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

Directory of Open Access Journals (Sweden)

Imtiaz Wasim

2018-01-01

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

Meshfree Local Radial Basis Function Collocation Method with Image Nodes

Energy Technology Data Exchange (ETDEWEB)

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

2017-07-15

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

Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

Directory of Open Access Journals (Sweden)

Lee Ken Yap

2015-01-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

A collocation finite element method with prior matrix condensation

International Nuclear Information System (INIS)

Sutcliffe, W.J.

1977-01-01

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

Application of collocation meshless method to eigenvalue problem

International Nuclear Information System (INIS)

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

2012-01-01

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

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

African Journals Online (AJOL)

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

Sinc-collocation method for solving the Blasius equation

International Nuclear Information System (INIS)

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

2009-01-01

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

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

KAUST Repository

Babuška, Ivo; Nobile, Fabio; Tempone, Raul

2010-01-01

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

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

Directory of Open Access Journals (Sweden)

Olumuyiwa A. Agbolade

2017-01-01

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

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

Science.gov (United States)

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

2018-06-01

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

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

Science.gov (United States)

Rogers, J M; McCulloch, A D

1994-08-01

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

Crosstalk statistics via collocation method

NARCIS (Netherlands)

Diouf, F.; Canavero, Flavio

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-10-15

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

Geostationary satellites collocation

CERN Document Server

Li, Hengnian

2014-01-01

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

Numerical simulation of GEW equation using RBF collocation method

Directory of Open Access Journals (Sweden)

Hamid Panahipour

2012-08-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-07-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

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

KAUST Repository

Yücel, Abdulkadir C.

2013-12-01

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

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-03-28

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

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

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

2016-01-01

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

Collocations and collocation types in ESP textbooks: Quantitative pedagogical analysis

Directory of Open Access Journals (Sweden)

Bogdanović Vesna Ž.

2016-01-01

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

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

Science.gov (United States)

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

2006-07-01

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

Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

OpenAIRE

Choe, Hui-Chol; Kang, Yong-Suk

2013-01-01

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

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

KAUST Repository

Motamed, Mohammad

2012-08-31

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

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

Science.gov (United States)

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

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

Changqing Yang

2012-01-01

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

Discretization of the induced-charge boundary integral equation.

Science.gov (United States)

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Discretization of the induced-charge boundary integral equation.

Energy Technology Data Exchange (ETDEWEB)

Bardhan, J. P.; Eisenberg, R. S.; Gillespie, D.; Rush Univ. Medical Center

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

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

KAUST Repository

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

2010-01-01

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

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

KAUST Repository

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

2016-01-01

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

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

KAUST Repository

Haji Ali, Abdul Lateef

2016-01-06

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

Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

Directory of Open Access Journals (Sweden)

Qinghai Zhao

2015-01-01

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

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

Science.gov (United States)

Khan, Sami Ullah; Ali, Ishtiaq

2018-03-01

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

Collocations in Marine Engineering English

Directory of Open Access Journals (Sweden)

Mirjana Borucinsky

2016-05-01

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

Mobile Collocated Interactions

DEFF Research Database (Denmark)

Lucero, Andrés; Clawson, James; Lyons, Kent

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

A. Karimi Dizicheh

2013-01-01

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

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

International Nuclear Information System (INIS)

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

2008-01-01

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

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

DEFF Research Database (Denmark)

Kolmogorov, Dmitry

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

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

Directory of Open Access Journals (Sweden)

Ali H. Bhrawy

2014-01-01

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

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

NARCIS (Netherlands)

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

2010-01-01

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

Collocation Impact on Team Effectiveness

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M Eccles

2010-11-01

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

Proxemic Mobile Collocated Interactions

DEFF Research Database (Denmark)

Porcheron, Martin; Lucero, Andrés; Quigley, Aaron

2016-01-01

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

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

International Nuclear Information System (INIS)

Lee, Wei-Ming

2012-01-01

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

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Science.gov (United States)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

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

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

International Nuclear Information System (INIS)

Avila, Gustavo; Carrington, Tucker

2015-01-01

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

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

KAUST Repository

Parsani, Matteo

2016-10-04

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

Analysis of an upstream weighted collocation approximation to the transport equation

International Nuclear Information System (INIS)

Shapiro, A.; Pinder, G.F.

1981-01-01

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

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

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

Science.gov (United States)

Goudarzi, Zahra; Moini, M. Raouf

2012-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

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

2016-12-01

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

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

International Nuclear Information System (INIS)

Patra, A.; Saha Ray, S.

2014-01-01

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

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

KAUST Repository

Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

2012-01-01

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

Multi-element probabilistic collocation method in high dimensions

International Nuclear Information System (INIS)

Foo, Jasmine; Karniadakis, George Em

2010-01-01

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

Discrete elements method of neutron transport

International Nuclear Information System (INIS)

Mathews, K.A.

1988-01-01

In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

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

KAUST Repository

Yücel, Abdulkadir C.

2010-07-01

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

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

International Nuclear Information System (INIS)

Maschek, W.

1976-07-01

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

Bessel collocation approach for approximate solutions of Hantavirus infection model

Directory of Open Access Journals (Sweden)

Suayip Yuzbasi

2017-11-01

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

An empirical understanding of triple collocation evaluation measure

Science.gov (United States)

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

2013-04-01

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

Verb-Noun Collocation Proficiency and Academic Years

Directory of Open Access Journals (Sweden)

Fatemeh Ebrahimi-Bazzaz

2014-01-01

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

An embedded formula of the Chebyshev collocation method for stiff problems

Science.gov (United States)

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

2017-12-01

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

Measuring receptive collocational competence across proficiency levels

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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.

International Conference eXtended Discretization MethodS

CERN Document Server

Benvenuti, Elena

2016-01-01

This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.

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

Science.gov (United States)

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

2014-11-01

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

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

Science.gov (United States)

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

2018-01-01

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

Transport survey calculations using the spectral collocation method

International Nuclear Information System (INIS)

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

1989-01-01

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

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

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-05-01

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

Mobile Collocated Interactions With Wearables

DEFF Research Database (Denmark)

Lucero, Andrés; Wilde, Danielle; Robinson, Simon

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

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

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

DEFF Research Database (Denmark)

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

2011-01-01

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

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

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Elaheh Hamed Mahvelati

2012-11-01

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

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

Directory of Open Access Journals (Sweden)

Winfried Auzinger

2006-01-01

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

Slovene-English Contrastive Phraseology: Lexical Collocations

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Primož Jurko

2010-05-01

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

Evaluating a new test of whole English collocations

DEFF Research Database (Denmark)

Revier, Robert Lee

2009-01-01

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

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

Science.gov (United States)

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.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

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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.

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

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Salih Yalcinbas

2016-01-01

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

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

Science.gov (United States)

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

2015-10-01

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

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

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Ishfaq Ahmad Ganaie

2013-01-01

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

The Presentation and Treatment of Collocations as Secondary ...

African Journals Online (AJOL)

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

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

African Journals Online (AJOL)

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

Semantic Analysis of Verbal Collocations with Lexical Functions

CERN Document Server

Gelbukh, Alexander

2013-01-01

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

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

Science.gov (United States)

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

2013-01-01

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

Productive knowledge of collocations may predict academic literacy

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Van Dyk, Tobie

2016-12-01

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

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

African Journals Online (AJOL)

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

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

Science.gov (United States)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Lexical and Grammatical Collocations in Writing Production of EFL Learners

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Maryam Bahardoust

2012-05-01

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

Discrete elements method of neutral particle transport

International Nuclear Information System (INIS)

Mathews, K.A.

1983-01-01

A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-10-01

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

The relationship between productive knowledge of collocations and ...

African Journals Online (AJOL)

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

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

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

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

KAUST Repository

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

2013-01-01

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

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

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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.

Direct Discrete Method for Neutronic Calculations

International Nuclear Information System (INIS)

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

2002-01-01

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

Teaching collocations

DEFF Research Database (Denmark)

Revier, Robert Lee; Henriksen, Birgit

2006-01-01

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

Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors

Czech Academy of Sciences Publication Activity Database

Musil, Tomáš; Jakl, Ondřej

2007-01-01

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

On Collocations and Their Interaction with Parsing and Translation

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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 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.

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

International Nuclear Information System (INIS)

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

2005-01-01

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

Improving academic literacy by teaching collocations | Nizonkiza ...

African Journals Online (AJOL)

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

Application of an efficient Bayesian discretization method to biomedical data

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Gopalakrishnan Vanathi

2011-07-01

Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

Science.gov (United States)

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

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

International Nuclear Information System (INIS)

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

2008-01-01

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

Multiband discrete ordinates method: formalism and results; Methode multibande aux ordonnees discretes: formalisme et resultats

Energy Technology Data Exchange (ETDEWEB)

Luneville, L

1998-06-01

The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author) 15 refs.

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

Science.gov (United States)

Parand, K.; Nikarya, M.

2017-11-01

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

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

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M. Rahimi-Gorji

2015-06-01

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

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

DEFF Research Database (Denmark)

Revier, Robert Lee

2014-01-01

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

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

Science.gov (United States)

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

2018-06-01

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

Systematization of Accurate Discrete Optimization Methods

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V. A. Ovchinnikov

2015-01-01

Full Text Available The object of study of this paper is to define accurate methods for solving combinatorial optimization problems of structural synthesis. The aim of the work is to systemize the exact methods of discrete optimization and define their applicability to solve practical problems.The article presents the analysis, generalization and systematization of classical methods and algorithms described in the educational and scientific literature.As a result of research a systematic presentation of combinatorial methods for discrete optimization described in various sources is given, their capabilities are described and properties of the tasks to be solved using the appropriate methods are specified.

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

KAUST Repository

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

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

khalid ali

2016-11-01

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

Supporting Collocation Learning with a Digital Library

Science.gov (United States)

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

2010-01-01

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

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

African Journals Online (AJOL)

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

Acceleration techniques for the discrete ordinate method

International Nuclear Information System (INIS)

Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas

2013-01-01

In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.

RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

KAUST Repository

Farrell, Patricio; Wendland, Holger

2013-01-01

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

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

African Journals Online (AJOL)

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

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

Directory of Open Access Journals (Sweden)

Qingzhou Mao

2015-06-01

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

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

Science.gov (United States)

2010-10-01

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

HIGHLY-ACCURATE MODEL ORDER REDUCTION TECHNIQUE ON A DISCRETE DOMAIN

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L. D. Ribeiro

2015-09-01

Full Text Available AbstractIn this work, we present a highly-accurate technique of model order reduction applied to staged processes. The proposed method reduces the dimension of the original system based on null values of moment-weighted sums of heat and mass balance residuals on real stages. To compute these sums of weighted residuals, a discrete form of Gauss-Lobatto quadrature was developed, allowing a high degree of accuracy in these calculations. The locations where the residuals are cancelled vary with time and operating conditions, characterizing a desirable adaptive nature of this technique. Balances related to upstream and downstream devices (such as condenser, reboiler, and feed tray of a distillation column are considered as boundary conditions of the corresponding difference-differential equations system. The chosen number of moments is the dimension of the reduced model being much lower than the dimension of the complete model and does not depend on the size of the original model. Scaling of the discrete independent variable related with the stages was crucial for the computational implementation of the proposed method, avoiding accumulation of round-off errors present even in low-degree polynomial approximations in the original discrete variable. Dynamical simulations of distillation columns were carried out to check the performance of the proposed model order reduction technique. The obtained results show the superiority of the proposed procedure in comparison with the orthogonal collocation method.

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

KAUST Repository

Bäck, Joakim

2010-09-17

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

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

African Journals Online (AJOL)

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

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

Science.gov (United States)

Chen, Lidan

2017-01-01

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

RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

KAUST Repository

Farrell, Patricio

2013-01-01

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

Lexical richness and collocational competence in second-language writing

NARCIS (Netherlands)

Vedder, I.; Benigno, V.

2016-01-01

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

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

Directory of Open Access Journals (Sweden)

Xuexia Zhang

2017-04-01

Full Text Available This paper proposes a probabilistic power flow (PPF method considering continuous and discrete variables (continuous and discrete power flow, CDPF for power systems. The proposed method—based on the cumulant method (CM and multiple deterministic power flow (MDPF calculations—can deal with continuous variables such as wind power generation (WPG and loads, and discrete variables such as fuel cell generation (FCG. In this paper, continuous variables follow a normal distribution (loads or a non-normal distribution (WPG, and discrete variables follow a binomial distribution (FCG. Through testing on IEEE 14-bus and IEEE 118-bus power systems, the proposed method (CDPF has better accuracy compared with the CM, and higher efficiency compared with the Monte Carlo simulation method (MCSM.

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

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

International Nuclear Information System (INIS)

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

1983-01-01

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

Discretization vs. Rounding Error in Euler's Method

Science.gov (United States)

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

SPANDOM - source projection analytic nodal discrete ordinates method

International Nuclear Information System (INIS)

Kim, Tae Hyeong; Cho, Nam Zin

1994-01-01

We describe a new discrete ordinates nodal method for the two-dimensional transport equation. We solve the discrete ordinates equation analytically after the source term is projected and represented in polynomials. The method is applied to two fast reactor benchmark problems and compared with the TWOHEX code. The results indicate that the present method accurately predicts not only multiplication factor but also flux distribution

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

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Saudin Saudin

2017-05-01

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

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

African Journals Online (AJOL)

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

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

African Journals Online (AJOL)

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

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

Science.gov (United States)

Chen, Hao-Jan Howard

2011-01-01

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

Digital Resonant Controller based on Modified Tustin Discretization Method

Directory of Open Access Journals (Sweden)

STOJIC, D.

2016-11-01

Full Text Available Resonant controllers are used in power converter voltage and current control due to their simplicity and accuracy. However, digital implementation of resonant controllers introduces problems related to zero and pole mapping from the continuous to the discrete time domain. Namely, some discretization methods introduce significant errors in the digital controller resonant frequency, resulting in the loss of the asymptotic AC reference tracking, especially at high resonant frequencies. The delay compensation typical for resonant controllers can also be compromised. Based on the existing analysis, it can be concluded that the Tustin discretization with frequency prewarping represents a preferable choice from the point of view of the resonant frequency accuracy. However, this discretization method has a shortcoming in applications that require real-time frequency adaptation, since complex trigonometric evaluation is required for each frequency change. In order to overcome this problem, in this paper the modified Tustin discretization method is proposed based on the Taylor series approximation of the frequency prewarping function. By comparing the novel discretization method with commonly used two-integrator-based proportional-resonant (PR digital controllers, it is shown that the resulting digital controller resonant frequency and time delay compensation errors are significantly reduced for the novel controller.

Multiband discrete ordinates method: formalism and results

International Nuclear Information System (INIS)

Luneville, L.

1998-06-01

The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author)

A spectral element-FCT method for the compressible Euler equations

International Nuclear Information System (INIS)

Giannakouros, J.; Karniadakis, G.E.

1994-01-01

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

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

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-07-01

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

The discrete cones method for two-dimensional neutron transport calculations

International Nuclear Information System (INIS)

Watanabe, Y.; Maynard, C.W.

1986-01-01

A novel method, the discrete cones method (DC/sub N/), is proposed as an alternative to the discrete ordinates method (S/sub N/) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by partitioning a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the S/sub N/ method, the ray effects, can be eliminated. The DC/sub N/ method has been formulated for X-Y geometry and a program has been creaed by modifying the standard S/sub N/ program TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty

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

Science.gov (United States)

Nguyen, Thi My Hang; Webb, Stuart

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Şuayip Yüzbaşı

2015-02-01

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

Translating English Idioms and Collocations

Directory of Open Access Journals (Sweden)

Rochayah Machali

2004-01-01

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

A Low Complexity Discrete Radiosity Method

OpenAIRE

Chatelier , Pierre Yves; Malgouyres , Rémy

2006-01-01

International audience; Rather than using Monte Carlo sampling techniques or patch projections to compute radiosity, it is possible to use a discretization of a scene into voxels and perform some discrete geometry calculus to quickly compute visibility information. In such a framework , the radiosity method may be as precise as a patch-based radiosity using hemicube computation for form-factors, but it lowers the overall theoretical complexity to an O(N log N) + O(N), where the O(N) is largel...

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

KAUST Repository

Malenova, G.

2016-09-08

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

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

KAUST Repository

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

2016-01-01

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

Numerical methods for stochastic partial differential equations with white noise

CERN Document Server

Zhang, Zhongqiang

2017-01-01

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

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

KAUST Repository

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

2012-01-01

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

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

KAUST Repository

Beck, Joakim

2012-09-01

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

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

Science.gov (United States)

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

2018-02-01

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

Learning and Teaching L2 Collocations: Insights from Research

Science.gov (United States)

Szudarski, Pawel

2017-01-01

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

Comparative study of discretization methods of microarray data for inferring transcriptional regulatory networks

Directory of Open Access Journals (Sweden)

Ji Wei

2010-10-01

Full Text Available Abstract Background Microarray data discretization is a basic preprocess for many algorithms of gene regulatory network inference. Some common discretization methods in informatics are used to discretize microarray data. Selection of the discretization method is often arbitrary and no systematic comparison of different discretization has been conducted, in the context of gene regulatory network inference from time series gene expression data. Results In this study, we propose a new discretization method "bikmeans", and compare its performance with four other widely-used discretization methods using different datasets, modeling algorithms and number of intervals. Sensitivities, specificities and total accuracies were calculated and statistical analysis was carried out. Bikmeans method always gave high total accuracies. Conclusions Our results indicate that proper discretization methods can consistently improve gene regulatory network inference independent of network modeling algorithms and datasets. Our new method, bikmeans, resulted in significant better total accuracies than other methods.

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

Directory of Open Access Journals (Sweden)

Rafe S. Zaabalawi

2017-01-01

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

Multilevel Fast Multipole Method for Higher Order Discretizations

DEFF Research Database (Denmark)

Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

2014-01-01

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

The Use of English Collocations in Reader's Digest

OpenAIRE

Sinaga, Yudita Putri Nurani; Sinaga, Lidiman Sahat Martua

2014-01-01

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

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1997-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1996-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

Corpora and Collocations in Chinese-English Dictionaries for Chinese Users

Science.gov (United States)

Xia, Lixin

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Irena SRDANOVIĆ

2011-05-01

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

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

Directory of Open Access Journals (Sweden)

Xiaokui Yue

2014-01-01

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

Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks

Science.gov (United States)

Menon, Sujatha; Mukundan, Jayakaran

2012-01-01

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

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

Science.gov (United States)

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

2012-07-01

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

GUESSING VERB-ADVERB COLLOCATIONS: ARAB EFL ...

African Journals Online (AJOL)

user

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

Derivation of new 3D discrete ordinate equations

International Nuclear Information System (INIS)

Ahrens, C. D.

2012-01-01

The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)

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

Directory of Open Access Journals (Sweden)

Muntaha A. Abdulwahid

2017-01-01

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

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

Science.gov (United States)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

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

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

OpenAIRE

Simpson, Adam John

2006-01-01

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

COLLOCATION PHRASES IN RELATION TO OTHER LEXICAL PHRASES IN CROATIAN

Directory of Open Access Journals (Sweden)

Goranka Blagus Bartolec

2012-01-01

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

Relation work in collocated and distributed collaboration

DEFF Research Database (Denmark)

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

2014-01-01

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

Discrete gradient methods for solving variational image regularisation models

International Nuclear Information System (INIS)

Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B

2017-01-01

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)

Discrete linear canonical transform computation by adaptive method.

Science.gov (United States)

Zhang, Feng; Tao, Ran; Wang, Yue

2013-07-29

The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.

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

Directory of Open Access Journals (Sweden)

Miao Haiyan

2015-05-01

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

Influence of discretization method on the digital control system performance

Directory of Open Access Journals (Sweden)

Futás József

2003-12-01

Full Text Available The design of control system can be divided into two steps. First the process or plant have to be convert into mathematical model form, so that its behavior can be analyzed. Then an appropriate controller have to be design in order to get the desired response of the controlled system. In the continuous time domain the system is represented by differential equations. Replacing a continuous system into discrete time form is always an approximation of the continuous system. The different discretization methods give different digital controller performance. The methods presented on the paper are Step Invariant or Zero Order Hold (ZOH Method, Matched Pole-Zero Method, Backward difference Method and Bilinear transformation. The above mentioned discretization methods are used in developing PI position controller of a dc motor. The motor model was converted by the ZOH method. The performances of the different methods are compared and the results are presented.

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

KAUST Repository

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

2011-01-01

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

Sputtering calculations with the discrete ordinated method

International Nuclear Information System (INIS)

Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.

1977-01-01

The purpose of this work is to investigate the applicability of the discrete ordinates (S/sub N/) method to light ion sputtering problems. In particular, the neutral particle discrete ordinates computer code, ANISN, was used to calculate sputtering yields. No modifications to this code were necessary to treat charged particle transport. However, a cross section processing code was written for the generation of multigroup cross sections; these cross sections include a modification to the total macroscopic cross section to account for electronic interactions and small-scattering-angle elastic interactions. The discrete ordinates approach enables calculation of the sputtering yield as functions of incident energy and angle and of many related quantities such as ion reflection coefficients, angular and energy distributions of sputtering particles, the behavior of beams penetrating thin foils, etc. The results of several sputtering problems as calculated with ANISN are presented

Solving the discrete KdV equation with homotopy analysis method

International Nuclear Information System (INIS)

Zou, L.; Zong, Z.; Wang, Z.; He, L.

2007-01-01

In this Letter, we apply the homotopy analysis method to differential-difference equations. We take the discrete KdV equation as an example, and successfully obtain double periodic wave solutions and solitary wave solutions. It illustrates the validity and the great potential of the homotopy analysis method in solving discrete KdV equation. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is very effective and convenient

An Efficient Approach for Identifying Stable Lobes with Discretization Method

Directory of Open Access Journals (Sweden)

Baohai Wu

2013-01-01

Full Text Available This paper presents a new approach for quick identification of chatter stability lobes with discretization method. Firstly, three different kinds of stability regions are defined: absolute stable region, valid region, and invalid region. Secondly, while identifying the chatter stability lobes, three different regions within the chatter stability lobes are identified with relatively large time intervals. Thirdly, stability boundary within the valid regions is finely calculated to get exact chatter stability lobes. The proposed method only needs to test a small portion of spindle speed and cutting depth set; about 89% computation time is savedcompared with full discretization method. It spends only about10 minutes to get exact chatter stability lobes. Since, based on discretization method, the proposed method can be used for different immersion cutting including low immersion cutting process, the proposed method can be directly implemented in the workshop to promote machining parameters selection efficiency.

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

Science.gov (United States)

Macis, Marijana; Schmitt, Norbert

2017-01-01

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

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Zhao, J.M., E-mail: jmzhao@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); Tan, J.Y., E-mail: tanjy@hit.edu.cn [School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China); Liu, L.H., E-mail: lhliu@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China)

2013-01-01

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

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

OpenAIRE

Bergström, Kerstin

2008-01-01

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

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

Kate H

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

Spline methods for conversation equations

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1991-01-01

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

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

International Nuclear Information System (INIS)

Gerstl, S.A.W.; Zardecki, A.

1985-01-01

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

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

Directory of Open Access Journals (Sweden)

Liina Vassiljev

2015-04-01

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

A residual Monte Carlo method for discrete thermal radiative diffusion

International Nuclear Information System (INIS)

Evans, T.M.; Urbatsch, T.J.; Lichtenstein, H.; Morel, J.E.

2003-01-01

Residual Monte Carlo methods reduce statistical error at a rate of exp(-bN), where b is a positive constant and N is the number of particle histories. Contrast this convergence rate with 1/√N, which is the rate of statistical error reduction for conventional Monte Carlo methods. Thus, residual Monte Carlo methods hold great promise for increased efficiency relative to conventional Monte Carlo methods. Previous research has shown that the application of residual Monte Carlo methods to the solution of continuum equations, such as the radiation transport equation, is problematic for all but the simplest of cases. However, the residual method readily applies to discrete systems as long as those systems are monotone, i.e., they produce positive solutions given positive sources. We develop a residual Monte Carlo method for solving a discrete 1D non-linear thermal radiative equilibrium diffusion equation, and we compare its performance with that of the discrete conventional Monte Carlo method upon which it is based. We find that the residual method provides efficiency gains of many orders of magnitude. Part of the residual gain is due to the fact that we begin each timestep with an initial guess equal to the solution from the previous timestep. Moreover, fully consistent non-linear solutions can be obtained in a reasonable amount of time because of the effective lack of statistical noise. We conclude that the residual approach has great potential and that further research into such methods should be pursued for more general discrete and continuum systems

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

Science.gov (United States)

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

2012-01-01

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

New formulation of the discrete element method

Science.gov (United States)

Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon

2018-01-01

A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Sensitivity of Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations

Science.gov (United States)

2016-06-12

Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) and (2) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete Element Method (DEM) can model individual particle directly, and

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

KAUST Repository

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

2016-01-01

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

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

KAUST Repository

Nobile, Fabio

2016-01-09

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

Stochastic Collocation Applications in Computational Electromagnetics

Directory of Open Access Journals (Sweden)

Dragan Poljak

2018-01-01

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

The discrete adjoint method for parameter identification in multibody system dynamics.

Science.gov (United States)

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

International Nuclear Information System (INIS)

Zhu, Jiandao; Collette, Matthew

2015-01-01

The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events

Improving academic literacy by teaching collocations

African Journals Online (AJOL)

Kate H

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

A variational synthesis nodal discrete ordinates method

International Nuclear Information System (INIS)

Favorite, J.A.; Stacey, W.M.

1999-01-01

A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik [Pusan National University, Busan (Korea, Republic of); Jeong, Hae Kwon [POSCO, Pohang (Korea, Republic of); Balachandar, S. [University of Florida, Florida (United States)

2013-02-15

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

International Nuclear Information System (INIS)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik; Jeong, Hae Kwon; Balachandar, S.

2013-01-01

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

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

KAUST Repository

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

2016-01-01

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

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

KAUST Repository

Haji Ali, Abdul Lateef

2016-08-26

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

Evaluating the performance of collocated optical disdrometers: LPM and PARSIVEL

Science.gov (United States)

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

2017-04-01

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

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

Czech Academy of Sciences Publication Activity Database

Anderle, Milan; Čelikovský, Sergej

2017-01-01

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

Communication Collocations of the Lexeme Geld in General and Business German

Directory of Open Access Journals (Sweden)

Mirna Hocenski-Dreiseidl

2010-07-01

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

Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method

DEFF Research Database (Denmark)

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2014-01-01

The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models the probabi......The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models...... the probability distribution of the Y-STR haplotypes. Creating a consistent statistical model of the haplotypes enables us to perform a wide range of analyses. Previously, haplotype frequency estimation using the discrete Laplace method has been validated. In this paper we investigate how the discrete Laplace...... method can be used for cluster analysis to further validate the discrete Laplace method. A very important practical fact is that the calculations can be performed on a normal computer. We identified two sub-clusters of the Eastern and Western European Y-STR haplotypes similar to results of previous...

Evaluation of the streaming-matrix method for discrete-ordinates duct-streaming calculations

International Nuclear Information System (INIS)

Clark, B.A.; Urban, W.T.; Dudziak, D.J.

1983-01-01

A new deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) is applied to two realistic duct-shielding problems. The results are compared to standard discrete-ordinates and Monte Carlo calculations. The SMHM shows promise as an alternative deterministic streaming method to standard discrete-ordinates

From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

Science.gov (United States)

Finster, Felix

This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

Energy Technology Data Exchange (ETDEWEB)

Vaillon, R; Lallemand, M; Lemonnier, D [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France)

1997-12-31

The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

Energy Technology Data Exchange (ETDEWEB)

Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)

1996-12-31

The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

Privacy Data Decomposition and Discretization Method for SaaS Services

Directory of Open Access Journals (Sweden)

Changbo Ke

2017-01-01

Full Text Available In cloud computing, user functional requirements are satisfied through service composition. However, due to the process of interaction and sharing among SaaS services, user privacy data tends to be illegally disclosed to the service participants. In this paper, we propose a privacy data decomposition and discretization method for SaaS services. First, according to logic between the data, we classify the privacy data into discrete privacy data and continuous privacy data. Next, in order to protect the user privacy information, continuous data chains are decomposed into discrete data chain, and discrete data chains are prevented from being synthesized into continuous data chains. Finally, we propose a protection framework for privacy data and demonstrate its correctness and feasibility with experiments.

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

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

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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.

Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem

Science.gov (United States)

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

2015-12-01

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

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

Directory of Open Access Journals (Sweden)

Liang Xue

2018-04-01

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

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

Directory of Open Access Journals (Sweden)

Vasily A. Belyaev

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Mustapha Hajebi

2017-12-01

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

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

KAUST Repository

Nobile, Fabio

2014-01-06

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-05-15

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

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

Science.gov (United States)

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

2015-10-01

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

A fourth order spline collocation approach for a business cycle model

Science.gov (United States)

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

2013-10-01

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

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

Directory of Open Access Journals (Sweden)

Moisés Almela

2011-10-01

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

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

International Nuclear Information System (INIS)

Ma Xiang; Zabaras, Nicholas

2009-01-01

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

The discrete cones methods for two-dimensional neutral particle transport problems with voids

International Nuclear Information System (INIS)

Watanabe, Y.; Maynard, C.W.

1983-01-01

One of the most widely applied deterministic methods for time-independent, two-dimensional neutron transport calculations is the discrete ordinates method (DSN). The DSN solution, however, fails to be accurate in a void due to the ray effect. In order to circumvent this drawback, the authors have been developing a novel approximation: the discrete cones method (DCN), where a group of particles in a cone are simultaneously traced instead of particles in discrete directions for the DSN method. Programs, which apply to the DSN method in a non-vacuum region and the DCN method in a void, have been written for transport calculations in X-Y coordinates. The solutions for test problems demonstrate mitigation of the ray effect in voids without loosing the computational efficiency of the DSN method

Development of three-dimensional program based on Monte Carlo and discrete ordinates bidirectional coupling method

International Nuclear Information System (INIS)

Han Jingru; Chen Yixue; Yuan Longjun

2013-01-01

The Monte Carlo (MC) and discrete ordinates (SN) are the commonly used methods in the design of radiation shielding. Monte Carlo method is able to treat the geometry exactly, but time-consuming in dealing with the deep penetration problem. The discrete ordinate method has great computational efficiency, but it is quite costly in computer memory and it suffers from ray effect. Single discrete ordinates method or single Monte Carlo method has limitation in shielding calculation for large complex nuclear facilities. In order to solve the problem, the Monte Carlo and discrete ordinates bidirectional coupling method is developed. The bidirectional coupling method is implemented in the interface program to transfer the particle probability distribution of MC and angular flux of discrete ordinates. The coupling method combines the advantages of MC and SN. The test problems of cartesian and cylindrical coordinate have been calculated by the coupling methods. The calculation results are performed with comparison to MCNP and TORT and satisfactory agreements are obtained. The correctness of the program is proved. (authors)

Discrete ordinates transport methods for problems with highly forward-peaked scattering

International Nuclear Information System (INIS)

Pautz, S.D.

1998-04-01

The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Improvement of spatial discretization error on the semi-analytic nodal method using the scattered source subtraction method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro

2006-01-01

In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)

Accurate Evaluation of European and American Options Under the CGMY Process

NARCIS (Netherlands)

Almendral, A.; Oosterlee, C.W.

2007-01-01

A finite?difference method for integro?differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second?order

The large discretization step method for time-dependent partial differential equations

Science.gov (United States)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Multimodal interaction design in collocated mobile phone use

NARCIS (Netherlands)

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

2011-01-01

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

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

Directory of Open Access Journals (Sweden)

Dušan Gabrovšek

2014-05-01

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

Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

Directory of Open Access Journals (Sweden)

Sandvik Leiv

2011-04-01

Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

Discrete variational methods and their application to electronic structures

International Nuclear Information System (INIS)

Ellis, D.E.

1987-01-01

Some general concepts concerning Discrete Variational methods are developed and applied to problems of determination of eletronic spectra, charge densities and bonding of free molecules, surface-chemisorbed species and bulk solids. (M.W.O.) [pt

Diffusion-synthetic acceleration methods for discrete-ordinates problems

International Nuclear Information System (INIS)

Larsen, E.W.

1984-01-01

The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems an the status of current efforts aimed at solving these problems

Discrete Element Modeling

Energy Technology Data Exchange (ETDEWEB)

Morris, J; Johnson, S

2007-12-03

The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

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

African Journals Online (AJOL)

user

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

Analysis of a discrete element method and coupling with a compressible fluid flow method

International Nuclear Information System (INIS)

Monasse, L.

2011-01-01

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2010-01-01

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

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

DEFF Research Database (Denmark)

Henriksen, Birgit; Westbrook, Pete

2017-01-01

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

A generalized endogenous grid method for discrete-continuous choice

OpenAIRE

John Rust; Bertel Schjerning; Fedor Iskhakov

2012-01-01

This paper extends Carroll's endogenous grid method (2006 "The method of endogenous gridpoints for solving dynamic stochastic optimization problems", Economic Letters) for models with sequential discrete and continuous choice. Unlike existing generalizations, we propose solution algorithm that inherits both advantages of the original method, namely it avoids all root finding operations, and also efficiently deals with restrictions on the continuous decision variable. To further speed up the s...

Discrete Data Qualification System and Method Comprising Noise Series Fault Detection

Science.gov (United States)

Fulton, Christopher; Wong, Edmond; Melcher, Kevin; Bickford, Randall

2013-01-01

A Sensor Data Qualification (SDQ) function has been developed that allows the onboard flight computers on NASA s launch vehicles to determine the validity of sensor data to ensure that critical safety and operational decisions are not based on faulty sensor data. This SDQ function includes a novel noise series fault detection algorithm for qualification of the output data from LO2 and LH2 low-level liquid sensors. These sensors are positioned in a launch vehicle s propellant tanks in order to detect propellant depletion during a rocket engine s boost operating phase. This detection capability can prevent the catastrophic situation where the engine operates without propellant. The output from each LO2 and LH2 low-level liquid sensor is a discrete valued signal that is expected to be in either of two states, depending on whether the sensor is immersed (wet) or exposed (dry). Conventional methods for sensor data qualification, such as threshold limit checking, are not effective for this type of signal due to its discrete binary-state nature. To address this data qualification challenge, a noise computation and evaluation method, also known as a noise fault detector, was developed to detect unreasonable statistical characteristics in the discrete data stream. The method operates on a time series of discrete data observations over a moving window of data points and performs a continuous examination of the resulting observation stream to identify the presence of anomalous characteristics. If the method determines the existence of anomalous results, the data from the sensor is disqualified for use by other monitoring or control functions.

The discrete ordinates method for solving the azimuthally dependent transport equation in plane geometry

International Nuclear Information System (INIS)

Chalhoub, Ezzat Selim

1997-01-01

The method of discrete ordinates is applied to the solution of the slab albedo problem with azimuthal dependence in transport theory. A new set of quadratures appropriate to the problem is introduced. In addition to the ANISN code, modified to include the proposed formalism, two new programs, PEESNC and PEESNA, which were created on the basis of the discrete ordinates formalism, using the direct integration method and the analytic solution method respectively, are used in the generation of results for a few sample problems. Program PEESNC was created to validate the results obtained with the discrete ordinates method and the finite difference approximation (ANISN), while program PEESNA was developed in order to implement an analytical discrete ordinates formalism, which provides more accurate results. The obtained results for selected sample problems are compared with highly accurate numerical results published in the literature. Compared to ANISN and PEESNC, program PEESNA presents a greater efficiency in execution time and much more precise numerical results. (author)

The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks

DEFF Research Database (Denmark)

Iskhakov, Fedor; Jørgensen, Thomas H.; Rust, John

2017-01-01

We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid-point method (EGM) to discrete-continuous (DC) p...

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

International Nuclear Information System (INIS)

Norris, Edward T.; Liu, Xin; Hsieh, Jiang

2015-01-01

Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

DEFF Research Database (Denmark)

Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

2014-01-01

The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...

Time dependence linear transport III convergence of the discrete ordinate method

International Nuclear Information System (INIS)

Wilson, D.G.

1983-01-01

In this paper the uniform pointwise convergence of the discrete ordinate method for weak and strong solutions of the time dependent, linear transport equation posed in a multidimensional, rectangular parallelepiped with partially reflecting walls is established. The first result is that a sequence of discrete ordinate solutions converges uniformly on the quadrature points to a solution of the continuous problem provided that the corresponding sequence of truncation errors for the solution of the continuous problem converges to zero in the same manner. The second result is that continuity of the solution with respect to the velocity variables guarantees that the truncation erros in the quadrature formula go the zero and hence that the discrete ordinate approximations converge to the solution of the continuous problem as the discrete ordinate become dense. An existence theory for strong solutions of the the continuous problem follows as a result

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

Directory of Open Access Journals (Sweden)

Shuang Wang

2012-01-01

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

A parametric level-set method for partially discrete tomography

NARCIS (Netherlands)

A. Kadu (Ajinkya); T. van Leeuwen (Tristan); K.J. Batenburg (Joost)

2017-01-01

textabstractThis paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We express the geometry of the anomaly using a level-set function,

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

Science.gov (United States)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

Directory of Open Access Journals (Sweden)

H. O. Bakodah

2013-01-01

Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

Optimization of Low-Thrust Spiral Trajectories by Collocation

Science.gov (United States)

Falck, Robert D.; Dankanich, John W.

2012-01-01

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

A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

International Nuclear Information System (INIS)

Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

2015-01-01

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that

Formal methods for discrete-time dynamical systems

CERN Document Server

Belta, Calin; Aydin Gol, Ebru

2017-01-01

This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Application of network methods for understanding evolutionary dynamics in discrete habitats.

Science.gov (United States)

Greenbaum, Gili; Fefferman, Nina H

2017-06-01

In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.

Application of direct discrete method (DDM) to multigroup neutron transport problems

International Nuclear Information System (INIS)

Vosoughi, Naser; Salehi, Ali Akbar; Shahriari, Majid

2003-01-01

The Direct Discrete Method (DDM), which produced excellent results for one-group neutron transport problems, has been developed for multigroup energy. A multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without associated coolant regions with two boundary conditions. The calculations are illustrated for two-group energy by graphs showing the fast and thermal fluxes. The validity of the results are tested against the results obtained by the ANISN code. (author)

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

Science.gov (United States)

Ying, Yang

2015-01-01

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

Modelling of Granular Materials Using the Discrete Element Method

DEFF Research Database (Denmark)

Ullidtz, Per

1997-01-01

With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...

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

Energy Technology Data Exchange (ETDEWEB)

Alwan, Aravind; Aluru, N.R.

2013-12-15

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

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

International Nuclear Information System (INIS)

Alwan, Aravind; Aluru, N.R.

2013-01-01

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

Diffusion-synthetic acceleration methods for the discrete-ordinates equations

International Nuclear Information System (INIS)

Larsen, E.W.

1983-01-01

The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas beind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems

Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

International Nuclear Information System (INIS)

Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

2005-01-01

In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

Discrete Ordinates Method-Like Computation with Group Condensation and Angle Collapsing in Transport Theory

International Nuclear Information System (INIS)

Won, Jong Hyuck; Cho, Nam Zin

2010-01-01

In group condensation for transport method, it is well-known that angle-dependent total cross section is generated. To remove this difficulty on angledependent total cross section, we normally perform the group condensation on total cross section by using scalar flux weight as used in neutron diffusion method. In this study, angle-dependent total cross section is directly applied to the discrete ordinates method. In addition, angle collapsing concept is introduced based on equivalence to reduce calculational burden of transport computation. We also show numerical results for a heterogeneous 1-D slab problem with local/global iteration, in which fine-group discrete ordinates calculation is used in local problem while few-group angle collapsed discrete ordinates calculation is used in global problem iteratively

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

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Mohsen Shahrokhi

2014-05-01

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

Application of methods of discrete mathematics at modular synthesis of mechatronic devices

OpenAIRE

Nikiforov, S.; Nikiforov, B.; Mandarov, E.; Rabdanova, N.

2010-01-01

The article is devoted to application of methods of discrete mathematics (the theory of counts, the method of matrix code and others) and synthesis of executive mechanisms of mechatronic handling devices

Comparison of the methods for discrete approximation of the fractional-order operator

Directory of Open Access Journals (Sweden)

Zborovjan Martin

2003-12-01

Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

Representation of discrete Steklov-Poincare operator arising in domain decomposition methods in wavelet basis

Energy Technology Data Exchange (ETDEWEB)

Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)

1996-12-31

This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.

On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

KAUST Repository

Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

2014-01-01

SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.

On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

KAUST Repository

Collier, Nathan

2014-09-17

SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

Discrete variational derivative method a structure-preserving numerical method for partial differential equations

CERN Document Server

Furihata, Daisuke

2010-01-01

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

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

Directory of Open Access Journals (Sweden)

Postolea Sorina

2016-12-01

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

Simplified discrete ordinates method in spherical geometry

International Nuclear Information System (INIS)

Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.

1999-01-01

The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations

General method to find the attractors of discrete dynamic models of biological systems

Science.gov (United States)

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

General method to find the attractors of discrete dynamic models of biological systems.

Science.gov (United States)

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

An energy recondensation method using the discrete generalized multigroup energy expansion theory

International Nuclear Information System (INIS)

Zhu Lei; Forget, Benoit

2011-01-01

Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.

Wielandt method applied to the diffusion equations discretized by finite element nodal methods

International Nuclear Information System (INIS)

Mugica R, A.; Valle G, E. del

2003-01-01

Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)

Infrared and visual image fusion method based on discrete cosine transform and local spatial frequency in discrete stationary wavelet transform domain

Science.gov (United States)

Jin, Xin; Jiang, Qian; Yao, Shaowen; Zhou, Dongming; Nie, Rencan; Lee, Shin-Jye; He, Kangjian

2018-01-01

In order to promote the performance of infrared and visual image fusion and provide better visual effects, this paper proposes a hybrid fusion method for infrared and visual image by the combination of discrete stationary wavelet transform (DSWT), discrete cosine transform (DCT) and local spatial frequency (LSF). The proposed method has three key processing steps. Firstly, DSWT is employed to decompose the important features of the source image into a series of sub-images with different levels and spatial frequencies. Secondly, DCT is used to separate the significant details of the sub-images according to the energy of different frequencies. Thirdly, LSF is applied to enhance the regional features of DCT coefficients, and it can be helpful and useful for image feature extraction. Some frequently-used image fusion methods and evaluation metrics are employed to evaluate the validity of the proposed method. The experiments indicate that the proposed method can achieve good fusion effect, and it is more efficient than other conventional image fusion methods.

Discrete nodal integral transport-theory method for multidimensional reactor physics and shielding calculations

International Nuclear Information System (INIS)

Lawrence, R.D.; Dorning, J.J.

1980-01-01

A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method

Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

DEFF Research Database (Denmark)

Johansen, Villads Egede

2015-01-01

The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer proble...

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

Science.gov (United States)

Zhang, D.; Liao, Q.

2016-12-01

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

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

Directory of Open Access Journals (Sweden)

Pentti Järvi

2004-10-01

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

An application of multigrid methods for a discrete elastic model for epitaxial systems

International Nuclear Information System (INIS)

Caflisch, R.E.; Lee, Y.-J.; Shu, S.; Xiao, Y.-X.; Xu, J.

2006-01-01

We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief

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

Science.gov (United States)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

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

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

Directory of Open Access Journals (Sweden)

Suleiman Banihani

2013-01-01

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

Particular solution of the discrete-ordinate method.

Science.gov (United States)

Qin, Yi; Box, Michael A; Jupp, David L

2004-06-20

We present two methods that can be used to derive the particular solution of the discrete-ordinate method (DOM) for an arbitrary source in a plane-parallel atmosphere, which allows us to solve the transfer equation 12-18% faster in the case of a single beam source and is even faster for the atmosphere thermal emission source. We also remove the divide by zero problem that occurs when a beam source coincides with a Gaussian quadrature point. In our implementation, solution for multiple sources can be obtained simultaneously. For each extra source, it costs only 1.3-3.6% CPU time required for a full solution. The GDOM code that we developed previously has been revised to integrate with the DOM. Therefore we are now able to compute the Green's function and DOM solutions simultaneously.

An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

Science.gov (United States)

Subramanian, Ramanathan Vishnampet Ganapathi

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme

Discrete Particle Method for Simulating Hypervelocity Impact Phenomena

Directory of Open Access Journals (Sweden)

Erkai Watson

2017-04-01

Full Text Available In this paper, we introduce a computational model for the simulation of hypervelocity impact (HVI phenomena which is based on the Discrete Element Method (DEM. Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms-1. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

Science.gov (United States)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Discrete calculus methods for counting

CERN Document Server

Mariconda, Carlo

2016-01-01

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...

The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

Institute of Scientific and Technical Information of China (English)

YanpingCHEN; YunqingHUANG

1998-01-01

This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Discrete method for design of flow distribution in manifolds

International Nuclear Information System (INIS)

Wang, Junye; Wang, Hualin

2015-01-01

Flow in manifold systems is encountered in designs of various industrial processes, such as fuel cells, microreactors, microchannels, plate heat exchanger, and radial flow reactors. The uniformity of flow distribution in manifold is a key indicator for performance of the process equipment. In this paper, a discrete method for a U-type arrangement was developed to evaluate the uniformity of the flow distribution and the pressure drop and then was used for direct comparisons between the U-type and the Z-type. The uniformity of the U-type is generally better than that of the Z-type in most of cases for small ζ and large M. The U-type and the Z-type approach each other as ζ increases or M decreases. However, the Z-type is more sensitive to structures than the U-type and approaches uniform flow distribution faster than the U-type as M decreases or ζ increases. This provides a simple yet powerful tool for the designers to evaluate and select a flow arrangement and offers practical measures for industrial applications. - Highlights: • Discrete methodology of flow field designs in manifolds with U-type arrangements. • Quantitative comparison between U-type and Z-type arrangements. • Discrete solution of flow distribution with varying flow coefficients. • Practical measures and guideline to design of manifold systems.

A discrete optimization method for nuclear fuel management

International Nuclear Information System (INIS)

Argaud, J.P.

1993-01-01

Nuclear fuel management can be seen as a large discrete optimization problem under constraints, and optimization methods on such problems are numerically costly. After an introduction of the main aspects of nuclear fuel management, this paper presents a new way to treat the combinatorial problem by using information included in the gradient of optimized cost function. A new search process idea is to choose, by direct observation of the gradient, the more interesting changes in fuel loading patterns. An example is then developed to illustrate an operating mode of the method. Finally, connections with classical simulated annealing and genetic algorithms are described as an attempt to improve search processes. 16 refs., 2 figs

Applications of discrete element method in modeling of grain postharvest operations

Science.gov (United States)

Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

New developments in the discrete ordinate method for the resolution of the radiative transfer equation

International Nuclear Information System (INIS)

Ben Jaffel, L.; Vidal-Madjar, A.

1989-01-01

The discrete ordinate method for the resolution of the radiative transfer equation is developed. We show that the construction of a quasi-analytical solution to the corresponding matrix diagonalization problem reduces the time calculation and allows the use of more dense discrete frequency and angle grids. Comparison with previous work is made, showing that the present method reduces by more than a factor of ten the computational time, and is more appropriate in all cases

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

Directory of Open Access Journals (Sweden)

V. P. Shapeev

2014-01-01

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

Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Pade approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings

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

DEFF Research Database (Denmark)

Simurda, Matej; Lassen, Benny; Duggen, Lars

2017-01-01

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

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Discrete event simulation of crop operations in sweet pepper in support of work method innovation

NARCIS (Netherlands)

Ooster, van 't Bert; Aantjes, Wiger; Melamed, Z.

2017-01-01

Greenhouse Work Simulation, GWorkS, is a model that simulates crop operations in greenhouses for the purpose of analysing work methods. GWorkS is a discrete event model that approaches reality as a discrete stochastic dynamic system. GWorkS was developed and validated using cut-rose as a case

Time Discretization Techniques

KAUST Repository

Gottlieb, S.; Ketcheson, David I.

2016-01-01

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

Dynamic modeling method for infrared smoke based on enhanced discrete phase model

Science.gov (United States)

Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo

2018-03-01

The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

International Nuclear Information System (INIS)

Coelho, Pedro J.

2014-01-01

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

Adaptive Discrete Hypergraph Matching.

Science.gov (United States)

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

Yunying Zheng

2011-01-01

Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.

Discrete Element Method simulations of standing jumps in granular flows down inclines

Directory of Open Access Journals (Sweden)

Méjean Ségolène

2017-01-01

Full Text Available This paper describes a numerical set-up which uses Discrete Element Method to produce standing jumps in flows of dry granular materials down a slope in two dimensions. The grain-scale force interactions are modeled by a visco-elastic normal force and an elastic tangential force with a Coulomb threshold. We will show how it is possible to reproduce all the shapes of the jumps observed in a previous laboratory study: diffuse versus steep jumps and compressible versus incompressible jumps. Moreover, we will discuss the additional measurements that can be done thanks to discrete element modelling.

Modeling of asphalt by means of discrete element method – an initial study

DEFF Research Database (Denmark)

Feng, Huan; Hededal, Ole; Stang, Henrik

of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples....... Results from initial tests will be presented and the future development of the model towards characterising asphalt from its composition will be outlined....

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre

2017-04-19

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

Science.gov (United States)

Sarvari, S. M. Hosseini

2017-09-01

The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

Science.gov (United States)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

International Nuclear Information System (INIS)

Ching, J.T.

1975-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms

Gimme Context – towards New Domain-Specific Collocational Dictionaries

Directory of Open Access Journals (Sweden)

Sylvana Krausse

2011-04-01

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

A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

International Nuclear Information System (INIS)

Vargas, L.

1988-01-01

The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

Strategies in Translating Collocations in Religious Texts from Arabic into English

Science.gov (United States)

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

2010-01-01

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

Comparison of the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering.

Science.gov (United States)

da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques

2003-12-01

Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

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

KAUST Repository

Castrillon, Julio

2016-03-02

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

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

KAUST Repository

Beck, Joakim

2011-12-22

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

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

Science.gov (United States)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

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

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Energy Technology Data Exchange (ETDEWEB)

Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

2006-01-01

Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

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

A simple method of chaos control for a class of chaotic discrete-time systems

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing

2005-01-01

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system

Compatible Spatial Discretizations for Partial Differential Equations

Energy Technology Data Exchange (ETDEWEB)

Arnold, Douglas, N, ed.

2004-11-25

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

The adaptive collision source method for discrete ordinates radiation transport

International Nuclear Information System (INIS)

Walters, William J.; Haghighat, Alireza

2017-01-01

Highlights: • A new adaptive quadrature method to solve the discrete ordinates transport equation. • The adaptive collision source (ACS) method splits the flux into n’th collided components. • Uncollided flux requires high quadrature; this is lowered with number of collisions. • ACS automatically applies appropriate quadrature order each collided component. • The adaptive quadrature is 1.5–4 times more efficient than uniform quadrature. - Abstract: A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.

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

KAUST Repository

Farrell, Patricio

2015-04-30

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

The ADO-nodal method for solving two-dimensional discrete ordinates transport problems

International Nuclear Information System (INIS)

Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da

2017-01-01

Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.

Research on a Hierarchical Dynamic Automatic Voltage Control System Based on the Discrete Event-Driven Method

Directory of Open Access Journals (Sweden)

Yong Min

2013-06-01

Full Text Available In this paper, concepts and methods of hybrid control systems are adopted to establish a hierarchical dynamic automatic voltage control (HD-AVC system, realizing the dynamic voltage stability of power grids. An HD-AVC system model consisting of three layers is built based on the hybrid control method and discrete event-driven mechanism. In the Top Layer, discrete events are designed to drive the corresponding control block so as to avoid solving complex multiple objective functions, the power system’s characteristic matrix is formed and the minimum amplitude eigenvalue (MAE is calculated through linearized differential-algebraic equations. MAE is applied to judge the system’s voltage stability and security and construct discrete events. The Middle Layer is responsible for management and operation, which is also driven by discrete events. Control values of the control buses are calculated based on the characteristics of power systems and the sensitivity method. Then control values generate control strategies through the interface block. In the Bottom Layer, various control devices receive and implement the control commands from the Middle Layer. In this way, a closed-loop power system voltage control is achieved. Computer simulations verify the validity and accuracy of the HD-AVC system, and verify that the proposed HD-AVC system is more effective than normal voltage control methods.

Colorimetric determination of nitrate plus nitrite in water by enzymatic reduction, automated discrete analyzer methods

Science.gov (United States)

Patton, Charles J.; Kryskalla, Jennifer R.

2011-01-01

This report documents work at the U.S. Geological Survey (USGS) National Water Quality Laboratory (NWQL) to validate enzymatic reduction, colorimetric determinative methods for nitrate + nitrite in filtered water by automated discrete analysis. In these standard- and low-level methods (USGS I-2547-11 and I-2548-11), nitrate is reduced to nitrite with nontoxic, soluble nitrate reductase rather than toxic, granular, copperized cadmium used in the longstanding USGS automated continuous-flow analyzer methods I-2545-90 (NWQL laboratory code 1975) and I-2546-91 (NWQL laboratory code 1979). Colorimetric reagents used to determine resulting nitrite in aforementioned enzymatic- and cadmium-reduction methods are identical. The enzyme used in these discrete analyzer methods, designated AtNaR2 by its manufacturer, is produced by recombinant expression of the nitrate reductase gene from wall cress (Arabidopsis thaliana) in the yeast Pichia pastoris. Unlike other commercially available nitrate reductases we evaluated, AtNaR2 maintains high activity at 37°C and is not inhibited by high-phenolic-content humic acids at reaction temperatures in the range of 20°C to 37°C. These previously unrecognized AtNaR2 characteristics are essential for successful performance of discrete analyzer nitrate + nitrite assays (henceforth, DA-AtNaR2) described here.

A new method of simulating fiber suspensions and applications to channel Flows

KAUST Repository

Yang, Wei

2012-06-01

A successive iteration method is proposed to numerically simulate fiber suspensions. The computational field is discretized with the collocated finite volume method, and an ergodic hypothesis is adopted to greatly accelerate the solution to the Fokker - Planck equation. The method is employed in channel flows with different fiber volume fractions and aspect ratios, and its effectiveness is proved. The numerical results show that the existence of fibers significantly changes the pressure distribution, and the fiber aspect ratio has a greater effect on the velocity profile than on the volume faction. At the center of the channel, the velocity increases along the streamwise direction, while the velocity near the wall decreases slightly. The uncoupling and coupling solutions of the additional stress of the fiber suspensions are quite different. © 2012 Chinese Physical Society and IOP Publishing Ltd.

A new method of simulating fiber suspensions and applications to channel Flows

KAUST Repository

Yang, Wei; Zhou, Kun

2012-01-01

A successive iteration method is proposed to numerically simulate fiber suspensions. The computational field is discretized with the collocated finite volume method, and an ergodic hypothesis is adopted to greatly accelerate the solution to the Fokker - Planck equation. The method is employed in channel flows with different fiber volume fractions and aspect ratios, and its effectiveness is proved. The numerical results show that the existence of fibers significantly changes the pressure distribution, and the fiber aspect ratio has a greater effect on the velocity profile than on the volume faction. At the center of the channel, the velocity increases along the streamwise direction, while the velocity near the wall decreases slightly. The uncoupling and coupling solutions of the additional stress of the fiber suspensions are quite different. © 2012 Chinese Physical Society and IOP Publishing Ltd.

Fracture Failure of Reinforced Concrete Slabs Subjected to Blast Loading Using the Combined Finite-Discrete Element Method

Directory of Open Access Journals (Sweden)

Z. M. Jaini

Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.

Measuring Patient Preferences: An Overview of Methods with a Focus on Discrete Choice Experiments.

Science.gov (United States)

Hazlewood, Glen S

2018-05-01

There is increasing recognition of the importance of patient preferences and methodologies to measure them. In this article, methods to quantify patient preferences are reviewed, with a focus on discrete choice experiments. In a discrete choice experiment, patients are asked to choose between 2 or more treatments. The results can be used to quantify the relative importance of treatment outcomes and/or other considerations relevant to medical decision making. Conducting and interpreting a discrete choice experiment requires multiple steps and an understanding of the potential biases that can arise, which we review in this article with examples in rheumatic diseases. Copyright © 2018 Elsevier Inc. All rights reserved.

A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

OpenAIRE

Fedorenko, Sergei V.

2011-01-01

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

Science.gov (United States)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2012-01-01

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

Science.gov (United States)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

On simulation of no-slip condition in the method of discrete vortices

Science.gov (United States)

Shmagunov, O. A.

2017-10-01

When modeling flows of an incompressible fluid, it is convenient sometimes to use the method of discrete vortices (MDV), where the continuous vorticity field is approximated by a set of discrete vortex elements moving in the velocity field. The vortex elements have a clear physical interpretation, they do not require the construction of grids and are automatically adaptive, since they concentrate in the regions of greatest interest and successfully describe the flows of a non-viscous fluid. The possibility of using MDV in simulating flows of a viscous fluid was considered in the previous papers using the examples of flows past bodies with sharp edges with the no-penetration condition at solid boundaries. However, the appearance of vorticity on smooth boundaries requires the no-slip condition to be met when MDV is realized, which substantially complicates the initially simple method. In this connection, an approach is considered that allows solving the problem by simple means.

Improved stochastic approximation methods for discretized parabolic partial differential equations

Science.gov (United States)

Guiaş, Flavius

2016-12-01

We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

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

Science.gov (United States)

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

2017-02-01

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

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

Science.gov (United States)

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

Teaching vocabulary using collocations versus using definitions in EFL classes

OpenAIRE

Altınok, Şerife İper

2000-01-01

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

On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

International Nuclear Information System (INIS)

Barichello, L.B.; Siewert, C.E.

1998-01-01

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given

Discrete control systems

CERN Document Server

Okuyama, Yoshifumi

2014-01-01

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

Science.gov (United States)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Numerical solution of boundary-integral equations for molecular electrostatics.

Science.gov (United States)

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

A Laplace transform method for energy multigroup hybrid discrete ordinates

International Nuclear Information System (INIS)

Segatto, C.F.; Vilhena, M.T.; Barros, R.C.

2010-01-01

In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.

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

Directory of Open Access Journals (Sweden)

Jun Zhang

2018-01-01

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

Space discretization in SN methods: Features, improvements and convergence patterns

International Nuclear Information System (INIS)

Coppa, G.G.M.; Lapenta, G.; Ravetto, P.

1990-01-01

A comparative analysis of the space discretization schemes currently used in S N methods is performed and special attention is devoted to direct integration techniques. Some improvements are proposed in one- and two-dimensional applications, which are based on suitable choices for the spatial variation of the collision source. A study of the convergence pattern is carried out for eigenvalue calculations within the space asymptotic approximation by means of both analytical and numerical investigations. (orig.) [de

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics

International Nuclear Information System (INIS)

Le Bourdiec, S.

2007-03-01

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

Improved treatment of two-dimensional neutral particle transport through voids within the discrete ordinates method by use of generalized view factors

International Nuclear Information System (INIS)

Brockmann, H.

1992-01-01

Using the discrete ordinates method for the treatment of neutral particle transport through voids serious flux distortions may occur due to the restricted streaming of particles along discrete directions. For mitigating this type of ray effect the method of view factors is proposed which has been developed in the theory of thermal radiation for describing the radiant exchange among surfaces. In order to apply this method to transport theory generalized view factors are defined which regard the angular dependence of the radiation leaving the surfaces. The generalized view factors are calculated analytically for r-z cylinder geometries and by applying the view factor algebra. The method was realized in the discrete ordinates transport code DOT 4.2 and applied to an r-z analogue of the S I S (Square-In-Square) sample problem. The results of the proposed method are compared with those calculated by the common discrete ordinates method and the Monte Carlo method

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

Science.gov (United States)

Delzanno, G. L.

2015-11-01

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels.

Science.gov (United States)

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Science.gov (United States)

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

A discrete ordinate response matrix method for massively parallel computers

International Nuclear Information System (INIS)

Hanebutte, U.R.; Lewis, E.E.

1991-01-01

A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

International Nuclear Information System (INIS)

Berthe, P.M.

2013-01-01

In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

The basis spline method and associated techniques

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1989-01-01

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

Applications of the discrete element method in mechanical engineering

International Nuclear Information System (INIS)

Fleissner, Florian; Gaugele, Timo; Eberhard, Peter

2007-01-01

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

International Nuclear Information System (INIS)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-01-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

Science.gov (United States)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-10-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter-Gummel scheme to non-Boltzmann (e.g. Fermi-Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

A Semi-Discrete Landweber-Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information

Science.gov (United States)

Vogelgesang, Jonas; Schorr, Christian

2016-12-01

We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.

Novel Discrete Element Method for 3D non-spherical granular particles.

Science.gov (United States)

Seelen, Luuk; Padding, Johan; Kuipers, Hans

2015-11-01

Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.

Dimension Reduction and Discretization in Stochastic Problems by Regression Method

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

1996-01-01

The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ...

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

A low noise discrete velocity method for the Boltzmann equation with quantized rotational and vibrational energy

Science.gov (United States)

Clarke, Peter; Varghese, Philip; Goldstein, David

2018-01-01

A discrete velocity method is developed for gas mixtures of diatomic molecules with both rotational and vibrational energy states. A full quantized model is described, and rotation-translation and vibration-translation energy exchanges are simulated using a Larsen-Borgnakke exchange model. Elastic and inelastic molecular interactions are modeled during every simulated collision to help produce smooth internal energy distributions. The method is verified by comparing simulations of homogeneous relaxation by our discrete velocity method to numerical solutions of the Jeans and Landau-Teller equations, and to direct simulation Monte Carlo. We compute the structure of a 1D shock using this method, and determine how the rotational energy distribution varies with spatial location in the shock and with position in velocity space.

The linear characteristic method for spatially discretizing the discrete ordinates equations in (x,y)-geometry

International Nuclear Information System (INIS)

Larsen, E.W.; Alcouffe, R.E.

1981-01-01

In this article a new linear characteristic (LC) spatial differencing scheme for the discrete ordinates equations in (x,y)-geometry is described and numerical comparisons are given with the diamond difference (DD) method. The LC method is more stable with mesh size and is generally much more accurate than the DD method on both fine and coarse meshes, for eigenvalue and deep penetration problems. The LC method is based on computations involving the exact solution of a cell problem which has spatially linear boundary conditions and interior source. The LC method is coupled to the diffusion synthetic acceleration (DSA) algorithm in that the linear variations of the source are determined in part by the results of the DSA calculation from the previous inner iteration. An inexpensive negative-flux fixup is used which has very little effect on the accuracy of the solution. The storage requirements for LC are essentially the same as that for DD, while the computational times for LC are generally less than twice the DD computational times for the same mesh. This increase in computational cost is offset if one computes LC solutions on somewhat coarser meshes than DD; the resulting LC solutions are still generally much more accurate than the DD solutions. (orig.) [de

Solving Hammerstein Type Integral Equation by New Discrete Adomian Decomposition Methods

Directory of Open Access Journals (Sweden)

Huda O. Bakodah

2013-01-01

Full Text Available New discrete Adomian decomposition methods are presented by using some identified Clenshaw-Curtis quadrature rules. We investigate two mixed quadrature rules one of precision five and the other of precision seven. The first rule is formed by using the Fejér second rule of precision three and Simpson rule of precision three, while the second rule is formed by using the Fejér second rule of precision five and the Boole rule of precision five. Our methods were applied to a nonlinear integral equation of the Hammerstein type and some examples are given to illustrate the validity of our methods.

An angularly refineable phase space finite element method with approximate sweeping procedure

International Nuclear Information System (INIS)

Kophazi, J.; Lathouwers, D.

2013-01-01

An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S n -like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S n scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S 2 sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues.

Science.gov (United States)

Li, Kewei; Ogden, Ray W; Holzapfel, Gerhard A

2018-01-01

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost. © 2018 The Author(s).

Transformation Matrix for Time Discretization Based on Tustin’s Method

Directory of Open Access Journals (Sweden)

Yiming Jiang

2014-01-01

Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.

Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation

Directory of Open Access Journals (Sweden)

Hyung-Chu Lim

2008-12-01

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

Parallel iterative solution of the Hermite Collocation equations on GPUs II

International Nuclear Information System (INIS)

Vilanakis, N; Mathioudakis, E

2014-01-01

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

The method of lines solution of discrete ordinates method for non-grey media

International Nuclear Information System (INIS)

Cayan, Fatma Nihan; Selcuk, Nevin

2007-01-01

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach

Part 6. Internationalization and collocation of FBR fuel cycle facilities

International Nuclear Information System (INIS)

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

1980-01-01

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

Flows about a rotating circular cylinder by the discrete-vortex method

Science.gov (United States)

Kimura, Takeyoshi; Tsutahara, Michihisa

1987-01-01

A numerical study has been conducted for flows past a rotating circular cylinder at high Reynolds numbers, using the discrete-vortex method. It is noted that the reverse Magnus effect is caused by the retreat of the separation point on the acceleration side. At high rotating speed, the nascent vortices of opposite directions are mixed faster, the wake becomes narrower, and predominating frequencies in the lift force disappear.

Space-Time Discrete KPZ Equation

Science.gov (United States)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Unmanned aerial vehicle trajectory planning with direct methods

Science.gov (United States)

Geiger, Brian

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

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

International Nuclear Information System (INIS)

Yu, Dequan; Cong, Shu-Lin; Sun, Zhigang

2015-01-01

Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

Energy Technology Data Exchange (ETDEWEB)

Yu, Dequan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Cong, Shu-Lin, E-mail: shlcong@dlut.edu.cn [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Sun, Zhigang, E-mail: zsun@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026 (China)

2015-09-08

Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method.

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

Energy Technology Data Exchange (ETDEWEB)

Le Bourdiec, S

2007-03-15

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

In-plane material continuity for the discrete material optimization method

DEFF Research Database (Denmark)

Sørensen, Rene; Lund, Erik

2015-01-01

When performing discrete material optimization of laminated composite structures, the variation of the in-plane material continuity is typically governed by the size of the finite element discretization. For a fine mesh, this can lead to designs that cannot be manufactured due to the complexity...

Retrieving quasi-phase-matching structure with discrete layer-peeling method

DEFF Research Database (Denmark)

Zhang, Q. W.; Zeng, Xianglong; Wang, M.

2012-01-01

An approach to reconstruct a quasi-phase-matching grating by using a discrete layer-peeling algorithm is presented. Experimentally measured output spectra of Solc-type filters, based on uniform and chirped QPM structures, are used in the discrete layer-peeling algorithm. The reconstructed QPM...

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

Energy Technology Data Exchange (ETDEWEB)

Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

2017-04-01

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

Singular characteristic tracking algorithm for improved solution accuracy of the discrete ordinates method with isotropic scattering

International Nuclear Information System (INIS)

Duo, J. I.; Azmy, Y. Y.

2007-01-01

A new method, the Singular Characteristics Tracking algorithm, is developed to account for potential non-smoothness across the singular characteristics in the exact solution of the discrete ordinates approximation of the transport equation. Numerical results show improved rate of convergence of the solution to the discrete ordinates equations in two spatial dimensions with isotropic scattering using the proposed methodology. Unlike the standard Weighted Diamond Difference methods, the new algorithm achieves local convergence in the case of discontinuous angular flux along the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of verifying the results, the Method of Manufactured Solutions is used to generate analytical reference solutions that permit estimating the local error in the numerical solution. (authors)

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

Science.gov (United States)

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

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

Use of the Streaming Matrix Hybrid Method for discrete-ordinates fusion reactor calculations

International Nuclear Information System (INIS)

Battat, M.E.; Davidson, J.W.; Dudziak, D.J.; Thayer, G.R.

1984-01-01

The use of the discrete-ordinates method for solving two-dimensional, neutral-particle transport in fusion reactor blankets and shields is often limited by inherent inaccuracies due to the ray-effect. This effect presents a particular problem in the case of neutron streaming in the large internal void regions of a fusion reactor. A deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) has been incorporated in the two-dimensional discrete-ordinates code TRIDENT-CTR. Calculations have been performed for an actual inertial-confinement fusion (ICF) reactor design using TRIDENT-CTR both with and without the SMHM. Comparisons of the calculated fluxes indicate that substantial mitigation of the ray effect can be achieved with the SMHM. Calculations were performed for the Los Alamos FIRST STEP hybrid ICF reactor designed for tritium production. Conventional 238 U fuel rod assemblies surround the spherical steel target chamber to form an annular cylindrical blanket. An axial fuel region is included to complete the blanket

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

Directory of Open Access Journals (Sweden)

Orčić Lidija S.

2017-01-01

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

Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

International Nuclear Information System (INIS)

Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.

2016-01-01

Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Directory of Open Access Journals (Sweden)

Paul Brocklehurst

2015-01-01

Full Text Available Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM. In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue’s corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

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

Directory of Open Access Journals (Sweden)

Anna Nikolaevna Panamaryova

2013-10-01

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

Applied discrete-time queues

CERN Document Server

Alfa, Attahiru S

2016-01-01

This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

Time Discretization Techniques

KAUST Repository

Gottlieb, S.

2016-10-12

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.

An error estimate for Tremolieres method for the discretization of parabolic variational inequalities

International Nuclear Information System (INIS)

Uko, L.U.

1990-02-01

We study a scheme for the time-discretization of parabolic variational inequalities that is often easier to use than the classical method of Rothe. We show that if the data are compatible in a certain sense, then this scheme is of order ≥1/2. (author). 10 refs

Thickness optimization of fiber reinforced laminated composites using the discrete material optimization method

DEFF Research Database (Denmark)

Sørensen, Søren Nørgaard; Lund, Erik

2012-01-01

This work concerns a novel large-scale multi-material topology optimization method for simultaneous determination of the optimum variable integer thickness and fiber orientation throughout laminate structures with fixed outer geometries while adhering to certain manufacturing constraints....... The conceptual combinatorial/integer problem is relaxed to a continuous problem and solved on basis of the so-called Discrete Material Optimization method, explicitly including the manufacturing constraints as linear constraints....

Discrete Routh reduction

International Nuclear Information System (INIS)

Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

2006-01-01

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

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

KAUST Repository

Wang, Zhiheng

2014-12-10

A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.

In-plane Material Filters for the Discrete Material Optimization Method

DEFF Research Database (Denmark)

Sørensen, Rene; Lund, Erik

2015-01-01

, because the projection filter is a non-linear function of the design variables, the projected variables have to be re-scaled in a final so-called normalization filter. This is done to prevent the optimizer in creating superior, but non-physical pseudo-materials. The method is demonstrated on a series......This paper presents in-plane material filters for the Discrete Material Optimization method used for optimizing laminated composite structures. The filters make it possible for engineers to specify a minimum length scale which governs the minimum size of areas with constant material continuity....... Consequently, engineers can target the available production methods, and thereby increase its manufacturability while the optimizer is free to determine which material to apply together with an optimum location, shape, and size of these areas with constant material continuity. By doing so, engineers no longer...

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre; Ketcheson, David I.; Loczi, Lajos

2017-01-01

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations

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

Science.gov (United States)

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

2017-01-01

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

Application of real space Kerker method in simulating gate-all-around nanowire transistors with realistic discrete dopants*

International Nuclear Information System (INIS)

Li Chang-Sheng; Ma Lei; Guo Jie-Rong

2017-01-01

We adopt a self-consistent real space Kerker method to prevent the divergence from charge sloshing in the simulating transistors with realistic discrete dopants in the source and drain regions. The method achieves efficient convergence by avoiding unrealistic long range charge sloshing but keeping effects from short range charge sloshing. Numerical results show that discrete dopants in the source and drain regions could have a bigger influence on the electrical variability than the usual continuous doping without considering charge sloshing. Few discrete dopants and the narrow geometry create a situation with short range Coulomb screening and oscillations of charge density in real space. The dopants induced quasi-localized defect modes in the source region experience short range oscillations in order to reach the drain end of the device. The charging of the defect modes and the oscillations of the charge density are identified by the simulation of the electron density. (paper)

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

Science.gov (United States)

Ocko, Ilissa B.; Ginoux, Paul A.

2017-04-01

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

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

A method for accurate computation of elastic and discrete inelastic scattering transfer matrix

International Nuclear Information System (INIS)

Garcia, R.D.M.; Santina, M.D.

1986-05-01

A method for accurate computation of elastic and discrete inelastic scattering transfer matrices is discussed. In particular, a partition scheme for the source energy range that avoids integration over intervals containing points where the integrand has discontinuous derivative is developed. Five-figure accurate numerical results are obtained for several test problems with the TRAMA program which incorporates the porposed method. A comparison with numerical results from existing processing codes is also presented. (author) [pt

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods.

Science.gov (United States)

Coes, Alissa L; Paretti, Nicholas V; Foreman, William T; Iverson, Jana L; Alvarez, David A

2014-03-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19-23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method. Published by Elsevier B.V.

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods

Science.gov (United States)

Coes, Alissa L.; Paretti, Nicholas V.; Foreman, William T.; Iverson, Jana L.; Alvarez, David A.

2014-01-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19–23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method.

Parallel performance of the angular versus spatial domain decomposition for discrete ordinates transport methods

International Nuclear Information System (INIS)

Fischer, J.W.; Azmy, Y.Y.

2003-01-01

A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of

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

Science.gov (United States)

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

The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

International Nuclear Information System (INIS)

Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul