteristic curve. When compared the FROC curve with similar systems experts, the high ability of our system was confirmed. In this system, images of different thresholds, specifically 445, 450, 455 are processed and then put through a sensitivity analysis. The process garnered good results 100, 92 and 84%, respectively and a false positive rate per image 2.56, 0.86, 0.26, respectively have been calculated. Comparing other automatic mass detection systems, the proposed method has a few advantages over prior systems: Our process allows us to determine the amount of false positives and/or sensitivity parameters within the system. This can be determined by the importance of the detection work being done. The proposed system achieves 100% sensitivity and 2.56 false positive for every image.
Institute of Scientific and Technical Information of China (English)
张芹; 郭力; 张秉超
2012-01-01
针对混凝土中氯离子扩散过程中扩散系数的非均质性导致的非线性问题,采用区域分解法并融入无网格法中的径向基函数求解思想,建立了时空一致径向基函数配点法.该方法将时间和空间区域同时分解,在相应子域上对未知函数进行径向基函数展开.针对含有Neumann边界条件的非均质扩散问题建立了Hermite型近似函数配点求解方法.该方法避免了对时间域采用差分法求解引起的迭代求解困难,对求解非均质扩散系数的问题求解具有一定优势.用Matlab语言编制了相应的求解程序,通过2个非均质扩散问题算例,验证了所提方法的正确性和有效性.所提方法为研究复杂环境下混凝土结构的耐久性问题提供了一种新的数值方法.%According to the nonlinear problem caused by heterogeneous diffusivity in the diffusion process of chloride ion in concrete, a time-space consistent collocation method is developed with the domain decomposition method and the methodology of the radial basis function (RBF) in the mesh-less method. Unknown arguments are expanded via RBFs in the corresponding sub-domain with simultaneous decomposing of the time and space domain. Additionally, a Hermite collocation method of the RBF is constructed to solve the heterogeneous diffusion problem with Neumann boundary conditions. Compared with the finite difference process on solving time domain issues, the proposed method reduces the difficulty of iterative procedure and results in a more easy application to heterogeneous diffusion problems. The Matlab program of the developed method is subsequently implemented. Two numerical examples are performed to evaluate the accuracy and efficiency of the developed model. The examples clearly demonstrate that the developed method has more distinguished advantages than the finite element method in analyzing heterogeneous diffusion problems. The proposed method provides new guidelines for the
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Fenghui Huang
2012-01-01
Full Text Available A numerical scheme is presented for a class of time fractional differential equations with Dirichlet's and Neumann's boundary conditions. The model solution is discretized in time and space with a spectral expansion of Lagrange interpolation polynomial. Numerical results demonstrate the spectral accuracy and efficiency of the collocation spectral method. The technique not only is easy to implement but also can be easily applied to multidimensional problems.
Some theoretical aspects of elastic wave modeling with a recently developed spectral element method
Institute of Scientific and Technical Information of China (English)
WANG XiuMing; SERIANI Geza; LIN WeiJun
2007-01-01
A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Chebyshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.
Some theoretical aspects of elastic wave modeling with a recently developed spectral element method
Institute of Scientific and Technical Information of China (English)
SERIANI; Geza
2007-01-01
A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.
Secure Image Transmission over DFT-precoded OFDM-VLC systems based on Chebyshev Chaos scrambling
Wang, Zhongpeng; Qiu, Weiwei
2017-08-01
This paper proposes a physical layer image secure transmission scheme for discrete Fourier transform (DFT) precoded OFDM-based visible light communication systems by using Chebyshev chaos maps. In the proposed scheme, 256 subcarriers and QPSK modulation are employed. The transmitted digital signal of the image is encrypted with a Chebyshev chaos sequence. The encrypted signal is then transformed by a DFT precoding matrix to reduce the PAPR of the OFDM signal. After that, the encrypted and DFT-precoded OFDM are transmitted over a VLC channel. The simulation results show that the proposed image security transmission scheme can not only protect the DFT-precoded OFDM-based VLC from eavesdroppers but also improve BER performance.
Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot
Liang, Conghui; Ceccarelli, Marco; Takeda, Yukio
2012-12-01
In this paper, operation analysis of a Chebyshev-Pantograph leg mechanism is presented for a single degree of freedom (DOF) biped robot. The proposed leg mechanism is composed of a Chebyshev four-bar linkage and a pantograph mechanism. In contrast to general fully actuated anthropomorphic leg mechanisms, the proposed leg mechanism has peculiar features like compactness, low-cost, and easy-operation. Kinematic equations of the proposed leg mechanism are formulated for a computer oriented simulation. Simulation results show the operation performance of the proposed leg mechanism with suitable characteristics. A parametric study has been carried out to evaluate the operation performance as function of design parameters. A prototype of a single DOF biped robot equipped with two proposed leg mechanisms has been built at LARM (Laboratory of Robotics and Mechatronics). Experimental test shows practical feasible walking ability of the prototype, as well as drawbacks are discussed for the mechanical design.
Recent advances in (soil moisture) triple collocation analysis
Gruber, A.; Su, C.-H.; Zwieback, S.; Crow, W.; Dorigo, W.; Wagner, W.
2016-03-01
To date, triple collocation (TC) analysis is one of the most important methods for the global-scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method. Different notations that are used to formulate the TC problem are shown to be mathematically identical. While many studies have investigated issues related to possible violations of the underlying assumptions, only few TC modifications have been proposed to mitigate the impact of these violations. Moreover, assumptions, which are often understood as a limitation that is unique to TC analysis are shown to be common also to other conventional performance metrics. Noteworthy advances in TC analysis have been made in the way error estimates are being presented by moving from the investigation of absolute error variance estimates to the investigation of signal-to-noise ratio (SNR) metrics. Here we review existing error presentations and propose the combined investigation of the SNR (expressed in logarithmic units), the unscaled error variances, and the soil moisture sensitivities of the data sets as an optimal strategy for the evaluation of remotely-sensed soil moisture data sets.
Szatmári, Daniel
2015-12-01
Disadvantages of the currently used Křovák's map projection in the Slovak Republic, such as large scale distortion, became evident after the division of Czechoslovakia. The aim of this paper is to show the results of the optimization of cartographic projections using Chebyshev's theorem for conformal projections and its application to the territory of the Slovak Republic. The calculus used, the scale distortions achieved and their comparison with the scale distortions of currently used map projections will be demonstrated.
MAPPING LANDSLIDES IN LUNAR IMPACT CRATERS USING CHEBYSHEV POLYNOMIALS AND DEM’S
Directory of Open Access Journals (Sweden)
V. Yordanov
2016-06-01
Full Text Available Geological slope failure processes have been observed on the Moon surface for decades, nevertheless a detailed and exhaustive lunar landslide inventory has not been produced yet. For a preliminary survey, WAC images and DEM maps from LROC at 100 m/pixels have been exploited in combination with the criteria applied by Brunetti et al. (2015 to detect the landslides. These criteria are based on the visual analysis of optical images to recognize mass wasting features. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sections in order to obtain a parametric characterization useful for classification into different morphological shapes. Here a new implementation of Chebyshev polynomial approximation is proposed, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analyzing the absolute values off odd coefficients of estimated Chebyshev polynomials. A case study on the Cassini A crater has demonstrated the key-points of the proposed methodology and outlined the required future development to carry out.
Mapping Landslides in Lunar Impact Craters Using Chebyshev Polynomials and Dem's
Yordanov, V.; Scaioni, M.; Brunetti, M. T.; Melis, M. T.; Zinzi, A.; Giommi, P.
2016-06-01
Geological slope failure processes have been observed on the Moon surface for decades, nevertheless a detailed and exhaustive lunar landslide inventory has not been produced yet. For a preliminary survey, WAC images and DEM maps from LROC at 100 m/pixels have been exploited in combination with the criteria applied by Brunetti et al. (2015) to detect the landslides. These criteria are based on the visual analysis of optical images to recognize mass wasting features. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sections in order to obtain a parametric characterization useful for classification into different morphological shapes. Here a new implementation of Chebyshev polynomial approximation is proposed, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analyzing the absolute values off odd coefficients of estimated Chebyshev polynomials. A case study on the Cassini A crater has demonstrated the key-points of the proposed methodology and outlined the required future development to carry out.
The Fundamental Blossoming Inequality in Chebyshev Spaces—I: Applications to Schur Functions
Ait-Haddou, Rachid
2016-10-19
A classical theorem by Chebyshev says how to obtain the minimum and maximum values of a symmetric multiaffine function of n variables with a prescribed sum. We show that, given two functions in an Extended Chebyshev space good for design, a similar result can be stated for the minimum and maximum values of the blossom of the first function with a prescribed value for the blossom of the second one. We give a simple geometric condition on the control polygon of the planar parametric curve defined by the pair of functions ensuring the uniqueness of the solution to the corresponding optimization problem. This provides us with a fundamental blossoming inequality associated with each Extended Chebyshev space good for design. This inequality proves to be a very powerful tool to derive many classical or new interesting inequalities. For instance, applied to Müntz spaces and to rational Müntz spaces, it provides us with new inequalities involving Schur functions which generalize the classical MacLaurin’s and Newton’s inequalities. This work definitely demonstrates that, via blossoms, CAGD techniques can have important implications in other mathematical domains, e.g., combinatorics.
Chinese EFL Teachers' Attitudes toward Corpus Use in Collocation Instruction
Institute of Scientific and Technical Information of China (English)
郭敏
2014-01-01
The purpose of the present study was to investigate Chinese EFL (English as a Foreign Language) teachers ’attitudes to-ward corpus use in collocation instruction. Fourteen Chinese EFL teachers from seven different colleges or universities answered a questionnaire asking their perceptions about corpus use in collocation instruction. The statistical analysis revealed that significant difference (t=2.449, df.=9, p=.037<0.1) was found between males and females in their perception of the learnability of the search-ing technique in collocation corpus. Besides, the result also revealed that significant differences were found between novice and experienced teachers’perception of helpfulness of corpus in writing native-like sentences (t=5.75, df=11, p<0.1), identifying col-location errors in English (t=5.75, df=11, p<0.1), usefulness of corpus in searching for English collocations (t=2.93, df=12, p<0.1), and advocacy of corpus to colleagues(t=5.75, df=11, p<0.1). Finally, some pedagogical implications were put forward.
Chen, Weitian; Sica, Christopher T.; Meyer, Craig H.
2008-01-01
Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method. PMID:18956462
A nodal collocation approximation for the multidimensional P{sub L} equations
Energy Technology Data Exchange (ETDEWEB)
Capilla, M.; Talavera, C.F.; Ginestar, D. [Departamento de Matematica Aplicada. Universidad Politecnica de Valencia. Camino de Vera 14. E-46022 Valencia (Spain); Verdu, G. [Departamento de Ingenieria Quimica y Nuclear. Universidad Politecnica de Valencia. Camino de Vera 14, E-46022 Valencia (Spain)
2008-07-01
We develop a nodal collocation method for the P{sub L} equations, focusing on the eigenvalue problem known as the Lambda Modes transport problem. This method approximates the initial differential eigenvalue problem by a generalized algebraic eigenvalue problem, from which the k-effective and the stationary neutron flux distribution of the system can be computed, being able also to obtain the subcritical eigenvalues and their corresponding Eigenmodes. The method presented here generalizes the method for 1D geometries presented in a previous work to be able to treat multidimensional problems. (authors)
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
STRESS INTENSITY FACTORS FOR A FINITE PLATE WITH AN INCLINED CRACK BY BOUNDARY COLLOCATION
Institute of Scientific and Technical Information of China (English)
Xing Li; Xuemei You
2005-01-01
In this paper, we combine the Muskhelishvili's complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface,the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ (the obliquity of crack) on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.
Gablasova, Dana; Brezina, Vaclav; McEnery, Tony
2017-01-01
This article focuses on the use of collocations in language learning research (LLR). Collocations, as units of formulaic language, are becoming prominent in our understanding of language learning and use; however, while the number of corpus-based LLR studies of collocations is growing, there is still a need for a deeper understanding of factors…
Redefining Creativity--Analyzing Definitions, Collocations, and Consequences
Kampylis, Panagiotis G.; Valtanen, Juri
2010-01-01
How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,…
Automatic collocation extraction based on quintuple%基于五元组的词语搭配自动抽取
Institute of Scientific and Technical Information of China (English)
孙婷婷
2015-01-01
Collocation plays an important role in the field of linguistics. In recent years, it has become one of the major research directions in natural language processing. In order to realize the automatic extraction of collocations, the definitions of semantic collocation and syntactic collocation are given in this paper. For these two types of collocation, a quintuple-based collocation extraction method is also presented. Through the experiment based on statistics, it indicates that this method is advantageous to the collocation extraction. And among these statistics, mutual information is the best, the accuracy rate can go up to 80%.%词语搭配在语言学领域占有重要的地位，近年来，它已成为自然语言处理研究的重点方向之一。为了实现词语搭配的自动抽取，本文给出了语义搭配和句式搭配的定义，并针对这两类搭配，给出了一种基于五元组的词语搭配抽取方法。通过基于统计量的搭配提取实验，得出此方法有利于词语搭配的自动抽取。其中，基于互信息的搭配抽取效果最好，其准确率可达80%。
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
On Bernstein type inequalities and a weighted Chebyshev approximation problem on ellipses
Freund, Roland
1989-01-01
A classical inequality due to Bernstein which estimates the norm of polynomials on any given ellipse in terms of their norm on any smaller ellipse with the same foci is examined. For the uniform and a certain weighted uniform norm, and for the case that the two ellipses are not too close, sharp estimates of this type were derived and the corresponding extremal polynomials were determined. These Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Some new results were also presented for a weighted approximation problem of this type.
Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol
Directory of Open Access Journals (Sweden)
Hong Lai
2012-01-01
Full Text Available We apply semigroup property of enhanced Chebyshev polynomials to present an anonymous authentication protocol. This paper aims at improving security and reducing computational and storage overhead. The proposed scheme not only has much lower computational complexity and cost in the initialization phase but also allows the users to choose their passwords freely. Moreover, it can provide revocation of lost or stolen smart card, which can resist man-in-the-middle attack and off-line dictionary attack together with various known attacks.
Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials
Faustino, Nelson
2016-01-01
The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of solutions. The development of a well-adapted discrete Clifford calculus framework based on spinor fields allows us to represent, using solely projection based arguments, the solutions for the discretized Dirac equations from the knowledge of the solutions of the discretized Klein-Gordon equation. Implications of those findings on the interpretation of the lattice fermion doubling problem is briefly discussed.
Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map
2014-01-01
We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10113 key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970
Leonardi, Magda
1977-01-01
Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in both languages. (Text is in…
Leonardi, Magda
1977-01-01
Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in…
Leonardi, Magda
1977-01-01
Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in…
Gates, Robert L
2015-01-01
This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic collocation method (ALSGC) with a hierarchy of successively finer spatial discretizations (e.g. finite elements) of the underlying deterministic problem. To achieve this, we build strongly upon ideas from the Multilevel Monte Carlo method (MLMC), which represents a well-established technique for the reduction of computational complexity in problems affected by both deterministic and stochastic error contributions. The resulting approach is termed the Multilevel Adaptive Sparse Grid Collocation (MLASGC) method. Preliminary results for a low-dimensional, non-smooth parametric ODE problem are promising: the proposed MLASGC method exhibits an error/cost-relation of $\\varepsilon \\sim t^{-0.95}$ and therefore significantly outperforms the single-level ALSGC ($\\varepsilon \\sim t^{-0.65}$) a...
Simulations using meshfree methods
P, Kirana Kumara
2015-01-01
In this paper, attempt is made to solve a few problems using the Polynomial Point Collocation Method (PPCM), the Radial Point Collocation Method (RPCM), Smoothed Particle Hydrodynamics (SPH), and the Finite Point Method (FPM). A few observations on the accuracy of these methods are recorded. All the simulations in this paper are three dimensional linear elastostatic simulations, without accounting for body forces.
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
Beck, J.
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.
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo; Rodriguez, Martin [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M, E-mail: paolo.amore@gmail.com, E-mail: martinalexander.rv@gmail.com, E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2011-04-15
We show that some of the conclusions drawn recently about the performance and convergence of the little sinc functions collocation method are misleading. To this end, we prove the convergence of the method and recalculate the ground-state energy for the Pullen-Edmonds Hamiltonian. In addition, we show the results for another nonseparable Hamiltonian operator with a somewhat more complicated potential-energy function. (comment)
Teaching vocabulary using collocations versus using definitions in EFL classes
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...
Variational collocation for systems of coupled anharmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2010-04-15
By means of a collocation approach based on little sinc functions (LSF), we obtain accurate eigenvalues and eigenfunctions of the stationary Schroedinger equation for systems of coupled oscillators. Adjustable parameters introduced by means of scaling and rotation of the coordinates improve the rate of convergence of the approach. A careful comparison with the results published earlier by other authors shows the advantages of the present approach.
Yamaleev, Nail K.; Carpenter, Mark H.
2017-02-01
High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO) finite volume or weak-form finite element methods. Herein, a new family of fourth-order WENO spectral collocation schemes is developed, that are nonlinearly entropy stable for the one-dimensional compressible Navier-Stokes equations. Individual spectral elements are coupled using penalty type interface conditions. The resulting entropy stable WENO spectral collocation scheme achieves design order accuracy, maintains the WENO stencil biasing properties across element interfaces, and satisfies the summation-by-parts (SBP) operator convention, thereby ensuring nonlinear entropy stability in a diagonal norm. Numerical results demonstrating accuracy and nonoscillatory properties of the new scheme are presented for the one-dimensional Euler and Navier-Stokes equations for both continuous and discontinuous compressible flows.
CSIR Research Space (South Africa)
Sokoya, O
2008-05-01
Full Text Available The performance analysis of high rate space–time trellis-coded modulation (HR-STTCM) using the Gauss–Chebyshev quadrature technique is presented. HR-STTCM is an example of space–time codes that combine the idea used in trellis coded modulation (TCM...
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.
Airfoil Analysis with Uncertain Geometry using the Probabilistic Collocation method
Loeven, G.J.A.; Bijl, H.
2008-01-01
Due to manufacturing tolerances, the airfoil of a wing after production is never exactly the same as the designed airfoil. Also during operation the geometry may change due to aerodynamic loading, icing or wear of the construction. The geometry can, therefore, be treated as uncertain. Uncertainties
Institute of Scientific and Technical Information of China (English)
沈雪峰; 高成发; 潘树国
2011-01-01
传统的BP神经网络在GPS高程异常拟合应用有其一定的局限性,特别是在对于外推高程异常值方面,传统的BP神经网络的不足表现得尤为明显.针对高程异常的特性,既有趋势性也有随机性,结合BP神经网络的优点,提出一种改进型的BP神经网络高程异常拟合方法,利用最小二乘配置法综合考虑高程异常的趋势性和随机性的特点,采用BP神经网络方法对包括最小二乘配置法的模型误差的综合误差进行优化减弱,最后可得到新的高程异常.通过实例,将文中提出的新方法与曲面拟合法以及传统BP神经网络拟合法在内插和外推2方面进行比较分析,结果表明文中提出的新方法拟合效果最佳.%Traditional BP neural network has its limitations in the application of fitting GPS height anoma ly. Especially in regard to extrapolate the value of height anomaly, the lack of traditional BP neural net work has been particularly evident. Because of the characteristics of height anomaly, which has tendency and randomicity, combined with the advantages of BP neural network, an improved BP neural network height anomaly fitting method is presented in this paper. Least squares collocation method for comprehen sive consideration the tendency and randomicity of height anomaly is used and then get a new height anom aly by BP neural network fitting height anomaly errors. The new method presented in the paper has been demonstrated that the accuracy of this fitting model is better than surface fitting mode and traditional BP neural network fitting mode through comparative analysis in interpolation and extrapolation.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The design and analysis of special type beamformer, the Butler matrix, to achieve orthogonal beamforming networks is presented in this paper. A 4×4 microstrip planar array antenna is assumed to simulate a 4×4 Butler matrix to demonstrate orthogonal beamforming and beam steering. The dimensions of rectangular patches in the planar array are chosen according to the Dolph-Chebyshev current distribution in order to minimize the side-lobe level ratio for a given value of beamwidth. The simulations are carried out using an antenna design and analysis software PCAAD. It is shown that orthogonal beams can be formed to cover about 163° angle with a constant beam crossover level and high directivity.
Lim, Wei Jer; Neoh, Siew Chin; Norizan, Mohd Natashah; Mohamad, Ili Salwani
2015-05-01
Optimization for complex circuit design often requires large amount of manpower and computational resources. In order to optimize circuit performance, it is critical not only for circuit designers to adjust the component value but also to fulfill objectives such as gain, cutoff frequency, ripple and etc. This paper proposes Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize a ninth order multiple feedback Chebyshev low pass filter. Multi-objective Pareto-Based optimization is involved whereby the research aims to obtain the best trade-off for minimizing the pass-band ripple, maximizing the output gain and achieving the targeted cut-off frequency. The developed NSGA-II algorithm is executed on the NGSPICE circuit simulator to assess the filter performance. Overall results show satisfactory in the achievements of the required design specifications.
Energy Technology Data Exchange (ETDEWEB)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
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 "curse of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF could be even more computationally expensive than EnKF. Motivated by most recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to eliminate the inconsistency between model parameters and states. The performance of RAPCKF is tested with numerical cases of unsaturated flow models. 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.
Directory of Open Access Journals (Sweden)
Déogratias Nizonkiza
2012-10-01
Full Text Available The present study explores the relationship between controlled productive knowledge of collocations and L2 proficiency, the role of frequency in controlled productive knowledge of collocations, and the quantifiability of controlled productive collocational knowledge growth alongside L2 proficiency and word frequency levels. A proficiency measure and a productive collocation test modelled on Laufer and Nation (1999 were presented to Belgian and Burundian English majors. The results show that scores on both tests distinguish between proficiency levels and, furthermore, highly correlate. This suggests that controlled productive knowledge of collocations develops as proficiency increases, supporting earlier studies (Boers, Eyckmans, Kappel, Stengers, & Demecheleer, 2006; Bonk, 2001; Eyckmans, Boers, & Demecheleer, 2004; Gitsaki, 1999 that had established a relationship between collocational knowledge and L2 proficiency. The results also show that the more frequent the collocations, the better they are known, which highlights the crucial role played by frequency in knowing words (Nation & Beglar, 2007. Furthermore, the number of collocations added can be quantified and we observe moderat egains at beginner and advanced levels, and impressive gains at intermediate levels. This supports and extends Laufer’s (1998 and Zhong and Hirsh’s (2009 findings and lays basic ground work for teaching collocations, the amount of which should increase with proficiency levels.
Benchmarking the Collocation Stand-Alone Library and Toolkit (CSALT)
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.
Ray, Sudipta; Saha, Sandeep
2016-11-01
Numerical solution of engineering problems with interfacial discontinuities requires exact implementation of the jump conditions else the accuracy deteriorates significantly; particularly, achieving spectral accuracy has been limited due to complex interface geometry and Gibbs phenomenon. We adopt a novel implementation of the immersed-interface method that satisfies the jump conditions at the interfaces exactly, in conjunction with the Chebyshev-collocation method. We consider solutions to linear second order ordinary and partial differential equations having a discontinuity in their zeroth and first derivatives across an interface traced by a complex curve. The solutions obtained demonstrate the ability of the proposed method to achieve spectral accuracy for discontinuous solutions across tortuous interfaces. The solution methodology is illustrated using two model problems: (i) an ordinary differential equation with jump conditions forced by an infinitely differentiable function, (ii) Poisson's equation having a discontinuous solution across interfaces that are ellipses of varying aspect ratio. The use of more polynomials in the direction of the major axis than the minor axis of the ellipse increases the convergence rate of the solution.
Verb-Noun Collocations in Written Discourse of Iranian EFL Learners
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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. Keywords: Language proficiency, Verb-noun collocation, Witten discourse, Iranian EFL learners
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.
Gimme Context – towards New Domain-Specific Collocational Dictionaries
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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.
Study on the Causes and Countermeasures of the Lexical Collocation Mistakes in College English
Yan, Hansheng
2010-01-01
The lexical collocation in English is an important content in the linguistics theory, and also a research topic which is more and more emphasized in English teaching practice of China. The collocation ability of English decides whether learners could masterly use real English in effective communication. In many years' English teaching practice,…
A Corpus-based Analysis of Noun-verb Collocation of Knowledge
Institute of Scientific and Technical Information of China (English)
LIU Ting-ting
2016-01-01
Corpus-based analysis is adopted to study the acceptable noun-verb collocation of the word knowledge. Verbs like ac-quire, have etc. are found to be frequently collocate with knowledge, and the Chinese students’favorite patterns like learn knowledge, enlarge knowledge are not acceptable. The finding may encourage teachers to consider about the pedagogical value of corpus while teaching languages.
Collocation, Semantic Prosody, and Near Synonymy: A Cross-Linguistic Perspective
Xiao, Richard; McEnery, Tony
2006-01-01
This paper explores the collocational behaviour and semantic prosody of near synonyms from a cross-linguistic perspective. The importance of these concepts to language learning is well recognized. Yet while collocation and semantic prosody have recently attracted much interest from researchers studying the English language, there has been little…
Corpora and Collocations in Chinese-English Dictionaries for Chinese Users
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…
Cross-Linguistic Influence: Its Impact on L2 English Collocation Production
Phoocharoensil, Supakorn
2013-01-01
This research study investigated the influence of learners' mother tongue on their acquisition of English collocations. Having drawn the linguistic data from two groups of Thai EFL learners differing in English proficiency level, the researcher found that the native language (L1) plays a significant role in the participants' collocation learning…
Not Just "Small Potatoes": Knowledge of the Idiomatic Meanings of Collocations
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…
English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information
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…
基于Chebyshev的概率公钥密码体制%Probabilistic public-key cryptosystem based on Chebyshev
Institute of Scientific and Technical Information of China (English)
程学海; 徐江峰
2013-01-01
This paper introduced the definition and the properties of Chebyshev polynomial.According to the deterministic public-key cryptosystem of Chebyshev polynomial,found that it couldn't resist chosen cipher-text attacks.Combining with the security model against chosen cipher-text attacks,this paper proposed the probabilistic public-key cryptosystem of Chebyshev polynomial.The analysis show that the proposed cryptosystem is correct.Through the result of the reduction proof,the proposed cryptosystem can resist the adaptive chosen cipher-text attacks and has the IND-CCA2 security.%介绍了Chebyshev多项式的定义和相关性质,针对确定性Chebyshev多项式公钥密码体制进行了研究,发现其不能抵抗选择密文攻击.结合抵抗选择密文攻击的安全模型,提出了基于有限域的Chebyshev多项式的概率公钥密码体制,分析结果表明该密码体制是正确的.通过归约证明,该密码体制能够抵挡适应性选择密文攻击,具有抵抗选择密文攻击的IND-CCA2安全性.
APPLICATION OF FEA TO THE COLLOCATION OF ACTUATOR/SENSOR IN THE INTELLIGENT STRUCTURES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The piezothermoelectric actuator/sensor collocation for advanced intelligent structure is studied. The quasi-static equations of piezothermoelasticity are used to analyze the coupling effects between the displacement, temperature and electric fields of piezothermoelasticity continua and the governing equations for piezothermoelectric continua are derived to discuss the effects of coupling factors on the control/sensing performance in intelligent structure. Based on those analyses,a finite element analysis model of distributed piezothermoelectric continua is developed later. The thermal stress and deformation of a beam are calculated by FEA method so as to determine the optimal actuator/sensor placement. Based on the results of the optimal analysis procedure of actuator/sensor placement, some conclusions of actuator/sensor placement are obtained. Thus, the optimal actuator/sensor placement for piezothermoelectric intelligent structure can be found from the actuator/sensor placements available so that intelligent system will have the best controllability and observability.
Power-scalable video encoder for mobile devices based on collocated motion estimation
Jung, Joel; Bourge, Arnaud
2004-01-01
In this paper, a method for designing low-power video schemes is presented. Algorithms that imply a very low dissipation are required for new applications where the energy source is limited, e.g. mobile phones including a camera and video features. Whereas it can be observed that video standards are mainly designed around coding efficiency, we propose to take into account power consumption characteristics directly when designing the algorithm. More precisely, we give some guidelines for the design of low-power video codecs in the scope of modern hardware architectures and we introduce the notion of power scalability. We present an original encoder based on so-called 'Collocated Motion Estimation' designed using the proposed methodology. Experimental results show that we remain close to the coding efficiency of the reference H.264 baseline encoder while the power consumption is largely reduced in our solution. Moreoever this encoder is scalable in memory transfer and computational complexity.
Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
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.
Energy Technology Data Exchange (ETDEWEB)
Singh, Sandeep; Shukla, K. K. [Motilal Nehru National Institute of Technology, Allahabad (India); Shingh, Jeeoot [Department of Mechanical Engineering, Birla Institute of Technology Mesra, Ranchi (India)
2013-02-15
Meshless collocations utilizing Gaussian and Multi quadric radial basis functions for the stability analysis of orthotropic and cross ply laminated composite plates subjected to thermal and mechanical loading are presented. The governing differential equations of plate are based on higher order shear deformation theory considering two different transverse shear stress functions. The plate governing differential equations are discretized using radial basis functions to cast a set of simultaneous equations. The convergence of both radial basis functions is studied for different values of shape parameters. Several numerical examples are undertaken to demonstrate the accuracy of present method and the effects of orthotropy ratio of the material, span to thickness ratio of the plate, and fiber orientation on critical load/temperature are also presented.
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
Cagnone, J. S.; Nadarajah, S. K.
2012-02-01
This paper presents a procedure for adaptive polynomial refinement in the context of the lifting collocation penalty (LCP) formulation. The LCP scheme is a high-order unstructured discretization method unifying the discontinuous Galerkin, spectral volume, and spectral difference schemes in single differential formulation. Due to the differential nature of the scheme, the treatment of inter-cell fluxes for spatially varying polynomial approximations is not straightforward. Specially designed elements are proposed to tackle non-conforming polynomial approximations. These elements are constructed such that a conforming interface between polynomial approximations of different degrees is recovered. The stability and conservation properties of the scheme are analyzed and various inviscid compressible flow calculations are performed to demonstrate the potential of the proposed approach.
Implementation of an efficient segregated algorithm IDEAL on 3D collocated grid system
Institute of Scientific and Technical Information of China (English)
SUN DongLiang; QU ZhiGuo; HE YaLing; Tao WenQuan
2009-01-01
The segregated algorithm-IDEAL (inner doubly-iterative efficient algorithm for linked-equations) is an efficient and stable algorithm. In this algorithm, there exist inner doubly-iterative processes for pressure equation, which almost completely overcome two approximations in SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of iteration process. In this paper, implementation of the IDEAL algorithm on a 3D collocated grid system is conducted. The interface velocity is calculated by the modified momentum interpolation method (MMIM), by which the converged result is independent of the under-relaxation factor. Finally, five three-dimensional incompressible fluid flow and heat transfer problems are provided to compare the convergence rate and robustness between the IDEAL and three other most widely-used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison it can be concluded that the IDEAL algorithm is more robust and efficient than the three other algorithms.
Mannoni, A; Flesia, C; Bruscaglioni, P; Ismaelli, A
1996-12-20
Lidar measurements are often interpreted on the basis of two fundamental assumptions: absence of multiple scattering and sphericity of the particles that make up the diffusing medium. There are situations in which neither holds true. We focus our interest on multiply-scattered returns from homogeneous layers of monodisperse, randomly oriented, axisymmetric nonspherical particles. T(2) Chebyshev particles have been chosen and their single-scattering properties have been reviewed. A Monte Carlo procedure has been employed to calculate the backscattered signal for several fields of view. Comparisons with the case of scattering from equivalent (equal-volume) spheres have been carried out (narrow polydispersions have been used to smooth the phase functions' oscillations). Our numerical effort highlights a considerable variability in the intensity of the multiply-scattered signal, which is a consequence of the strong dependence of the backscattering cross section on deformation of the particles. Even more striking effects have been noted for depolarization; peculiar behavior was observed at moderate optical depths when particles characterized by a large backscattering depolarization ratio were employed in our simulations. The sensitivity of depolarization to even small departures from sphericity, in spite of random orientation of the particles, has been confirmed. The results obtained with the Monte Carlo codes have been successfully checked with an analytical formula for double scattering.
Energy Technology Data Exchange (ETDEWEB)
Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang
2010-09-01
This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.
Local validation of EU-DEM using Least Squares Collocation
Ampatzidis, Dimitrios; Mouratidis, Antonios; Gruber, Christian; Kampouris, Vassilios
2016-04-01
In the present study we are dealing with the evaluation of the European Digital Elevation Model (EU-DEM) in a limited area, covering few kilometers. We compare EU-DEM derived vertical information against orthometric heights obtained by classical trigonometric leveling for an area located in Northern Greece. We apply several statistical tests and we initially fit a surface model, in order to quantify the existing biases and outliers. Finally, we implement a methodology for orthometric heights prognosis, using the Least Squares Collocation for the remaining residuals of the first step (after the fitted surface application). Our results, taking into account cross validation points, reveal a local consistency between EU-DEM and official heights, which is better than 1.4 meters.
On the interpretation of least squares collocation. [for geodetic data reduction
Tapley, B. D.
1976-01-01
A demonstration is given of the strict mathematical equivalence between the least squares collocation and the classical minimum variance estimates. It is shown that the least squares collocation algorithms are a special case of the modified minimum variance estimates. The computational efficiency of several forms of the general minimum variance estimation algorithm is discussed. It is pointed out that for certain geodetic applications the least square collocation algorithm may provide a more efficient formulation of the results from the point of view of the computations required.
Stenroos, Matti; Haueisen, Jens
2008-09-01
In electrocardiographic imaging, epicardial potentials are reconstructed computationally from electrocardiographic measurements. The reconstruction is typically done with the help of the boundary element method (BEM), using the point collocation weighting and constant or linear basis functions. In this paper, we evaluated the performance of constant and linear point collocation and Galerkin BEMs in the epicardial potential problem. The integral equations and discretizations were formulated in terms of the single- and double-layer operators. All inner element integrals were calculated analytically. The computational methods were validated against analytical solutions in a simplified geometry. On the basis of the validation, no method was optimal in all testing scenarios. In the forward computation of the epicardial potential, the linear Galerkin (LG) method produced the smallest errors. The LG method also produced the smallest discretization error on the epicardial surface. In the inverse computation of epicardial potential, the electrode-specific transfer matrix performed better than the full transfer matrix. The Tikhonov 2 regularization outperformed the Tikhonov 0. In the optimal modeling conditions, the best BEM technique depended on electrode positions and chosen error measure. When large modeling errors such as omission of the lungs were present, the choice of the basis and weighting functions was not significant.
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.
Directory of Open Access Journals (Sweden)
Smith Simon J
1999-01-01
Full Text Available For a fixed integer and , let denote the th fundamental polynomial for Hermite–Fejér interpolation on the Chebyshev nodes . (So is the unique polynomial of degree at most which satisfies , and whose first derivatives vanish at each . In this paper it is established that It is also shown that is an increasing function of , and the best possible bound so that for all , and is obtained. The results generalise those for Lagrange interpolation, obtained by P. Erdős and G. Grünwald in 1938.
Takahasi, Hiroki
2016-09-01
It is well-known that the geometric pressure function tin {{R}}mapsto sup _{μ }{ h_μ (T_2)-tint log |dT_2(x)|dμ (x)} of the Chebyshev quadratic map T_2(x)=1-2x^2 (xin {{R}}) is not differentiable at t=-1. We show that this phase transition can be "removed", by an arbitrarily small singular perturbation of the map T_2 into Hénon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to Hénon-like dynamics near the first bifurcation.
Xing, Yufei; Spina, Domenico; Li, Ang; Dhaene, Tom; Bogaerts, Wim
2016-05-01
Abstract Integrated photonics, and especially silicon photonics, has been rapidly expanded its catalog of building blocks and functionalities. Now, it is maturing fast towards circuit-level integration to serve more complex applications in industry. However, performance variability due to the fabrication process and operational conditions can limit the yield of large-scale circuits. It is essential to assess this impact at the design level with an efficient variability analysis: how variations in geometrical, electrical and optical parameters propagate into components performance. In particular when implementing wavelength-selective filters, many primary functional parameters are affected by fabrication-induced variability. The key functional parameters that we assess in this paper are the waveguide propagation constant (the effective index, essential to define the exact length of a delay line) and the coupling coefficients in coupling structure (necessary to set the power distribution over different delay lines). The Monte Carlo (MC) method is the standard method for variability analysis, thanks to its accuracy and easy implementation. However, due to its slow convergence, it requires a large set of samples (simulations or measurements), making it computationally or experimentally expensive. More efficient methods to assess such variability can be used, such as generalized polynomial chaos (gPC) expansion or stochastic collocation. In this paper, we demonstrate stochastic collocation (SC) as an efficient alternative to MC or gPC to characterize photonic devices under the effect of uncertainty. The idea of SC is to interpolate stochastic solutions in the random space by interpolation polynomials. After sampling the deterministic problem at a pre-defined set of nodes in random space, the interpolation is constructed. SC drastically reduces computation and measurement cost. Also, like MC method, sampling-based SC is easy to implement. Its computation cost can be
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.
2015-06-01
ER D C/ G SL T R- 15 -1 3 Field Jet Erosion Tests on the Mississippi River Collocated Demonstration Section, Plaquemines Parish...default. ERDC/GSL TR-15-13 June 2015 Field Jet Erosion Tests on the Mississippi River Collocated Demonstration Section, Plaquemines Parish...Prepared for U.S. Army Corps of Engineers Washington, DC 20314-1000 ERDC/GSL TR-15-13 ii Abstract Field jet erosion tests (JETs) were
Age of Acquisition Effects in Chinese EFL learners’ Delexicalized Verb and Collocation Acquisition
Miao Haiyan
2015-01-01
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 resp...
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.
Particle Choices and Collocation in Cameroon English Phrasal Verbs
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Napoleon Epoge
2016-02-01
Full Text Available The meaning of some phrasal verbs can be guessed from the meanings of the parts (to sit down = sit + down, run after = run + after and the meaning of some others have to be learned (to put up (a visitor = accommodate, to hold up = cause delay or try to rob someone due to their syntactic and semantic complexities. In this regard, the syntactic and semantic properties are expected to be the same in every English speaking context. Thus, this paper aims to explore the input-oriented syntactic and semantic properties of phrasal verbs in Cameroon English. Findings reveal that the syntactic property of some phrasal verbs undergoes innovative processes such as particle substitution (to round up a point, omission (to bite more than you can chew, and redundancy (to meet up with the requirements; while the semantic property undergoes the process of semantic extension (to came out with a pathetic story to justify ones absence from office; to come out with a wonderful strategy to curb corruption, and semantic shift (to put up with someone for one semester. This reveals that, in the New English context such as Cameroon, users resort to the domestication of the alien language as a functional and dominant paradigm to combat cultural imperialism and express new identity.Keywords: Cameroon English, collocation, particle, phrasal verb, semantics, syntax
Evaluating the performance of collocated optical disdrometers: LPM and PARSIVEL
Angulo-Martinez, Marta; Begueria, Santiago; Latorre, Borja
2017-04-01
Optical disdrometers are present weather sensors with the ability of providing integrate information of precipitation like intensity and reflectivity together with discrete information of drop sizes and velocities distribution (DSVD) of the hydrometeors crossing the laser beam sampling area. These sensors constitute a step forward in comparison with pluviometers towards a more complete characterisation of precipitation. Their use is spreading in many research fields for several applications. Understanding the differences from one another helps in the election of the sensor and point out limitations to be fixed in future versions. Four collocated optical disdrometers, two Laser Precipitation Monitors (LPM-Thies Clima) and two PARSIVEL, 1-minute measurements of 800 natural rainfall events were compared. Results showed a general agreement in integrated variables, like intensity or liquid water content. Nevertheless, comparing raw data, as the number of particles and DSVD, great differences were found. LPM generally measures more and smaller drops than PARSIVEL and this difference increases with rainfall intensity. These results may affect especially the reflectivity value every disdrometer provide. A complete description of the measurements obtained, quantifiying the differences is provided, indicating their possible sources.
Estimates of Mode-S EHS aircraft-derived wind observation errors using triple collocation
de Haan, Siebren
2016-08-01
Information on the accuracy of meteorological observation is essential to assess the applicability of the measurements. In general, accuracy information is difficult to obtain in operational situations, since the truth is unknown. One method to determine this accuracy is by comparison with the model equivalent of the observation. The advantage of this method is that all measured parameters can be evaluated, from 2 m temperature observation to satellite radiances. The drawback is that these comparisons also contain the (unknown) model error. By applying the so-called triple-collocation method , on two independent observations at the same location in space and time, combined with model output, and assuming uncorrelated observations, the three error variances can be estimated. This method is applied in this study to estimate wind observation errors from aircraft, obtained utilizing information from air traffic control surveillance radar with Selective Mode Enhanced Surveillance capabilities Mode-S EHS, see. Radial wind measurements from Doppler weather radar and wind vector measurements from sodar, together with equivalents from a non-hydrostatic numerical weather prediction model, are used to assess the accuracy of the Mode-S EHS wind observations. The Mode-S EHS wind (zonal and meridional) observation error is estimated to be less than 1.4 ± 0.1 m s-1 near the surface and around 1.1 ± 0.3 m s-1 at 500 hPa.
DEFF Research Database (Denmark)
Tscherning, Carl Christian
2015-01-01
The method of Least-Squares Collocation (LSC) may be used for the modeling of the anomalous gravity potential (T) and for the computation (prediction) of quantities related to T by a linear functional. Errors may also be estimated. However, when using an isotropic covariance function or equivalen...... on gravity anomalies (at 10 km altitude) predicted from GOCE Tzz. This has given an improved agreement between errors based on the differences between values derived from EGM2008 (to degree 512) and predicted gravity anomalies.......The method of Least-Squares Collocation (LSC) may be used for the modeling of the anomalous gravity potential (T) and for the computation (prediction) of quantities related to T by a linear functional. Errors may also be estimated. However, when using an isotropic covariance function or equivalent...... outside the data area. On the other hand, a comparison of predicted quantities with observed values show that the error also varies depending on the local data standard deviation. This quantity may be (and has been) estimated using the GOCE second order vertical derivative, Tzz, in the area covered...
Directory of Open Access Journals (Sweden)
A.K. Parida
2016-09-01
Full Text Available In this paper Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system is presented for the prediction and analysis of financial and electrical energy market data. The normally used TSK-type feedforward fuzzy neural network is unable to take the full advantage of the use of the linear fuzzy rule base in accurate input–output mapping and hence the consequent part of the rule base is made nonlinear using polynomial or arithmetic basis functions. Further the Chebyshev polynomial functions provide an expanded nonlinear transformation to the input space thereby increasing its dimension for capturing the nonlinearities and chaotic variations in financial or energy market data streams. Also the locally recurrent neuro-fuzzy information system (LRNFIS includes feedback loops both at the firing strength layer and the output layer to allow signal flow both in forward and backward directions, thereby making the LRNFIS mimic a dynamic system that provides fast convergence and accuracy in predicting time series fluctuations. Instead of using forward and backward least mean square (FBLMS learning algorithm, an improved Firefly-Harmony search (IFFHS learning algorithm is used to estimate the parameters of the consequent part and feedback loop parameters for better stability and convergence. Several real world financial and energy market time series databases are used for performance validation of the proposed LRNFIS model.
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
De Groote, Friedl; Kinney, Allison L; Rao, Anil V; Fregly, Benjamin J
2016-10-01
Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.
Using the Corpus to Research the Collocations of Go in SEFC Textbooks%利用语料库调查SEFC教材中动词GO的搭配
Institute of Scientific and Technical Information of China (English)
李庭国
2012-01-01
Using the corpus-based method to research the collocations of GO in SEFC textbooks.The statistic data shows that there are three main collocation patterns of GO in the textbooks： GO＋ prep.,GO ＋adv.and GO＋n.%利用语料库的研究方法,通过检索软件AntConc 3.2.0w调查SEFC教材中动词GO的搭配。调查结果表明在SEFC这套教材中动词GO主要有三种搭配范式分别是：GO＋介词、GO＋副词和GO＋名词。
Identical appended series of points as invariants in the collocal general-colinear fields
Directory of Open Access Journals (Sweden)
Krasić Sonja
2003-01-01
Full Text Available In order to bring the collocal collinear fields from the general into the perspective position, it is required to determine the identical appended series of points. Because of the properties depending on the projectivity that is given by the four appended points (straight lines the appended identical series of the points and types are ranked among the invariants of general-collinear and perspectively-collinear fields. The procedure of determination of appended identical series of points is comprised of the following: in the set of ∞1 of perspectively similar series in one field (whose center of perspective is a point on the vanishing line, find those that are identical to all the series in the set ∞1 of perspective identical series of points in the other field (whose center of perspective is the point on the infinitely distant straight line. In the procedure, one begins from the appended similar methods obtained by the general method. The procedure is simplified by the introduction of the specially given similar series of points.
A nodal collocation approximation for the multi-dimensional P{sub L} equations - 2D applications
Energy Technology Data Exchange (ETDEWEB)
Capilla, M. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)], E-mail: tcapilla@mat.upv.es; Talavera, C.F. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)], E-mail: talavera@mat.upv.es; Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)], E-mail: dginesta@mat.upv.es; Verdu, G. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)], E-mail: gverdu@iqn.upv.es
2008-10-15
A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P{sub L} equations. In this work, the derivation of the P{sub 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.
Energy Technology Data Exchange (ETDEWEB)
Radecki, Peter P [Los Alamos National Laboratory; Farinholt, Kevin M [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory; Bement, Matthew T [Los Alamos National Laboratory
2008-01-01
The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.
Ozer, Ekin; Feng, Dongming; Feng, Maria Q.
2017-10-01
State-of-the-art multisensory technologies and heterogeneous sensor networks propose a wide range of response measurement opportunities for structural health monitoring (SHM). Measuring and fusing different physical quantities in terms of structural vibrations can provide alternative acquisition methods and improve the quality of the modal testing results. In this study, a recently introduced SHM concept, SHM with smartphones, is focused to utilize multisensory smartphone features for a hybridized structural vibration response measurement framework. Based on vibration testing of a small-scale multistory laboratory model, displacement and acceleration responses are monitored using two different smartphone sensors, an embedded camera and accelerometer, respectively. Double-integration or differentiation among different measurement types is performed to combine multisensory measurements on a comparative basis. In addition, distributed sensor signals from collocated devices are processed for modal identification, and performance of smartphone-based sensing platforms are tested under different configuration scenarios and heterogeneity levels. The results of these tests show a novel and successful implementation of a hybrid motion sensing platform through multiple sensor type and device integration. Despite the heterogeneity of motion data obtained from different smartphone devices and technologies, it is shown that multisensory response measurements can be blended for experimental modal analysis. Getting benefit from the accessibility of smartphone technology, similar smartphone-based dynamic testing methodologies can provide innovative SHM solutions with mobile, programmable, and cost-free interfaces.
A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation
Rieser, Daniel; Mayer-Guerr, Torsten
2014-05-01
The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.
Institute of Scientific and Technical Information of China (English)
袁江南
2016-01-01
In this paper, Chebyshev polynomials were drawn into the design of digital predistorters. The recursion generation character was exploited and a generation method of odd even order separation presented, which avoids high order power operations and saves resources. Simulation shows that the effects and convergence performances of Chebyshev polynomials predistorter are superior to that of common and orthogonal polynomials now available. The design is implemented in field⁃programmable gate array ( FPGA ) . Fix point simulation shows that the predistorter can effectively suppress out⁃band spectrum leakages. Its adjacent channel leakage radio( ACLR) performance is about 5~10 dB superior to that of memory polynomials.%将切比雪夫多项式引入到数字预失真器的设计中，利用其特有的递归生成特性，提出了一种奇偶阶分离的生成方法，避免了高阶幂次操作并节约了资源。仿真表明，切比雪夫多项式预失真器的效果和收敛性能均优于现有的普通以及正交多项式。在现场可编程门阵列（ field⁃programmable gate array， FPGA）上实现了设计，经过定点仿真验证，所设计的预失真器可以有效地抑制带外频谱泄漏，邻道泄漏比（ adjacent channel leakage radio， ACLR ）比普通记忆多项式有5～10 dB的提升。
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.
Institute of Scientific and Technical Information of China (English)
DONG Zhao-feng
2016-01-01
As for the English lexical collocation, there has been a great amount of researches conducted by Chinese and foreign scholars. However, less people has offered the explanation in allusion to the collocation which isn’t confined to the grammatical domain. Therefore, the thesis aims to depart from the research of the grammatical unaccountability of the lexical collocation to deeply investigate the reason of it from the point view of etymology, semantics, pragmatics and cultural category by taking“fe-male secretary”as an example. In addition, the thesis intends to search for an effective learning way to help learners improve their learning efficiency and use the English lexicon correctly as a native speaker.
Hageman, Louis A
2004-01-01
This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Assuming minimal mathematical background, it profiles the relative merits of several general iterative procedures. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a "red/black" block form, adaptive computational algorithms for the successive overrelaxation (SOR) method, and comp
Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin
2008-01-01
Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation…
Krummes, Cedric; Ensslin, Astrid
2015-01-01
Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…
Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity
Haji Ali, Abdul Lateef
2016-08-26
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM
Willberg, Martin; Lieb, Verena; Pail, Roland; Schmidt, Michael
2017-04-01
The analysis of the Earth's gravity field plays an important role in various disciplines of geosciences. While modern satellite gravity missions make it possible to define a globally consistent geoid with centimeter accuracy and a spatial resolution of 80-100km, it stays a major challenge to consistently combine global low-resolution data with regional high-resolution gravity information. Therefore, a variety of different regional gravity field modelling methods have been established during the last decades. In our analysis, we investigate the spectral combination of heterogeneous gravity data within two different calculation methods: First, the statistical approach of Least Squares Collocation (LSC) which uses the covariance information of input and output data to result in a full variance-covariance matrix. Second, the Multi-Resolution Representation (MRR) based on spherical radial basis functions. The MRR combines a low-pass filtered global geopotential model with satellite gradiometer and/or terrestrial gravity data by means of band-pass filtering. We examine the theoretical concepts and the computational differences and similarities between both approaches. Through fast changing topography, mountains as well as oceanic regions, our study area in the South American Andes is challenging and perfectly suitable for this examination. The use of synthetic data in closed-loop tests enables us to a very detailed investigation of predicted and actual accuracies of geoid determination. Furthermore, we point out respective advantages and disadvantages and link them to the calculation concepts of the two methods. The results contribute to the project "Optimally combined regional geoid models for the realization of height systems in developing countries (ORG4heights)" and, thus, aim to finally integrate the regional solutions into a global vertical reference frame.
Institute of Scientific and Technical Information of China (English)
陈伸义
2011-01-01
语词搭配是现代诗修辞的基本功。一味坚持传统准确和谐标准是有问题的。现代诗语的陌生化要求语词拒绝常态组合。寻求多方位超常搭配主要有三种突破手段：突破语义限制；突破感官限制；突破日常习惯限制。语词的超常搭配，貌似是纯技术语义场，实乃与诗人整个生命精神境域维系一体。诗人的职责，是不断转动手中的魔方，让纷飞的“碎片”重组耳目一新的“图景”。%Lexical collocation is one of the basic skills of the modem poetry rhetoric. It is not normal to adhere to traditional standards of accuracy harmony blindly. Modem poetry language defamiliarization requires anomalous lexical collocation. There are three main methods to realize multi - faceted anomalous collocation： break semantic restrictions; break sensory limitations and daily hab- its limitations. Anomalous lexical collocation seems to be semantic field, but in fact, it integrates with the poet＇ s spirit. The poet is responsible for using anomalous lexical collocation to restructure refreshing pictures.
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.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Data-worth analysis through probabilistic collocation-based Ensemble Kalman Filter
Dai, Cheng; Xue, Liang; Zhang, Dongxiao; Guadagnini, Alberto
2016-09-01
We propose a new and computationally efficient data-worth analysis and quantification framework keyed to the characterization of target state variables in groundwater systems. We focus on dynamically evolving plumes of dissolved chemicals migrating in randomly heterogeneous aquifers. An accurate prediction of the detailed features of solute plumes requires collecting a substantial amount of data. Otherwise, constraints dictated by the availability of financial resources and ease of access to the aquifer system suggest the importance of assessing the expected value of data before these are actually collected. Data-worth analysis is targeted to the quantification of the impact of new potential measurements on the expected reduction of predictive uncertainty based on a given process model. Integration of the Ensemble Kalman Filter method within a data-worth analysis framework enables us to assess data worth sequentially, which is a key desirable feature for monitoring scheme design in a contaminant transport scenario. However, it is remarkably challenging because of the (typically) high computational cost involved, considering that repeated solutions of the inverse problem are required. As a computationally efficient scheme, we embed in the data-worth analysis framework a modified version of the Probabilistic Collocation Method-based Ensemble Kalman Filter proposed by Zeng et al. (2011) so that we take advantage of the ability to assimilate data sequentially in time through a surrogate model constructed via the polynomial chaos expansion. We illustrate our approach on a set of synthetic scenarios involving solute migrating in a two-dimensional random permeability field. Our results demonstrate the computational efficiency of our approach and its ability to quantify the impact of the design of the monitoring network on the reduction of uncertainty associated with the characterization of a migrating contaminant plume.
The Effect of Corpus-Based Activities on Verb-Noun Collocations in EFL Classes
Ucar, Serpil; Yükselir, Ceyhun
2015-01-01
This current study sought to reveal the impacts of corpus-based activities on verb-noun collocation learning in EFL classes. This study was carried out on two groups--experimental and control groups- each of which consists of 15 students. The students were preparatory class students at School of Foreign Languages, Osmaniye Korkut Ata University.…
THE SA MPLING OF COLLOCATION THROUGH SPORTS TEXTS IN WRITTEN PRESS
Directory of Open Access Journals (Sweden)
Muhammet K URT
2015-08-01
Full Text Available From the beginning of the history to the today’s world, the ongoing relations, such as cultural, economic and political with Arabic countries have created a need to learn and teach this l anguage. For this purpose, many materials have been formed. Apart from these, press language organs in language teaching and learning play a very important role. In this context, the written press newsletters should be examined to facilitate foreign langua ge learning and teaching and to create resources for teachers and students. Collocation structures have an important place in such an examination. To minimize the use of the word incorrectly, foreign language learners must use these words according to the natural structure of the language. This creates a need to learn structures which are reffered to as collocations. The aim of this study is to explain Arabic collocations through sport texts. In this respect, sport bulletins selected from newspapers in Arab ic printed media will be investigated with the purpose of exemplifying collocations. This study is a survey research. Examples will be gathered from texts selected from printed media and findings will be obtained .
Reynolds, Barry Lee
2016-01-01
Lack of knowledge in the conventional usage of collocations in one's respective field of expertise cause Taiwanese students to produce academic writing that is markedly different than more competent writing. This is because Taiwanese students are first and foremost English as a Foreign language (EFL) readers and may have difficulties picking up on…
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
Teaching vocabulary through collocations in EFL Classes: The case of Turkey
Directory of Open Access Journals (Sweden)
Çakır, Abdülkadir
2012-01-01
Full Text Available When vocabulary teaching is taken into account in EFL classes in Turkish state primary schools, teachers generally prefer to use classical techniques. The purpose of this study is to find out the effect of a relatively new vocabulary teaching technique; teaching vocabulary through collocations. Pre-test/Post-test Control Group Design was employed in this study. Fifty-nine (59 seventh (7th grade students from two classrooms in a lower-middle class, suburban state primary school in Konya, Turkey participated in this study. The experimental group was taught new words using collocation technique; the control group was taught new words using classical techniques such as synonym, antonym, definition and mother tongue translation as it was in the previous reading classes before the study. The statistical analysis revealed that teaching vocabulary through collocations results in a better learning of the words than presenting them using classical techniques and enhances retention of new vocabulary items. Teaching vocabulary through collocations can be an effective factor in helping students remember and use the new words easily in primary school EFL classes. Therefore, teachers of English could be encouraged to attach more importance to vocabulary teaching rather than the acquisition of grammar and the use of current vocabulary teaching strategies in their classes.
Reynolds, Barry Lee
2016-01-01
Lack of knowledge in the conventional usage of collocations in one's respective field of expertise cause Taiwanese students to produce academic writing that is markedly different than more competent writing. This is because Taiwanese students are first and foremost English as a Foreign language (EFL) readers and may have difficulties picking up on…
The Role of Language for Thinking and Task Selection in EFL Learners' Oral Collocational Production
Wang, Hung-Chun; Shih, Su-Chin
2011-01-01
This study investigated how English as a foreign language (EFL) learners' types of language for thinking and types of oral elicitation tasks influence their lexical collocational errors in speech. Data were collected from 42 English majors in Taiwan using two instruments: (1) 3 oral elicitation tasks and (2) an inner speech questionnaire. The…
Frequent Collocates and Major Senses of Two Prepositions in ESL and ENL Corpora
Nkemleke, Daniel
2009-01-01
This contribution assesses in quantitative terms frequent collocates and major senses of "between" and "through" in the corpus of Cameroonian English (CCE), the corpus of East-African (Kenya and Tanzania) English which is part of the International Corpus of English (ICE) project (ICE-EA), and the London Oslo/Bergen (LOB) corpus of British English.…
Strategies in Translating Collocations in Religious Texts from Arabic into English
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…
Processing and Learning of Enhanced English Collocations: An Eye Movement Study
Choi, Sungmook
2017-01-01
Research to date suggests that textual enhancement may positively affect the learning of multiword combinations known as collocations, but may impair recall of unenhanced text. However, the attentional mechanisms underlying such effects remain unclear. In this study, 38 undergraduate students were divided into two groups: one read a text…
On Factorization, Interconnection and Reduction of Collocated Port-Hamiltonian Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
Based on a geometric interpretation of nonlinear balanced reduction some implications of this approach are analyzed in the case of collocated port-Hamiltonian systems which have a certain balance in its structure. Furthermore, additional examples of reduction for this class of systems are presented.
Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors
Balakrishnan, A. V.
1994-01-01
This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.
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
Sokolova, L V; Cherkasova, A S
2015-01-01
Texts or words/pseudowords are often used as stimuli for human verbal activity research. Our study pays attention to decoding processes of grammatical constructions consisted of two-three words--collocations. Russian and English collocation sets without any narrative were presented to Russian-speaking students with different English language skill. Stimulus material had two types of collocations: paradigmatic and syntagmatic. 30 students (average age--20.4 ± 0.22) took part in the study, they were divided into two equal groups depending on their English language skill (linguists/nonlinguists). During reading brain bioelectrical activity of cortex has been registered from 12 electrodes in alfa-, beta-, theta-bands. Coherent function reflecting cooperation of different cortical areas during reading collocations has been analyzed. Increase of interhemispheric and diagonal connections while reading collocations in different languages in the group of students with low knowledge of foreign language testifies of importance of functional cooperation between the hemispheres. It has been found out that brain bioelectrical activity of students with good foreign language knowledge during reading of all collocation types in Russian and English is characterized by economization of nervous substrate resources compared to nonlinguists. Selective activation of certain cortical areas has also been observed (depending on the grammatical construction type) in nonlinguists group that is probably related to special decoding system which processes presented stimuli. Reading Russian paradigmatic constructions by nonlinguists entailed increase between left cortical areas, reading of English syntagmatic collocations--between right ones.
Chen, Maosi; Zempila, Melina-Maria; Davis, John M.; King, Robert W.; Gao, Wei
2016-09-01
The difficulty of in-situ calibration on the 940 nm channel of Multi-Filter Rotating Shadowband Radiometer (MFRSR) stems from the distinctive non-linear relationship between the amount of precipitable water vapor (PW) and its optical depth (i.e. curve of growth) compared to the counterpart of aerosols. Previous approaches, the modified Langley methods (MLM), require exact aerosol optical depth (AOD) values and a constant PW value at all points participating the regression. Instead, we propose a new method that substitutes the PW optical depth derived from collocated GPS zenith wet delay retrieval in conjunction with meteorology data and requires a constant AOD value at all points participating the regression. The main benefits of the new method include: (1) Aerosol stability is easier to fulfill than PW stability; (2) AOD stability could be inferred from adjacent channels (e.g. 672 and 870 nm) of MFRSR itself without measurements of a collocated AERONET sun photometer; and (3) When applicable, the time interval of GPS derived PW (i.e. 3 minutes) is more compatible with the MFRSR sampling interval (i.e. 3 minutes) than AERONET interpolated AOD (i.e. 15 minutes). Both MLM and the new method were applied to the MFRSR of USDA UV-B Monitoring and Research Program at the station in Billings, Oklahoma (active for 18 years so far) on July 28, 2015. The performances of the two methods are compared in order to assess their accuracy and the advantages and disadvantages.
Phillips, J. R.
1996-01-01
In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.
An efficient algorithm for solving nonlinear system of differential equations and applications
Directory of Open Access Journals (Sweden)
Mustafa GÜLSU
2015-10-01
Full Text Available In this article, we apply Chebyshev collocation method to obtain the numerical solutions of nonlinear systems of differential equations. This method transforms the nonlinear systems of differential equation to nonlinear systems of algebraic equations. The convergence of the numerical method are given and their applicability is illustrated with some examples.
On computation of Hough functions
Wang, Houjun; Boyd, John P.; Akmaev, Rashid A.
2016-04-01
Hough functions are the eigenfunctions of the Laplace tidal equation governing fluid motion on a rotating sphere with a resting basic state. Several numerical methods have been used in the past. In this paper, we compare two of those methods: normalized associated Legendre polynomial expansion and Chebyshev collocation. Both methods are not widely used, but both have some advantages over the commonly used unnormalized associated Legendre polynomial expansion method. Comparable results are obtained using both methods. For the first method we note some details on numerical implementation. The Chebyshev collocation method was first used for the Laplace tidal problem by Boyd (1976) and is relatively easy to use. A compact MATLAB code is provided for this method. We also illustrate the importance and effect of including a parity factor in Chebyshev polynomial expansions for modes with odd zonal wave numbers.
DEFF Research Database (Denmark)
Westbrook, Pete
Despite the large body of research into formulaic language and fluency, there seems to be a lack of empirical evidence for how collocations, often considered a subset of formulaic language, might impact on fluency. To address this problem, this dissertation examined to what extent correlations...... might exist between overall language proficiency, collocational competence and spoken fluency in non-native English-speaking university lecturers. The data came from 15 20-minute mini-lectures recorded between 2009 and 2011 for an English oral proficiency test for lecturers employed at the University...... of Copenhagen. The 15 lecturers came from three departments: Large Animal Science, Information Technology and Mathematics. Test examiners’ global and fluency scores from the test were analysed against collocational competence, measured as collocations produced per thousand words spoken, and three temporal...
Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming
Shi, Yun Yuan; Young, D. H.
1991-01-01
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem
The convergence problem of collocation solutions in the framework of the stochastic interpretation
Sansò, F.; Venuti, G.
2011-01-01
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. "Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic" Dante Alighieri, La Divina Commedia, Inferno, IV - 136
Design and Application of a Collocated Capacitance Sensor for Magnetic Bearing Spindle
Shin, Dongwon; Liu, Seon-Jung; Kim, Jongwon
1996-01-01
This paper presents a collocated capacitance sensor for magnetic bearings. The main feature of the sensor is that it is made of a specific compact printed circuit board (PCB). The signal processing unit has been also developed. The results of the experimental performance evaluation on the sensitivity, resolution and frequency response of the sensor are presented. Finally, an application example of the sensor to the active control of a magnetic bearing is described.
Active vibration control of a sandwich plate by non-collocated positive position feedback
Ferrari, Giovanni; Amabili, Marco
2015-04-01
The active vibration control of a free rectangular sandwich plate by using the Positive Position Feedback (PPF) algorithm was experimentally investigated in a previous study. Four normal modes were controlled by four nearly collocated couples of piezoelectric sensors and actuators. The experimental results of the control showed some limitation, especially in the Multi-Input Multi-Output (MIMO) configuration. This was attributed to the specific type of sensors and their conditioning, as well as to the phase shifts present in the vibration at different points of the structure. An alternative approach is here undertaken by abandoning the configuration of quasi-perfect collocation between sensor and actuator. The positioning of the piezoelectric patches is still led by the strain energy value distribution on the plate; each couple of sensor and actuator is now placed on the same face of the plate but in two distinct positions, opposed and symmetrical with respect to the geometric center of the plate. Single-Input Single-Output (SISO) PPF is tested and the transfer function parameters of the controller are tuned according to the measured values of modal damping. Then the participation matrices necessary for the MIMO control algorithm are determined by means of a completely experimental procedure. PPF is able to mitigate the vibration of the first four natural modes, in spite of the rigid body motions due to the free boundary conditions. The amplitude reduction achieved with the non-collocated configuration is much larger than the one obtained with the nearby collocated one. The phase lags were addressed in the MIMO algorithm by correction phase delays, further increasing the performance of the controller.
Ophaug, Vegard; Gerlach, Christian
2017-05-01
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.
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.
Numerical methods for hypersonic boundary layer stability
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Institute of Scientific and Technical Information of China (English)
张潇潇; 胡宏
2015-01-01
In this paper,we derive some interesting identities involving golden ratio, Fibonacci sequences, Lucas sequences and the first and second type of Chebyshev polynomials by using the arctangent function.%根据Fibonacci数列和两类Chebyshev多项式的基本性质，利用反正切函数得出了一些关于黄金分割数与 Fibonacci 数列及 Lucas 数列的恒等式，同时获得了一些涉及两类Chebyshev多项式之间关系的恒等式。
Facial Organ Words and Collocations in Dickens' Works
Institute of Scientific and Technical Information of China (English)
杨敏艺
2015-01-01
The emergence of computer is tailed by modern corpus study which increases its popularity in linguistic studies with its tremendous storage and fast processing speed. In accordance with the unrelenting updated computer technology, the performance of corpus researches has been improving. And it is imposing among those traditional methods of linguistic studies because its objective data and the quantitative description of language use, both of which operating under the spirit of science. This article aims to analyze facial organ-eye used in Dickens' works and show how Dickens used this word through a corpus-based approach.
40 CFR 53.33 - Test Procedure for Methods for Lead (Pb).
2010-07-01
... subject to XRF with subsequent extraction for other analyses, then a single PM10 reference sampler may be... selected to provide Pb concentrations in the specified range. (d) Collocated samplers. The ambient air intake points of all the candidate and reference method collocated samplers shall be positioned at...
Numerical Modeling of Tidal Effects in Polytropic Accretion Discs
Godon, P.
1996-01-01
A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion discs, under the assumption of a polytropic equation of state and a standard alpha viscosity prescription.
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 T...
The application of the Galerkin method to solving PIES for Laplace's equation
Bołtuć, Agnieszka; Zieniuk, Eugeniusz
2016-06-01
The paper presents the application of the Galerkin method to solving the parametric integral equation system (PIES) on the example of Laplace's equation. The main aim of the paper is the analysis of the effectiveness of two methods for PIES solving: the collocation method and the Galerkin method. Researches were performed on two examples with analytical solutions. Tests concern mainly the accuracy of obtained numerical solutions and their stability. For both analyzed methods calculations were made with the various number of expressions in the approximation series, whilst in the collocation method two variants of the arrangement of collocation points were considered. We also compared the complexity of both methods using the execution time.
Mitra, S; Finn, L S
2005-01-01
Inspiraling compact binaries are promising sources of gravitational waves for ground and space-based laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. Current analysis methodology samples the matched filter output at parameter values chosen so that the correlation between successive samples is 97% for which the filtered output is closely correlated. Here we describe a straightforward and practical way of using interpolation to take advantage of the correlation between the matched filter output associated with nearby points in the parameter space to significantly reduce the number of matched filter evaluations without sacrificing the efficiency with which real signals are recognized. Because the computational cost of the analysis is driven almost exclusively by the matched filter evaluations...
Institute of Scientific and Technical Information of China (English)
岳福曹
2015-01-01
新疆维吾尔族大学生学习英语词汇的方法受传统语言教学的影响，只识记单词的音形义而忽略了词语的应用。文章运用搭配理论，分析了维吾尔族大学生英语词汇学习中的失误，并提出了运用搭配理论讲授英语词汇的方法。%The lexical learning by Uyghur college students in Xinjiang is influenced by the traditional language teaching and the students have merely memorized the sounds, spellings and meanings of the words but ignored the collocations and the use of them. The paper employs the collocation theory to analyze the mistakes which the Uyghur students made in their lexical learning in English and proposes some teaching methods with collocation.
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
Between initial familiarity and future use – a case of Collocated Collaborative Writing
DEFF Research Database (Denmark)
Bødker, Susanne; Polli, Anna Maria
2014-01-01
This paper reports on a design experiment in an art gallery, where we explored visitor practices of commenting on art, and how they were shaped in interaction with a newly designed collocated, collaborative writing technology. In particular we investigate what potentials previous practices carry ...... future use possibilities and initial familiarity based on everyday practices. These forms met and at times collided in a space where the actual use was shaped. We furthermore look back on initial assumptions made in design regarding a productive collaborative writing style, and confront...
Application of Collocated GPS and Seismic Sensors to Earthquake Monitoring and Early Warning
Directory of Open Access Journals (Sweden)
Bofeng Guo
2013-10-01
Full Text Available We explore the use of collocated GPS and seismic sensors for earthquake monitoring and early warning. The GPS and seismic data collected during the 2011 Tohoku-Oki (Japan and the 2010 El Mayor-Cucapah (Mexico earthquakes are analyzed by using a tightly-coupled integration. The performance of the integrated results is validated by both time and frequency domain analysis. We detect the P-wave arrival and observe small-scale features of the movement from the integrated results and locate the epicenter. Meanwhile, permanent offsets are extracted from the integrated displacements highly accurately and used for reliable fault slip inversion and magnitude estimation.
Solving the Coulomb Schrodinger equation in d=2+1 via sinc collocation
Koures, V G
1995-01-01
We solve the non-relativistic Coulomb Shrodinger equation in d = 2+1 via sinc collocation. We get excellent convergence using a generalized sinc basis set in position space. Since convergence in position space could not be obtained with more common numerical techniques, this result helps to corroborate the conjecture that the use of a localized basis set within the context of light cone quantization can yield much better convergence. All of the computations presented here were performed on an IBM-compatible PC with an Intel 486DX2-66 microchip.
Energy Technology Data Exchange (ETDEWEB)
Mahmood, Asad, E-mail: asadmahmood_86@yahoo.com [Department of Mathematics and Statistics, International Islamic University, Islamabad 44000 (Pakistan); Chen, Bin [School of Environment, Beijing Normal University, Beijing 100875 (China); Ghaffari, Abuzar [Department of Mathematics and Statistics, International Islamic University, Islamabad 44000 (Pakistan)
2016-10-15
Hydromagnetic stagnation point flow and heat transfer over a nonlinearly stretching/shrinking surface of micropolar fluid is investigated. The numerical simulation is carried out through Chebyshev Spectral Newton Iterative Scheme, after transforming the governing equations into dimensionless boundary layer form. The dual solutions are reported for different values of magnetic and material parameters against the limited range of stretching/shrinking parameter. It is also noted that second solution only occurs for the negative values of stretching/shrinking parameter, whereas for the positive values unique solution exists. The effects of dimensionless parameters are described through graphs. It is seen that the flow and heat transfer rates can be controlled through the material parameter and magnetic force. - Highlights: • Constitutive equations of micropolar fluid and heat transfer are employed. • Magnetic effect on velocity and temperature profile of micropolar fluid is observed. • Dual solution is reported in the region of stagnation point flow. • A numerical technique i.e. Chebyshev Spectral Newton Iterative Scheme is applied to obtain the desire results.
Jarmołowski, Wojciech
2017-07-01
Maximum likelihood (ML) and restricted maximum likelihood (REML) are nowadays very popular in geophysics, geodesy and many other fields. There is also a growing number of investigations into how to calculate covariance parameters by ML/REML accurately and fast, and assure the convergence of the iteration steps in derivative-based approaches. The latter condition is not satisfied in many solutions, as it requires composed procedures or takes an unacceptable amount of time. The article implements efficient Fisher scoring (FS) to covariance parameter estimation in least-squares collocation (LSC). FS is optimized through Levenberg-Marquardt (LM) optimization, which provides stability in convergence when estimating two covariance parameters necessary for LSC. The motivation for this work was a very large number of non-optimized FS in the literature, as well as a deficiency of its scientific and engineering applications. The example work adds some usefulness to maximum likelihood estimation (ML) and FS and shows a new application—an alternative approach to LSC—a parametrization with no empirical covariance estimation. The results of LM damping applied to FS (FSLM) require some additional research related with optimal LM parameter. However, the method appears to be a milestone in relation to non-optimized FS, in terms of convergence. The FS with LM provides a reliable convergence, whose speed can be adjusted by manipulating the LM parameter.
词汇搭配与英语词汇教学%Lexical Collocation and English Vocabulary Teaching
Institute of Scientific and Technical Information of China (English)
高婷婷
2014-01-01
词汇是英语学习的基础，词汇搭配的学习对学习者至关重要。英国语言学家威尔金斯(D,Wilkins)说过，“没有语法，人们可以表达的事物寥寥无几；而没有词汇，人们则无法表达任何事物。”英语词汇具有很强的搭配能力，利用英语词汇搭配，可以扩大词汇量，掌握单词的正确用法。本文主要探讨了什么是词汇搭配，词汇搭配的重要性以及英语中词汇搭配的教学实践，以期帮助英语学习者更有效地掌握英语词汇和语言。%Vocabulary is the fundamental of English learning, so the learning of lexical collocation is vital to learners. As British linguist D, Wilkins put it,"without grammar very little can be conveyed, while without vocabulary nothing can be conveyed". To learn English vocabulary, we should learn lexical collocation. We can use lexical collocation to enlarge our vocabulary and master their usage. This paper aims to talk about what lexical collocation is, the importance of lexical collocation and the teaching practice of English lexical collocation, in order to help English learners master English vocabulary and language effectively.
Novak, Jasminko; Schmidt, Susanne
Hedonic aspects are increasingly considered as an important factor in user acceptance of information systems, especially for activities with high self-fulfilling value for the users. In this paper we report on the results of an experiment investigating the hedonic qualities of an interactive large-display workspace for collocated collaboration in sales-oriented travel advisory. The results show a higher hedonic stimulation quality of a touch-based large-display travel advisory workspace than that of a traditional workspace with catalogues. Together with the feedback of both customers and travel agents this suggests the adequacy of using touch-based large-displays with visual workspaces for supporting the hedonic stimulation of user experience in collocated collaboration settings. The relation of high perception of hedonic quality to positive emotional attitudes towards the use of a large-display workspace indicates that even in utilitarian activities (e.g. reaching sales goals for travel agents) hedonic aspects can play an important role. This calls for reconsidering the traditional divide of hedonic vs. utilitarian systems in current literature, to a more balanced view towards systems which provide both utilitarian and hedonic sources of value to the user.
Figuring out Actors in Text Streams: Using Collocations to establish Incremental Mind-maps
Rothenberger, T; Tahirovic, E; Schommer, C
2008-01-01
The recognition, involvement, and description of main actors influences the story line of the whole text. This is of higher importance as the text per se represents a flow of words and expressions that once it is read it is lost. In this respect, the understanding of a text and moreover on how the actor exactly behaves is not only a major concern: as human beings try to store a given input on short-term memory while associating diverse aspects and actors with incidents, the following approach represents a virtual architecture, where collocations are concerned and taken as the associative completion of the actors' acting. Once that collocations are discovered, they become managed in separated memory blocks broken down by the actors. As for human beings, the memory blocks refer to associative mind-maps. We then present several priority functions to represent the actual temporal situation inside a mind-map to enable the user to reconstruct the recent events from the discovered temporal results.
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.
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Zhang, Jian; Sun, Haimeng; Wang, Wengang; Hu, Zhen; Yin, Xiaole; Ngo, Huu Hao; Guo, Wenshan; Fan, Jinlin
2017-01-01
In the present study, a novel seasonal plant collocation system (SPCS), specifically the Potamogeton crispus and Phragmites australis series system, was investigated to enhance the performance of surface flow constructed wetlands (SFCWs) at low temperature. Results of a year-round experiment showed that SPCS conquered the adverse effect of low temperature and achieved sustainable nutrients removal. In addition, during winter, removal efficiencies of NH4-N, TP, COD, and TN in SPCS were 18.1%, 17.6%, 10.1% and 5.2% higher than that in the control, respectively. P. crispus and P. australis complemented each other in terms of plant growth and plant uptake during the experiment period. Furthermore, it emerged that P. crispus could increase the quantity of ammonia oxidizing bacteria by 10.2%, due to its high oxygen enrichment ability. It is suggested that seasonal plant collocation has a promising future in SFCWs of areas being affected by climate change, e.g. northern China. Copyright © 2016 Elsevier Ltd. All rights reserved.
In ‘other’ words: Some thoughts on the transferability of collocations
Directory of Open Access Journals (Sweden)
Terence Odlin
2011-10-01
Full Text Available In discussions of cross-linguistic influence (also known as language transfer, the focus is usually on the influence of a particular structure in a particular instance of language contact, for instance, the negative transfer of serial verbs by Vietnamese learners of English: She has managed to rise the kite fly over the tallest building (Helms-Park, 2003. Even so, as Helms-Park acknowledges, serial verb constructions can and do surface in contact situations besides the one she studied in Canada, and they can involve speakers of different languages. While serial verb constructions have unique syntactic traits, the same point about the transferability of multiword constructions in different contact settings is applicable in other instances and with collocations that can be viewed as unique in their lexical as well as syntactic characteristics. The following article considers such a case, based in part on my own teaching experience but also on transfer research from other settings as well. After a discussion of a collocation that I call the repeated other pattern found in different settings, I briefly consider other cases of transfer having lexical and syntactic peculiarities and appearing in more than one contact situation. There will also be some discussion of factors that transfer researchers and language teachers would do well to consider.
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Leonard Rapi
2012-04-01
Full Text Available The aim of this paper is to investigate synonymic collocations in Thomas Hardy’s “Tess of the d’Urbervilles” and their translation into Albanian. Synonymic collocations are first investigated as to their semantic structure and the stylistic function they fulfill in the source text. Then, their Albanian equivalents are analyzed with the aim of comparing them with the expressions in the original in order to see how their semantic structure and their stylistic effects are reconstructed in the translated text.
CHINESE-UYGHUR PHRASES COLLOCATION AND ALIGNMENT%汉维语短语搭配的识别和对齐
Institute of Scientific and Technical Information of China (English)
禹龙; 田生伟; 杨飞宇
2011-01-01
提出一种简单实用的汉维语短语搭配的抽取方法.该方法不需要汉语分词、词性标注等预处理工作,根据语料中汉语字和维语单词的共现信息,避免语料中个别词汇数目极少而共现信息值较大出现噪音,采用t检验消除,相对于利用分词和词性标注等技术的抽取方法,该算法简单且时间效率较高.实验结果表明,该方法利用较小规模的语料库也能达到较好的短语搭配抽取效果.%This dissertation puts forward a simple and practical extraction method for Chinese and Uyghur phrases collocation. The method does not require Chinese word segmentation, POS tagging and other pre-processing works, according to co-occurrence information of Chinese characters and Uyghur words in the corpus, it avoids the existence of the noise caused by sparseness of exceptional words but with quite big co-occurrence information value in the corpus and uses t-test to eliminate the noise. Compared with traditional extraction methods based on word segmentation and POS tagging technologies, the algorithm is simple and time efficient. Experimental results show that the method can achieve preferable effect of phrases collocation extraction even using smaller corpus library.
Basic Methods for Computing Special Functions
Gil, Amparo; Segura, Javier; Temme, Nico; Simos, T. E.
2011-01-01
This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other metho...
中国学生英语搭配知识与运用研究%A Study on the Chinese Students' Acquisition of Collocational Knowledge
Institute of Scientific and Technical Information of China (English)
李文英
2004-01-01
In China the acquisition of collocations is considered as one of the most difficult points for the Chinese students in their foreign language learning. So far there are few empirical studies involving the Chinese students' acquisition of collocational knowledge. The author of the present thesis attempts to examine the acquisition of collocational knowledge in the Chinese students from the productive aspect by investigating the acquisition of collocations in the students at three proficiency levels: elementary, intermediate and advanced. The present study aims at finding out whether there are any proficiency-related differences in the acquisition of collocations, and which collocation types are acquired in the early stage of foreign language learning and which are acquired in the later stage. Altogether 110 students have participated in this study. The results have shown that there are indeed proficiency-related differences in the acquisition of collocations and that there are specific types of collocation that are acquired in the early stages of language learning, and some types are acquired in the later stages of language learning.
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Ruili Wen
2016-08-01
Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.
Kolmogorov, Dmitry; Zhu, Wei Jun; Sørensen, Niels N.; Sørensen, Jens Nørkær; Shen, Wen Zhong
2014-01-01
Direkte numerisk løsning af Navier-Stokes ligninger ved hjælp af Computational Fluid Dynamics (CFD) er anerkendt som en af de mest avancerede og præcise metoder til forudsigelse af luftstrømninger omkring vindmøller. Evnen af disse metoder til at indfange dynamikken i de komplekse strømninger, som optræder i umiddelbar nærhed af en vindmøllerotor, har gjort dem til uvurderlige værktøjer til forudsigelse af lokale vindfelter. Da direkte beregninger af en fuldt opløst strømning omkring en vindm...
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Nawal Gholami
2017-03-01
Full Text Available Few studies have investigated the effects of input-based and output-based instructions on collocational knowledge of EFL learners. Therefore, this study aimed to examine the effects of these instructional approaches on Iranian EFL learners’ productive knowledge of collocations. To this end, 80 senior high school students from three intact classes at Tali-e High School in Ahvaz, Iran, were selected. Each class was assigned to a control group (n = 28 and two experimental groups including the input group (n = 27 and the output group (n = 25. Twenty collocations were selected as the target collocations. Then, a pretest was administered to all groups. Two days after the last treatment session, an immediate posttest was given to the participants. A delayed posttest was also administered two weeks later. The results of Mixed-ANOVA, one-way ANOVA, and Tukey post hoc tests revealed that both input and output groups outperformed the control group on the immediate and delayed posttests. However, there were no significant differences between the input and output groups on the posttests. The implications and suggestions for future research are also presented.
Molina-Plaza, Silvia; de Gregorio-Godeo, Eduardo
2010-01-01
Within the context of on-going research, this paper explores the pedagogical implications of contrastive analyses of multiword units in English and Spanish based on electronic corpora as a CALL resource. The main tenets of collocations from a contrastive perspective--and the points of contact and departure between both languages--are discussed…
Alqarni, Ibrahim R.
2017-01-01
This study investigates the impact that study in Australia has on the lexical knowledge of Saudi Arabian students. It focuses on: 1) the effects that the length of study in Australia has on the acquisition of lexical collocations, as reflected by lexical knowledge tests, and 2) whether there is a significant gender difference in the acquisition of…
A Study of Learners' Usage of a Mobile Learning Application for Learning Idioms and Collocations
Amer, Mahmoud
2014-01-01
This study explored how four groups of language learners used a mobile software application developed by the researcher for learning idiomatic expressions and collocations. A total of 45 participants in the study used the application for a period of one week. Data for this study was collected from the application, a questionnaire, and follow-up…
Ördem, Eser; Paker, Turan
2016-01-01
The purpose of this study was to investigate whether teaching vocabulary via collocations would contribute to retention and use of foreign language, English. A quasi-experimental design was formed to see whether there would be a significant difference between the treatment and control groups. Three instruments developed were conducted to 60…
Mahmood, Asad; Chen, Bin; Ghaffari, Abuzar
2016-10-01
Hydromagnetic stagnation point flow and heat transfer over a nonlinearly stretching/shrinking surface of micropolar fluid is investigated. The numerical simulation is carried out through Chebyshev Spectral Newton Iterative Scheme, after transforming the governing equations into dimensionless boundary layer form. The dual solutions are reported for different values of magnetic and material parameters against the limited range of stretching/shrinking parameter. It is also noted that second solution only occurs for the negative values of stretching/shrinking parameter, whereas for the positive values unique solution exists. The effects of dimensionless parameters are described through graphs. It is seen that the flow and heat transfer rates can be controlled through the material parameter and magnetic force.
DEFF Research Database (Denmark)
Hyvönen, Niina; Kaarnioja, V.; Mustonen, L.
2017-01-01
The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the conductivity is the quantity of main interest in impedance...... tomography, a real-world measurement configuration includes other unknown parameters as well: The information on the contact resistances, electrode positions, and body shape is almost always incomplete. In this work, the dependence of the electrode measurements on all aforementioned model properties...... is parametrized via polynomial collocation. The availability of such a parametrization enables efficient simultaneous reconstruction of the conductivity and other unknowns by a Newton-type output least squares algorithm, which is demonstrated by two-dimensional numerical experiments based on both noisy simulated...
On Providing Downlink Services in Collocated Spectrum-Sharing Macro and Femto Networks
Chu, Xiaoli; López-Pérez, David; Tao, Xiaofeng
2012-01-01
Femtocells have been considered by the wireless industry as a cost-effective solution not only to improve indoor service providing, but also to unload traffic from already overburdened macro networks. Due to spectrum availability and network infrastructure considerations, a macro network may have to share spectrum with overlaid femtocells. In spectrum-sharing macro and femto networks, inter-cell interference caused by different transmission powers of macrocell base stations (MBS) and femtocell access points (FAP), in conjunction with potentially densely deployed femtocells, may create dead spots where reliable services cannot be guaranteed to either macro or femto users. In this paper, based on a thorough analysis of downlink (DL) outage probabilities (OP) of collocated spectrum-sharing orthogonal frequency division multiple access (OFDMA) based macro and femto networks, we devise a decentralized strategy for an FAP to self-regulate its transmission power level and usage of radio resources depending on its di...
Wilgan, Karina; Hurter, Fabian; Geiger, Alain; Rohm, Witold; Bosy, Jarosław
2016-08-01
Precise positioning requires an accurate a priori troposphere model to enhance the solution quality. Several empirical models are available, but they may not properly characterize the state of troposphere, especially in severe weather conditions. Another possible solution is to use regional troposphere models based on real-time or near-real time measurements. In this study, we present the total refractivity and zenith total delay (ZTD) models based on a numerical weather prediction (NWP) model, Global Navigation Satellite System (GNSS) data and ground-based meteorological observations. We reconstruct the total refractivity profiles over the western part of Switzerland and the total refractivity profiles as well as ZTDs over Poland using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays) developed at ETH Zürich. In these two case studies, profiles of the total refractivity and ZTDs are calculated from different data sets. For Switzerland, the data set with the best agreement with the reference radiosonde (RS) measurements is the combination of ground-based meteorological observations and GNSS ZTDs. Introducing the horizontal gradients does not improve the vertical interpolation, and results in slightly larger biases and standard deviations. For Poland, the data set based on meteorological parameters from the NWP Weather Research and Forecasting (WRF) model and from a combination of the NWP model and GNSS ZTDs shows the best agreement with the reference RS data. In terms of ZTD, the combined NWP-GNSS observations and GNSS-only data set exhibit the best accuracy with an average bias (from all stations) of 3.7 mm and average standard deviations of 17.0 mm w.r.t. the reference GNSS stations.
Wilgan, Karina; Hurter, Fabian; Geiger, Alain; Rohm, Witold; Bosy, Jarosław
2017-02-01
Precise positioning requires an accurate a priori troposphere model to enhance the solution quality. Several empirical models are available, but they may not properly characterize the state of troposphere, especially in severe weather conditions. Another possible solution is to use regional troposphere models based on real-time or near-real time measurements. In this study, we present the total refractivity and zenith total delay (ZTD) models based on a numerical weather prediction (NWP) model, Global Navigation Satellite System (GNSS) data and ground-based meteorological observations. We reconstruct the total refractivity profiles over the western part of Switzerland and the total refractivity profiles as well as ZTDs over Poland using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays) developed at ETH Zürich. In these two case studies, profiles of the total refractivity and ZTDs are calculated from different data sets. For Switzerland, the data set with the best agreement with the reference radiosonde (RS) measurements is the combination of ground-based meteorological observations and GNSS ZTDs. Introducing the horizontal gradients does not improve the vertical interpolation, and results in slightly larger biases and standard deviations. For Poland, the data set based on meteorological parameters from the NWP Weather Research and Forecasting (WRF) model and from a combination of the NWP model and GNSS ZTDs shows the best agreement with the reference RS data. In terms of ZTD, the combined NWP-GNSS observations and GNSS-only data set exhibit the best accuracy with an average bias (from all stations) of 3.7 mm and average standard deviations of 17.0 mm w.r.t. the reference GNSS stations.
Mathematical methods for physicists
Arfken, George B
1985-01-01
Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian tensors, dispersion theory, first-order differential equations, numerical application of Chebyshev polynomials, the fast Fourier transform, and transfer functions. Many of the physical examples provided in this book, which are used to illustrate the applications of mathematics, are taken from the fields of electromagnetic theory and quantum mechanics. The He
Comparison of Spectral and Differential Quadrature Methods for Solving the Burger-Huxley Equation
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Jalal Izadian
2013-06-01
Full Text Available In this paper, the Burger-Huxley equation is solved by two methods: Spectral method and Differential Quadrature Method (DQM. The Chebyshev-Gauss-Lobatto point distribution is utilized in spectral method. The integrity and computational accuracy of the spectral method in solving some test problems are demonstrated through various case studies. The results show that spectral method is more accurate than DQM.
Zyta Hakuba, Maria; Folini, Doris; Wild, Martin; Sanchez-Lorenzo, Arturo
2013-04-01
Anthropogenic climate change is physically speaking a perturbation of the atmospheric energy budget through the insertion of constituents such as greenhouse gases or aerosols. Changes in the atmospheric energy budget largely affect the global climate and hydrological cycle, but the quantification of the different energy balance components is still afflicted with large uncertainties. The overall aim of the present study is the assessment of the mean state and the spatio-temporal variations in the solar energy disposition, in which we focus on obtaining an accurate partitioning of absorbed solar radiation between the surface and the atmosphere. Surface based measurements of solar radiation (GEBA, BSRN) are combined with collocated satellite-retrieved surface albedo (MODIS, CERES FSW, or CM SAF GAC-SAL) and top-of-atmosphere net incoming solar radiation (CERES EBAF) to quantify the absorbed solar radiation (ASR) at the surface and within the atmosphere over Europe for the period 2001-2005. In a first step, we examine the quality and temporal homogeneity of the monthly time series beyond 2000 provided by GEBA in order to identify a subset of sufficient quality. We find the vast majority of monthly time series to be suitable for our purposes. Using the satellite-derived CM SAF surface solar radiation product at 0.03° spatial resolution, we assess the spatial representativeness of the GEBA and BSRN sites for their collocated 1° grid cells as we intend to combine the point measurements with the coarser resolved CERES EBAF products (1° resolution), and we find spatial sampling errors of on average 3 Wm-2 or 2% (normalized by point values). Based on the combination of 134 GEBA surface solar radiation (SSR) time series with MODIS white-sky albedo and CERES EBAF top-of-atmosphere net radiation (TOAnet), we obtain a European mean partitioning (2001-2005) of absorbed solar radiation (relative to total incoming radiation) of: ASRsurf= 41% and ASRatm= 25%, together equaling
An Analysis of Peak Wind Speed Data from Collocated Mechanical and Ultrasonic Anemometers
Short, David A.; Wells, Leonard; Merceret, Francis J.; Roeder, William P.
2007-01-01
This study compared peak wind speeds reported by mechanical and ultrasonic anemometers at Cape Canaveral Air Force Station and Kennedy Space Center (CCAFS/KSC) on the east central coast of Florida and Vandenberg Air Force Base (VAFB) on the central coast of California. Launch Weather Officers, forecasters, and Range Safety analysts need to understand the performance of wind sensors at CCAFS/KSC and VAFB for weather warnings, watches, advisories, special ground processing operations, launch pad exposure forecasts, user Launch Commit Criteria (LCC) forecasts and evaluations, and toxic dispersion support. The legacy CCAFS/KSC and VAFB weather tower wind instruments are being changed from propeller-and-vane (CCAFS/KSC) and cup-and-vane (VAFB) sensors to ultrasonic sensors under the Range Standardization and Automation (RSA) program. Mechanical and ultrasonic wind measuring techniques are known to cause differences in the statistics of peak wind speed as shown in previous studies. The 45th Weather Squadron (45 WS) and the 30th Weather Squadron (30 WS) requested the Applied Meteorology Unit (AMU) to compare data between the RSA ultrasonic and legacy mechanical sensors to determine if there are significant differences. Note that the instruments were sited outdoors under naturally varying conditions and that this comparison was not designed to verify either technology. Approximately 3 weeks of mechanical and ultrasonic wind data from each range from May and June 2005 were used in this study. The CCAFS/KSC data spanned the full diurnal cycle, while the VAFB data were confined to 1000-1600 local time. The sample of 1-minute data from numerous levels on five different towers on each range totaled more than 500,000 minutes of data (482,979 minutes of data after quality control). The ten towers were instrumented at several levels, ranging from 12 ft to 492 ft above ground level. The ultrasonic sensors were collocated at the same vertical levels as the mechanical sensors and
Institute of Scientific and Technical Information of China (English)
陈宇; 韦鹏程
2011-01-01
将Chebyshev多项式与模运算相结合,对其定义在实数域上进行了扩展,经过理论验证和数据分析,总结出实数域多项式应用于公钥密码的一些性质.利用RSA公钥算法和EIGamal公钥算法的算法结构,提出基于有限域离散Chebyshev多项式的公钥密码算法.该算法结构类似于RSA算法,其安全性基于大数因式分解的难度或者与El-Gamal的离散对数难度相当,能够抵抗对于RSA的选择密文攻击,并且易于软件实现.%By combining Chebyshev polynomials with modulus compute,extending Chebyshev polynomials' definition domain to real number, some conclusions were drawn by theoretic verification and data analysis. Making use of the framework of the traditional public-key algorithm RSA and ElGamal, proposed a chaotic public-key encryption algorithm based on extending discrete Chebyshev polynomials' definition domain to Real number. Its security is based on the intractability of the integer factorization problem as RSA,and it is able to resist the chosen cipher-text attack against RSA and easy to be implemented.
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.
The importance of temporal collocation for the evaluation of aerosol models with observations
Schutgens, N. A. J.; Partridge, D. G.; Stier, P.
2016-01-01
It is often implicitly assumed that over suitably long periods the mean of observations and models should be comparable, even if they have different temporal sampling. We assess the errors incurred due to ignoring temporal sampling and show that they are of similar magnitude as (but smaller than) actual model errors (20-60 %).Using temporal sampling from remote-sensing data sets, the satellite imager MODIS (MODerate resolution Imaging Spectroradiometer) and the ground-based sun photometer network AERONET (AErosol Robotic NETwork), and three different global aerosol models, we compare annual and monthly averages of full model data to sampled model data. Our results show that sampling errors as large as 100 % in AOT (aerosol optical thickness), 0.4 in AE (Ångström Exponent) and 0.05 in SSA (single scattering albedo) are possible. Even in daily averages, sampling errors can be significant. Moreover these sampling errors are often correlated over long distances giving rise to artificial contrasts between pristine and polluted events and regions. Additionally, we provide evidence that suggests that models will underestimate these errors. To prevent sampling errors, model data should be temporally collocated to the observations before any analysis is made.We also discuss how this work has consequences for in situ measurements (e.g. aircraft campaigns or surface measurements) in model evaluation.Although this study is framed in the context of model evaluation, it has a clear and direct relevance to climatologies derived from observational data sets.
Hocut, C.; Kit, E.; Liberzon, D.; Fernando, H. J. S.; Materhorn Team
2014-11-01
In the fall of 2012 and spring 2013, the Mountain Terrain Atmospheric Modeling and Observations Program (MATERHORN) conducted extensive field experiments at the Granite Mountain Atmospheric Science Testbed (GMAST), US Army Dugway Proving Grounds (DPG), Utah. This provided a unique opportunity to deploy tower mounted three-dimensional hot-film combo probes, consisting of sonic anemometers collocated with hot-film anemometers able to respond to the wind direction. The combo probes follow mean winds using a feedback control loop and use a Neural Network to calibrate the hot-films in-situ. Once calibrated, these probes can handle a vast range of background flow conditions and scales from mesoscale flow down to the Kolmogorov scale. Of particular interest are the observed variation in velocity spectra during the evenings. Sometimes the velocity spectra shows the turbulence is Kolmogorov and is isotropic at small scales while in other spectra there is evidence of turbulence production at finer scales. An explanation on different spectral shapes will be presented as well as the relevant length/time scales of the production events. Funded by ONR Grant N00014-11-1-0709.
Potential of collocated radiometer and wind profiler observations for monsoon studies
Balaji, B.; Prabha, Thara V.; Jaya Rao, Y.; Kiran, T.; Dinesh, G.; Chakravarty, Kaustav; Sonbawne, S. M.; Rajeevan, M.
2017-09-01
Collocated observations from microwave radiometer and wind profiler are used in a pilot study during the monsoon period to derive information on the thermodynamics and winds and association with rainfall characteristics. These instruments were operated throughout the monsoon season of 2015. Continuous vertical profiles of winds, temperature and humidity show significant promise for understanding the low-level jet, its periodicity and its association with moisture transport, clouds and precipitation embedded within the monsoon large-scale convection. Observations showed mutually beneficial in explaining variability that are part of the low frequency oscillations and the diurnal variability during monsoon. These observations highlight the importance of locally driven convective systems, in the presence of weak moisture transport over the area. The episodic moisture convergence showed a periodicity of 9 days which matches with the subsequent convection and precipitation and thermodynamic regimes. Inferences from the diurnal cycle of moisture transport and the convective activity, relationship with the low-level jet characteristics and thermodynamics are also illustrated.
The importance of temporal collocation for the evaluation of aerosol models with observations
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N. A. J. Schutgens
2015-09-01
Full Text Available It is often implicitly assumed that over suitably long periods the mean of observations and models should be comparable, even if they have different temporal sampling. We assess the errors incurred due to ignoring temporal sampling and show they are of similar magnitude as (but smaller than actual model errors (20–60 %. Using temporal sampling from remote sensing datasets (the satellite imager MODIS and the ground-based sun photometer network AERONET and three different global aerosol models, we compare annual and monthly averages of full model data to sampled model data. Our results show that sampling errors as large as 100 % in AOT (Aerosol Optical Thickness, 0.4 in AE (Ångström Exponent and 0.05 in SSA (Single Scattering Albedo are possible. Even in daily averages, sampling errors can be significant. More-over these sampling errors are often correlated over long distances giving rise to artificial contrasts between pristine and polluted events and regions. Additionally, we provide evidence that suggests that models will underestimate these errors. To prevent sampling errors, model data should be temporally collocated to the observations before any analysis is made. We also discuss how this work has consequences for in-situ measurements (e.g. aircraft campaigns or surface measurements in model evaluation.
Parametric study on a collocated PZT beam vibration absorber and power harvester
Energy Technology Data Exchange (ETDEWEB)
Huang, Shyh Chin [Mechanical Engineering, Ming Chi University of Technology, New Taipei (China); Tsai, Chao Yang [Mechanical Engineering Army Academy, R.O.C., Taoyuan (China); Liao, Hsiao Hui [LNG Construction and Project Division, CPC Corp., Taipei (China)
2016-11-15
The parametric effects of a PZT beam that is simultaneously used as a vibration absorber and a power harvester were investigated in this study. A cantilever beam paved with PZT layers and with added tip mass has been widely used as a harvester or sometimes as a Dynamic vibration absorber (DVA). However, the beam is rarely considered a collocated device. In this study, the first step was theoretical derivation of a distributed beam covered with bimorph PZT layers. Then, the beam was attached to a 1DOF vibratory main system. Two indicators for vibration absorption and power harvesting were defined. Numerical results demonstrated that the lumped mass ratio favored both of the abilities, but that the DVA mass ratio influenced these two abilities in exactly the opposite way. The conjunction of a harvester circuit into a DVA shifted its resonance frequency up to 5 % (an extreme case of open circuit R→∞). Simultaneous power harvesting diminished the absorption capability up to 35 % for each set of mass ratios. To achieve the maximum degree of power harvesting, a corresponding load resistance that somewhat increases with the lumped mass ratio is applied. Experimental results verified the existence of the best load resistance, but the measured harvested curve was lower than the theoretical calculation because of structure damping and deviations of PZT material properties.
Huang, Jingfeng; Hsu, N. Christina; Tsay, Si-Chee; Holben, Brent N.; Welton, Ellsworth J.; Smirnov, Alexander; Jeong, Myeong-Jae; Hansell, Richard A.; Berkoff, Timothy A.; Liu, Zhaoyan; Liu, Gin-Rong; Campbell, James R.; Liew, Soo Chin; Barnes, John E.
2012-08-01
Cirrus clouds, particularly subvisual high thin cirrus with low optical thickness, are difficult to screen in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to systematically examine the susceptibility of operational aerosol products to cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical feature mask (VFM) and the Moderate Resolution Imaging Spectroradiometer (MODIS) thin cirrus screening parameters for the purpose of evaluating cirrus contamination. Key results of this study include: (1) quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted; although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons; (2) challenges in matching up different data for analysis are highlighted and corresponding solutions proposed; and (3) estimates of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.
Les associations de marqueurs discursifs – De la cooccurrence libre à la collocation
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Dostie, Gaétane
2013-12-01
Full Text Available The question of the syntagmatic combinatorics of words belonging to the classes commonly addressed by grammatical tradition (such as nouns, verbs, adjectives and adverbs has been a subject of sustained reflection for several decades. The situation is different for discourse markers (DMs, which have gained substantial interest only recently (toward the end of the 1990s. This article takes as its starting point the idea that DMs are subject to the same types of syntagmatic associations as words belonging to the "ordinary" classes. By analogy with these classes, three types of syntagmatic associations are distinguished in the domain of DMs: the free discursive co-occurrence, the fixed expression (or discursive locution, and the semi-fixed expression (or discursive collocation. Of these types of word associations, the semi-fixed expression proves the most original and the most delicate to examine. It is therefore spe-cifically analyzed in this text, namely through a study of one marker in particular: don ([dɔ̃].
Feedback control of acoustic musical instruments: collocated control using physical analogs.
Berdahl, Edgar; Smith, Julius O; Niemeyer, Günter
2012-01-01
Traditionally, the average professional musician has owned numerous acoustic musical instruments, many of them having distinctive acoustic qualities. However, a modern musician could prefer to have a single musical instrument whose acoustics are programmable by feedback control, where acoustic variables are estimated from sensor measurements in real time and then fed back in order to influence the controlled variables. In this paper, theory is presented that describes stable feedback control of an acoustic musical instrument. The presentation should be accessible to members of the musical acoustics community who may have limited or no experience with feedback control. First, the only control strategy guaranteed to be stable subject to any musical instrument mobility is described: the sensors and actuators must be collocated, and the controller must emulate a physical analog system. Next, the most fundamental feedback controllers and the corresponding physical analog systems are presented. The effects that these controllers have on acoustic musical instruments are described. Finally, practical design challenges are discussed. A proof explains why changing the resonance frequency of a musical resonance requires much more control power than changing the decay time of the resonance.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.
Zulueta, R. C.; Metzger, S.; Ayres, E.; Luo, H.; Meier, C. L.; Barnett, D.; Sanclements, M.; Elmendorf, S.
2013-12-01
provides an evidence-based and repeatable method for combining sensor-based measurements and field sampling and observations at predefined levels of disturbance and spatial representativeness. The developed approach represents a general framework which is applicable to other environmental research sites where similar collocation is desired.
Institute of Scientific and Technical Information of China (English)
刘述钢; 刘宏立
2011-01-01
Low-voltage power line is a wired communication channel which is very complex. Its stability is poor and the communications are extremely easy to be destroyed. In this paper, we propose a combination couphng method of a transformer and a Chebyshev band-pass filter. Then we have carefully analyzed the structure of the coupled circuits and the principles of selecting components. The point-to-point communication capabilities are tested in the laboratory and the field, respectively. The results have demonstrated that the method proposed could completely meet the energy consumption information acquisition system for electric power consumer test technology specification of National Grid. The success ratio of the communication surpasses 98％ at 110 meters distance in the field environment. At the same time, the ratio is more than 80％ at 150 meters distance. This has indicated that the coupling circuit performance can effectively satisfy automatic metering reading.%低压电力线是一种通信环境十分恶劣的有线信道,其通信的稳定性差且极易被破坏.提出一种变压器与Chebyshev带通滤波器相结合的耦合方法,分析了耦合电路的结构和元件的设计原则.分别对实验室和现场环境中点对点通信能力进行数据统计,结果显示完全满足国家电网用电信息采集系统的检验技术规范,在现场环境中距离110m的范围内通信成功率超过98%,距离150 m时也可达80%以上,这表明了依照此方法设计的耦合电路性能完全能满足集中自动抄表要求.