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).

An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials

Directory of Open Access Journals (Sweden)

Jianping Liu

2016-01-01

Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.

Antireflection coatings with Chebyshev or Butterworth response - Design

Science.gov (United States)

Baumeister, Philip

1986-12-01

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

Shifted-modified Chebyshev filters

OpenAIRE

ŞENGÜL, Metin

2013-01-01

This paper introduces a new type of filter approximation method that utilizes shifted-modified Chebyshev filters. Construction of the new filters involves the use of shifted-modified Chebyshev polynomials that are formed using the roots of conventional Chebyshev polynomials. The study also includes 2 tables containing the shifted-modified Chebyshev polynomials and the normalized element values for the low-pass prototype filters up to degree 6. The transducer power gain, group dela...

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.

The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval

Directory of Open Access Journals (Sweden)

Majid Tavassoli Kajani

2013-01-01

Full Text Available We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-kind Chebyshev pseudospectral method that is indeed a combination of Tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.

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.

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).

Cosmographic analysis with Chebyshev polynomials

Science.gov (United States)

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

2018-05-01

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

A 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.

On the use of a spatial Chebyshev polynomials together with the collocation method in solving radiative transfer problem in a slab

International Nuclear Information System (INIS)

Haggag, M.H.; Al-Gorashi, A.K.; Machali, H.M.

2013-01-01

In this study, the integral form of the radiative transfer equation in planar slab with isotropic scattering has been studied by using the Chebyshev polynomial approximation which is called TN method. The scalar flux is expanded in terms of Chebyshev polynomials in the space variable. The expansion coefficients are solutions to a system of linear algebraic equations. Analytical expressions are given for the scalar and angular flux everywhere in the slab. Numerical calculations are done for the transmissivity and reflectivity of slabs with various values of the single scattering albedo. Calculations are also carried out for the transmitted and reflected angular intensity at the slab boundaries. Our numerical results are in a very good agreement with other results, as shown in the tables

Superiority of legendre polynomials to Chebyshev polynomial in ...

African Journals Online (AJOL)

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

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

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

KAUST Repository

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

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 algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

International Nuclear Information System (INIS)

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

2014-01-01

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

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

Science.gov (United States)

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

2013-01-01

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

Spectral 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.

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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.

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)

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-15

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

On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

Directory of Open Access Journals (Sweden)

Paul Barry

2013-01-01

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

Spectral element method for wave propagation on irregular domains

Indian Academy of Sciences (India)

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

Collocations in Marine Engineering English

Directory of Open Access Journals (Sweden)

Mirjana Borucinsky

2016-05-01

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

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

KAUST Repository

Hale, Nicholas

2014-02-06

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

Spectral element method for wave propagation on irregular domains

Indian Academy of Sciences (India)

Yan Hui Geng

2018-03-14

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

Derivation of reduced model for control system design using Chebyshev techniques

International Nuclear Information System (INIS)

Bistritz, Y.

1978-07-01

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

and chebyshev functions

Directory of Open Access Journals (Sweden)

Mohsen Razzaghi

2000-01-01

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

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....

Collocation Impact on Team Effectiveness

Directory of Open Access Journals (Sweden)

M Eccles

2010-11-01

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

Proxemic Mobile Collocated Interactions

DEFF Research Database (Denmark)

Porcheron, Martin; Lucero, Andrés; Quigley, Aaron

2016-01-01

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

Chebyshev Finite Difference Method for Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Boundary

2015-09-01

Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

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

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…

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.

Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

KAUST Repository

Ait-Haddou, Rachid

2013-08-01

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

Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

KAUST Repository

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

2013-01-01

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

Pseudo-random bit generator based on Chebyshev map

Science.gov (United States)

Stoyanov, B. P.

2013-10-01

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

The application of the Chebyshev-spectral method in transport phenomena

CERN Document Server

Guo, Weidong; Narayanan, Ranga

2012-01-01

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

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

Science.gov (United States)

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

2017-05-01

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

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

Science.gov (United States)

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

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

Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain

International Nuclear Information System (INIS)

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

2011-01-01

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

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

Science.gov (United States)

Temel, Burcin; Mills, Greg; Metiu, Horia

2008-03-27

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

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.

Measuring receptive collocational competence across proficiency levels

Directory of Open Access Journals (Sweden)

Déogratias Nizonkiza

2015-12-01

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

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

Science.gov (United States)

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

2016-06-01

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

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...

Spectral methods in numerical plasma simulation

International Nuclear Information System (INIS)

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

1989-01-01

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

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

Czech Academy of Sciences Publication Activity Database

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

2010-01-01

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

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

International Nuclear Information System (INIS)

Benasser Algehawi, Mohammed; Samsudin, Azman

2010-01-01

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

Schwarz and multilevel methods for quadratic spline collocation

Energy Technology Data Exchange (ETDEWEB)

Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)

1994-12-31

Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

Slovene-English Contrastive Phraseology: Lexical Collocations

Directory of Open Access Journals (Sweden)

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...

The Presentation and Treatment of Collocations as Secondary ...

African Journals Online (AJOL)

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

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

African Journals Online (AJOL)

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

Semantic Analysis of Verbal Collocations with Lexical Functions

CERN Document Server

Gelbukh, Alexander

2013-01-01

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

Productive knowledge of collocations may predict academic literacy

Directory of Open Access Journals (Sweden)

Van Dyk, Tobie

2016-12-01

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

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

African Journals Online (AJOL)

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

Lexical and Grammatical Collocations in Writing Production of EFL Learners

Directory of Open Access Journals (Sweden)

Maryam Bahardoust

2012-05-01

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

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

Science.gov (United States)

Mireles James, J. D.; Murray, Maxime

2017-12-01

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

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

Science.gov (United States)

Deprit, A.

1975-01-01

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

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

KAUST Repository

Ait-Haddou, Rachid

2016-10-19

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

The relationship between productive knowledge of collocations and ...

African Journals Online (AJOL)

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

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

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

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

Directory of Open Access Journals (Sweden)

M. Tavassoli Kajani

2012-01-01

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

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.

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

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

1994-01-01

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

Teaching collocations

DEFF Research Database (Denmark)

Revier, Robert Lee; Henriksen, Birgit

2006-01-01

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

On Collocations and Their Interaction with Parsing and Translation

Directory of Open Access Journals (Sweden)

Violeta Seretan

2013-10-01

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

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

Science.gov (United States)

Freund, Roland

1989-01-01

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

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.…

Verb-Noun Collocations in Written Discourse of Iranian EFL Learners

Directory of Open Access Journals (Sweden)

Fatemeh Ebrahimi-Bazzaz

2015-07-01

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

CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

Directory of Open Access Journals (Sweden)

S.H. Nasseri

2011-07-01

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

CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

Directory of Open Access Journals (Sweden)

S.H. Nasseri

2009-10-01

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

Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials

Directory of Open Access Journals (Sweden)

Tingting Wang

2015-01-01

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

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.

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

Science.gov (United States)

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

2017-07-01

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

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

International Nuclear Information System (INIS)

Foo, Jasmine; Wan Xiaoliang; Karniadakis, George Em

2008-01-01

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

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

DEFF Research Database (Denmark)

Revier, Robert Lee

2014-01-01

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

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

Indian Academy of Sciences (India)

2017-02-10

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

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

KAUST Repository

Hale, Nicholas; Townsend, Alex

2014-01-01

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

Supporting Collocation Learning with a Digital Library

Science.gov (United States)

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

2010-01-01

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

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

African Journals Online (AJOL)

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

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

Directory of Open Access Journals (Sweden)

Fakhrodin Mohammadi

2017-10-01

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

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 ...

Recent advances in radial basis function collocation methods

CERN Document Server

Chen, Wen; Chen, C S

2014-01-01

This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s ...

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...

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.

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

Science.gov (United States)

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

1992-01-01

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

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,…

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

Czech Academy of Sciences Publication Activity Database

Dzetkulič, Tomáš

2015-01-01

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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…

SOLUTION OF A MULTIVARIATE STRATIFIED SAMPLING PROBLEM THROUGH CHEBYSHEV GOAL PROGRAMMING

Directory of Open Access Journals (Sweden)

Mohd. Vaseem Ismail

2010-12-01

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

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…

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

Energy Technology Data Exchange (ETDEWEB)

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

2001-08-01

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

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

Directory of Open Access Journals (Sweden)

Chih-Hong Lin

2016-06-01

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

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.

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…

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

Directory of Open Access Journals (Sweden)

Rafe S. Zaabalawi

2017-01-01

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

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

Science.gov (United States)

Liang, Conghui; Ceccarelli, Marco; Takeda, Yukio

2012-12-01

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

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

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

Directory of Open Access Journals (Sweden)

Yu-Bo Jiao

2015-01-01

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

The Use of English Collocations in Reader's Digest

OpenAIRE

Sinaga, Yudita Putri Nurani; Sinaga, Lidiman Sahat Martua

2014-01-01

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

Corpora and Collocations in Chinese-English Dictionaries for Chinese Users

Science.gov (United States)

Xia, Lixin

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Irena SRDANOVIĆ

2011-05-01

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

Pseudospectral collocation methods for fourth order differential equations

Science.gov (United States)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

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

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

Science.gov (United States)

Streett, C. L.

1987-01-01

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

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…

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.

B-spline Collocation with Domain Decomposition Method

International Nuclear Information System (INIS)

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

2013-01-01

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

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.

GUESSING VERB-ADVERB COLLOCATIONS: ARAB EFL ...

African Journals Online (AJOL)

user

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

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

Directory of Open Access Journals (Sweden)

Muntaha A. Abdulwahid

2017-01-01

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

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...

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

Directory of Open Access Journals (Sweden)

Matthew Peacock

2012-04-01

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

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....

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.

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.

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 3D spectral anelastic hydrodynamic code for shearing, stratified flows

Science.gov (United States)

Barranco, Joseph A.; Marcus, Philip S.

2006-11-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g., the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time-integrated explicitly, the pressure/enthalpy terms are integrated semi-implicitly, and the Coriolis force and buoyancy terms are treated semi-analytically. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the message passing interface (MPI). As a demonstration of the code, we simulate the merger of two 3D vortices in the midplane of a protoplanetary disk.

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

OpenAIRE

Bergström, Kerstin

2008-01-01

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

Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol

Directory of Open Access Journals (Sweden)

Hong Lai

2012-01-01

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

NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

OpenAIRE

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

2017-01-01

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

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

Kate H

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

Spectral element method for vector radiative transfer equation

International Nuclear Information System (INIS)

Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

2010-01-01

A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

An 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

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

International Nuclear Information System (INIS)

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

1990-01-01

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

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

Directory of Open Access Journals (Sweden)

Muhammad Mubashir Bhatti

2016-05-01

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

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

Science.gov (United States)

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

2007-02-01

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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 time-spectral approach to numerical weather prediction

Science.gov (United States)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

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…

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

Directory of Open Access Journals (Sweden)

Saudin Saudin

2017-05-01

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

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

Directory of Open Access Journals (Sweden)

Hassan Saberi Nik

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Elaheh Hamed Mahvelati

2012-11-01

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

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

International Nuclear Information System (INIS)

Pasciak, J.E.

1982-01-01

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

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

International Nuclear Information System (INIS)

Jiménez-Teja, Y.; Benítez, N.

2012-01-01

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

Multidomain spectral solution of compressible viscous flows

International Nuclear Information System (INIS)

Kopriva, D.A.

1994-01-01

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

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

Science.gov (United States)

Cvitaš, Marko T; Althorpe, Stuart C

2013-08-14

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

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Science.gov (United States)

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

2016-01-01

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

Improving academic literacy by teaching collocations

African Journals Online (AJOL)

Kate H

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

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

DCOMP Award Lecture (Metropolis): A 3D Spectral Anelastic Hydrodynamic Code for Shearing, Stratified Flows

Science.gov (United States)

Barranco, Joseph

2006-03-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (eg, the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier-Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time integrated explicitly, whereas the Coriolis force, buoyancy terms, and pressure/enthalpy gradient are integrated semi- implicitly. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the Message Passing Interface (MPI). As a demonstration of the code, we simulate vortex dynamics in protoplanetary disks and the Kelvin-Helmholtz instability in the dusty midplanes of protoplanetary disks.

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.

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

National Research Council Canada - National Science Library

Mitchell, Jason

2002-01-01

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

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

Science.gov (United States)

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

2018-06-12

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

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

International Nuclear Information System (INIS)

Lee, Yoon Hee; Cho, Nam Zin

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-05-15

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

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.

Universal bounds on spectral measures of one-dimensional Schrödinger operators

CERN Document Server

Remling, C

2002-01-01

Consider a Schrödinger operator $H=-d^2/dx^2+V(x)$ on $L_2(0,\\infty)$ and suppose that an initial piece of the potential $V(x)$, $0spectral measure of intervals with a certain minimum length. This length scale is set by the eigenvalues of the problems on $[0,N]$. So in a sense (and perhaps somewhat surprisingly) the behavior of $V(x)$ becomes less important if $x$ grows. The results of this paper are developments of classical work of Chebyshev and Markov on orthogonal polynomials.

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.

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

KAUST Repository

Carpenter, Mark H.

2016-01-04

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

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.

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.)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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.

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.

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

African Journals Online (AJOL)

user

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

Discrete Chebyshev nets and a universal permutability theorem

International Nuclear Information System (INIS)

Schief, W K

2007-01-01

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

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

DEFF Research Database (Denmark)

Henriksen, Birgit; Westbrook, Pete

2017-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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

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

Science.gov (United States)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

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

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.

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…

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-07-01

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

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.

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

Directory of Open Access Journals (Sweden)

Mohsen Shahrokhi

2014-05-01

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

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

CSIR Research Space (South Africa)

Sokoya, O

2008-05-01

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

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

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.

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.

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.

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

International Nuclear Information System (INIS)

Flores-Lamas, H.

1994-01-01

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

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 ...

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 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.

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.

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

KAUST Repository

Chu, Chunlei

2012-07-01

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

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

Science.gov (United States)

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

2017-09-01

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

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.

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.

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

Directory of Open Access Journals (Sweden)

A.K. Parida

2016-09-01

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

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

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

Directory of Open Access Journals (Sweden)

Fuqiang Zhao

2017-01-01

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

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

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.

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

Science.gov (United States)

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

2014-09-01

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

Combined FVTD/PSTD Schemes with Enhanced Spectral Accuracy for the Design of Large-Scale EMC Applications

Directory of Open Access Journals (Sweden)

N. V. Kantartzis

2012-10-01

Full Text Available A generalized conformal time-domain method with adjustable spectral accuracy is introduced in this paper for the consistent analysis of large-scale electromagnetic compatibility problems. The novel 3-D hybrid schemes blend a stencil-optimized finite-volume time-domain and a multimodal Fourier-Chebyshev pseudo-spectral time-domain algorithm that split the overall space into smaller and flexible areas. A key asset is that both techniques are updated independently and interconnected by robust boundary conditions. Also, combining a family of spatial derivative approximators with controllable precision in general curvilinear coordinates, the proposed method launches a conformal field flux formulation to derive electromagnetic quantities in regions with fine details. For advanced grid reliability at dissimilar media interfaces, dispersion-reduced adaptive operators, which assign the proper weights to each spatial increment, are developed. So, the resulting discretization yields highly rigorous and computationally affordable simulations, devoid of lattice errors. Numerical results, addressing detailed comparisons of various realistic applications with reference or measurement data verify our methodology and reveal its significant applicability.

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

Directory of Open Access Journals (Sweden)

Zhao-Qing Wang

2014-01-01

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

Gimme Context – towards New Domain-Specific Collocational Dictionaries

Directory of Open Access Journals (Sweden)

Sylvana Krausse

2011-04-01

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

Strategies in Translating Collocations in Religious Texts from Arabic into English

Science.gov (United States)

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

2010-01-01

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

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.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

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

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

Science.gov (United States)

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

2016-12-01

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

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...

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

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.

A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

Directory of Open Access Journals (Sweden)

S. S. Motsa

2013-01-01

Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

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.

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...

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.

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.

A spectral scheme for Kohn-Sham density functional theory of clusters

Science.gov (United States)

Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.

2015-04-01

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems - the plane-wave method - is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

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.

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 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.

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

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

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.

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

Nightside studies of coherent HF Radar spectral width behaviour

Directory of Open Access Journals (Sweden)

E. E. Woodfield

2002-09-01

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

Nightside studies of coherent HF Radar spectral width behaviour

Directory of Open Access Journals (Sweden)

E. E. Woodfield

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

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

Directory of Open Access Journals (Sweden)

Waleed M. Abd-Elhameed

2016-09-01

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

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

Science.gov (United States)

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

2017-01-01

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

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

Science.gov (United States)

Ocko, Ilissa B.; Ginoux, Paul A.

2017-04-01

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

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

Directory of Open Access Journals (Sweden)

Arne Van Londersele

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Shu-xian Lun

2015-01-01

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

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

Science.gov (United States)

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

A 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

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

Science.gov (United States)

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

1998-01-01

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

A spectral scheme for Kohn–Sham density functional theory of clusters

Energy Technology Data Exchange (ETDEWEB)

Banerjee, Amartya S., E-mail: baner041@umn.edu; Elliott, Ryan S., E-mail: relliott@umn.edu; James, Richard D., E-mail: james@umn.edu

2015-04-15

Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

A spectral scheme for Kohn–Sham density functional theory of clusters

International Nuclear Information System (INIS)

Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.

2015-01-01

Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed

On Closed Form Calculation of Line Spectral Frequencies (LSF)

DEFF Research Database (Denmark)

Dalsgaard, Paul; Andersen, Ove

2014-01-01

of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symmetric and anti-symmetric polynomials defined as a series expansion of reduced Chebyshev polynomials of the first kind. Two variants of closed form functions are presented — each characterised by using...

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

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

Science.gov (United States)

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

2006-07-01

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Pham Thuy Dung

2016-12-01

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

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

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

Directory of Open Access Journals (Sweden)

Diva Cardoso de CAMARGO

2013-12-01

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

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

International Nuclear Information System (INIS)

Leskovar, M.

2000-01-01

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

Collocation mismatch uncertainties in satellite aerosol retrieval validation

Science.gov (United States)

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

2018-02-01

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

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

Directory of Open Access Journals (Sweden)

J.-P. Villain

2002-11-01

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

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

Directory of Open Access Journals (Sweden)

J.-P. Villain

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

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

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

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

NARCIS (Netherlands)

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

2012-01-01

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

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.

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)

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.

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.

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Science.gov (United States)

Kaporin, I. E.

2012-02-01

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

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

OpenAIRE

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

2017-01-01

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

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

DEFF Research Database (Denmark)

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

2002-01-01

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

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.

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.

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

Science.gov (United States)

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

2017-12-01

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

Spectrally accurate initial data in numerical relativity

Science.gov (United States)

Battista, Nicholas A.

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

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)

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

Science.gov (United States)

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

2017-05-01

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

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

Science.gov (United States)

Warnez, M. T.; Johnsen, E.

2015-06-01

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

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.

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.

Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

Science.gov (United States)

Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

2018-03-01

-channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

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

Science.gov (United States)

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

2010-09-01

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

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.

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

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

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

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

Science.gov (United States)

Wang, Che; Wang, Hong

2017-02-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-08-01

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

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

Directory of Open Access Journals (Sweden)

Pedro Patiño García

2013-04-01

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

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.

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

Directory of Open Access Journals (Sweden)

D. Baleanu

2013-01-01

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

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

DEFF Research Database (Denmark)

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

2015-01-01

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

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

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

Science.gov (United States)

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

2015-12-01

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

Algorithm for Compressing Time-Series Data

Science.gov (United States)

Hawkins, S. Edward, III; Darlington, Edward Hugo

2012-01-01

An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").

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.

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

DEFF Research Database (Denmark)

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

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-07-01

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

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

Science.gov (United States)

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

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

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

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

Directory of Open Access Journals (Sweden)

Tony Berber Sardinha

2006-01-01

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

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

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

International Nuclear Information System (INIS)

Kupka, F.

1997-11-01

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

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

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

Science.gov (United States)

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

2016-03-01

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

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.

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.

Overdetermined shooting methods for computing standing water waves with spectral accuracy

International Nuclear Information System (INIS)

Wilkening, Jon; Yu Jia

2012-01-01

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

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

Science.gov (United States)

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

2008-11-01

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

Collocated Dataglyphs for large-message storage and retrieval

Science.gov (United States)

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

2004-06-01

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

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Spectral gamuts and spectral gamut mapping

Science.gov (United States)

Rosen, Mitchell R.; Derhak, Maxim W.

2006-01-01

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

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

Science.gov (United States)

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

2013-04-01

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

Hybrid 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.

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.

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

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

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

Science.gov (United States)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

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

Evaluating the performance of collocated optical disdrometers: LPM and PARSIVEL

Science.gov (United States)

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

2017-04-01

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

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

DEFF Research Database (Denmark)

Bødker, Susanne; Polli, Anna Maria

2014-01-01

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

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.

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

Science.gov (United States)

Darbeheshti, N.; Featherstone, W. E.

2009-06-01

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

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

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

International Nuclear Information System (INIS)

Islam, Tanvir; Srivastava, Prashant K.

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

M. Rahimi-Gorji

2015-06-01

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

Linear stability analysis of laminar flow near a stagnation point in the slip flow regime

Science.gov (United States)

Essaghir, E.; Oubarra, A.; Lahjomri, J.

2017-12-01

The aim of the present contribution is to analyze the effect of slip parameter on the stability of a laminar incompressible flow near a stagnation point in the slip flow regime. The analysis is based on the traditional normal mode approach and assumes parallel flow approximation. The Orr-Sommerfeld equation that governs the infinitesimal disturbance of stream function imposed to the steady main flow, which is an exact solution of the Navier-Stokes equation satisfying slip boundary conditions, is obtained by using the powerful spectral Chebyshev collocation method. The results of the effect of slip parameter K on the hydrodynamic characteristics of the base flow, namely the velocity profile, the shear stress profile, the boundary layer, displacement and momentum thicknesses are illustrated and discussed. The numerical data for these characteristics, as well as those of the eigenvalues and the corresponding wave numbers recover the results of the special case of no-slip boundary conditions. They are found to be in good agreement with previous numerical calculations. The effects of slip parameter on the neutral curves of stability, for two-dimensional disturbances in the Reynolds-wave number plane, are then obtained for the first time in the slip flow regime for stagnation point flow. Furthermore, the evolution of the critical Reynolds number against the slip parameter is established. The results show that the critical Reynolds number for instability is significantly increased with the slip parameter and the flow turn out to be more stable when the effect of rarefaction becomes important.

Global stability analysis of axisymmetric boundary layer over a circular cylinder

Science.gov (United States)

Bhoraniya, Ramesh; Vinod, Narayanan

2018-05-01

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.

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.

Study on dynamic behavior analysis of towed line array sensor

Directory of Open Access Journals (Sweden)

Hyun Kyoung Shin

2012-03-01

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

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 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...

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

Science.gov (United States)

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

2007-01-01

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

Continuous Groundwater Monitoring Collocated at USGS Streamgages

Science.gov (United States)

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

2012-12-01

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

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

Directory of Open Access Journals (Sweden)

Timothy J. Dickey

2008-03-01

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

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

Science.gov (United States)

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

2016-12-01

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

Evaluating factorial kriging for seismic attributes filtering: a geostatistical filter applied to reservoir characterization; Avaliacao da krigagem fatorial na filtragem de atributos sismicos: um filtro geoestatistico aplicado a caracterizacao de reservatorios

Energy Technology Data Exchange (ETDEWEB)

Mundim, Evaldo Cesario

1999-02-01

In this dissertation the Factorial Kriging analysis for the filtering of seismic attributes applied to reservoir characterization is considered. Factorial Kriging works in the spatial, domain in a similar way to the Spectral Analysis in the frequency domain. The incorporation of filtered attributes via External Drift Kriging and Collocated Cokriging in the estimate of reservoir characterization is discussed. Its relevance for the reservoir porous volume calculation is also evaluated based on comparative analysis of the volume risk curves derived from stochastic conditional simulations with collocated variable and stochastic conditional simulations with collocated variable and stochastic conditional simulations with external drift. results prove Factorial Kriging as an efficient technique for the filtering of seismic attributes images, of which geologic features are enhanced. The attribute filtering improves the correlation between the attributes and the well data and the estimates of the reservoir properties. The differences between the estimates obtained by External Drift Kriging and Collocated Cokriging are also reduced. (author)

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

Science.gov (United States)

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

2012-01-01

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

Understanding Soliton Spectral Tunneling as a Spectral Coupling Effect

DEFF Research Database (Denmark)

Guo, Hairun; Wang, Shaofei; Zeng, Xianglong

2013-01-01

Soliton eigenstate is found corresponding to a dispersive phase profile under which the soliton phase changes induced by the dispersion and nonlinearity are instantaneously counterbalanced. Much like a waveguide coupler relying on a spatial refractive index profile that supports mode coupling...... between channels, here we suggest that the soliton spectral tunneling effect can be understood supported by a spectral phase coupler. The dispersive wave number in the spectral domain must have a coupler-like symmetric profile for soliton spectral tunneling to occur. We show that such a spectral coupler...

Computation of High-Frequency Waves with Random Uncertainty

KAUST Repository

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

2016-01-01

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

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.

Piecewise spectrally band-pass for compressive coded aperture spectral imaging

International Nuclear Information System (INIS)

Qian Lu-Lu; Lü Qun-Bo; Huang Min; Xiang Li-Bin

2015-01-01

Coded aperture snapshot spectral imaging (CASSI) has been discussed in recent years. It has the remarkable advantages of high optical throughput, snapshot imaging, etc. The entire spatial-spectral data-cube can be reconstructed with just a single two-dimensional (2D) compressive sensing measurement. On the other hand, for less spectrally sparse scenes, the insufficiency of sparse sampling and aliasing in spatial-spectral images reduce the accuracy of reconstructed three-dimensional (3D) spectral cube. To solve this problem, this paper extends the improved CASSI. A band-pass filter array is mounted on the coded mask, and then the first image plane is divided into some continuous spectral sub-band areas. The entire 3D spectral cube could be captured by the relative movement between the object and the instrument. The principle analysis and imaging simulation are presented. Compared with peak signal-to-noise ratio (PSNR) and the information entropy of the reconstructed images at different numbers of spectral sub-band areas, the reconstructed 3D spectral cube reveals an observable improvement in the reconstruction fidelity, with an increase in the number of the sub-bands and a simultaneous decrease in the number of spectral channels of each sub-band. (paper)

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.

Sparse Generalized Fourier Series via Collocation-based Optimization

Science.gov (United States)

2014-11-01

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

ULTRAVIOLET RAMAN SPECTRAL SIGNATURE ACQUISITION: UV RAMAN SPECTRAL FINGERPRINTS.

Energy Technology Data Exchange (ETDEWEB)

SEDLACEK,III, A.J.FINFROCK,C.

2002-09-01

As a member of the science-support part of the ITT-lead LISA development program, BNL is tasked with the acquisition of UV Raman spectral fingerprints and associated scattering cross-sections for those chemicals-of-interest to the program's sponsor. In support of this role, the present report contains the first installment of UV Raman spectral fingerprint data on the initial subset of chemicals. Because of the unique nature associated with the acquisition of spectral fingerprints for use in spectral pattern matching algorithms (i.e., CLS, PLS, ANN) great care has been undertaken to maximize the signal-to-noise and to minimize unnecessary spectral subtractions, in an effort to provide the highest quality spectral fingerprints. This report is divided into 4 sections. The first is an Experimental section that outlines how the Raman spectra are performed. This is then followed by a section on Sample Handling. Following this, the spectral fingerprints are presented in the Results section where the data reduction process is outlined. Finally, a Photographs section is included.

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.

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.

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.

Spectral evolution of GRBs with negative spectral lag using Fermi GBM observations

Science.gov (United States)

Chakrabarti, Arundhati; Chaudhury, Kishor; Sarkar, Samir K.; Bhadra, Arunava

2018-06-01

The positive spectral lag of Gamma Ray Bursts (GRBs) is often explained in terms of hard-to-soft spectral evolution of GRB pulses. While positive lags of GRBs is very common, there are few GRB pulses that exhibits negative spectral lags. In the present work we examine whether negative lags of GRBs also can be interpreted in terms of spectral evolution of GRB pulses or not. Using Fermi-GBM data, we identify two GRBs, GRB 090426C and GRB 150213A, with clean pulses that exhibit negative spectral lag. An indication of soft to hard transition has been noticed for the negative spectral lag events from the spectral evolution study. The implication of the present findings on the models of GRB spectral lags are discussed.

Finite length Taylor Couette flow

Science.gov (United States)

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

1987-01-01

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

From spectral holeburning memory to spatial-spectral microwave signal processing

International Nuclear Information System (INIS)

Babbitt, Wm Randall; Barber, Zeb W; Harrington, Calvin; Mohan, R Krishna; Sharpe, Tia; Bekker, Scott H; Chase, Michael D; Merkel, Kristian D; Stiffler, Colton R; Traxinger, Aaron S; Woidtke, Alex J

2014-01-01

Many storage and processing systems based on spectral holeburning have been proposed that access the broad bandwidth and high dynamic range of spatial-spectral materials, but only recently have practical systems been developed that exceed the performance and functional capabilities of electronic devices. This paper reviews the history of the proposed applications of spectral holeburning and spatial-spectral materials, from frequency domain optical memory to microwave photonic signal processing systems. The recent results of a 20 GHz bandwidth high performance spectrum monitoring system with the additional capability of broadband direction finding demonstrates the potential for spatial-spectral systems to be the practical choice for solving demanding signal processing problems in the near future. (paper)

Spectral Imaging by Upconversion

DEFF Research Database (Denmark)

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

2011-01-01

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

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

International Nuclear Information System (INIS)

Chithambo, M.L.

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

E.C. Biscaia Junior

2001-06-01

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

A note on the solution of general Falkner-Skan problem by two novel semi-analytical techniques

Directory of Open Access Journals (Sweden)

Ahmed Khidir

2015-12-01

Full Text Available The aim of this paper is to give a presentation of two new iterative methods for solving non-linear differential equations, they are successive linearisation method and spectral homotopy perturbation method. We applied these techniques on the non-linear boundary value problems of Falkner-Skan type. The methods used to find a recursive former for higher order equations that are solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. The methods are illustrated by progressively applying the technique to the Blasius boundary layer equation, the Falkner-Skan equation and finally, the magnetohydrodynamic (MHD Falkner-Skan equation. The solutions are compared to other methods in the literature such as the homotopy analysis method and the spectral-homotopy analysis method with focus on the accuracy and convergence of this new techniques.

Examination of Spectral Transformations on Spectral Mixture Analysis

Science.gov (United States)

Deng, Y.; Wu, C.

2018-04-01

While many spectral transformation techniques have been applied on spectral mixture analysis (SMA), few study examined their necessity and applicability. This paper focused on exploring the difference between spectrally transformed schemes and untransformed scheme to find out which transformed scheme performed better in SMA. In particular, nine spectrally transformed schemes as well as untransformed scheme were examined in two study areas. Each transformed scheme was tested 100 times using different endmember classes' spectra under the endmember model of vegetation- high albedo impervious surface area-low albedo impervious surface area-soil (V-ISAh-ISAl-S). Performance of each scheme was assessed based on mean absolute error (MAE). Statistical analysis technique, Paired-Samples T test, was applied to test the significance of mean MAEs' difference between transformed and untransformed schemes. Results demonstrated that only NSMA could exceed the untransformed scheme in all study areas. Some transformed schemes showed unstable performance since they outperformed the untransformed scheme in one area but weakened the SMA result in another region.

Miniaturized dielectric waveguide filters

OpenAIRE

Sandhu, MY; Hunter, IC

2016-01-01

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

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

Science.gov (United States)

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

Diffusion in multicomponent systems: a free energy approach

International Nuclear Information System (INIS)

Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian

2004-01-01

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

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

KAUST Repository

Wright, G. B.

2010-07-01

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

Hybrid Lanczos-type product methods

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

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

2015-03-01

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

Spectral image reconstruction using an edge preserving spatio-spectral Wiener estimation.

Science.gov (United States)

Urban, Philipp; Rosen, Mitchell R; Berns, Roy S

2009-08-01

Reconstruction of spectral images from camera responses is investigated using an edge preserving spatio-spectral Wiener estimation. A Wiener denoising filter and a spectral reconstruction Wiener filter are combined into a single spatio-spectral filter using local propagation of the noise covariance matrix. To preserve edges the local mean and covariance matrix of camera responses is estimated by bilateral weighting of neighboring pixels. We derive the edge-preserving spatio-spectral Wiener estimation by means of Bayesian inference and show that it fades into the standard Wiener reflectance estimation shifted by a constant reflectance in case of vanishing noise. Simulation experiments conducted on a six-channel camera system and on multispectral test images show the performance of the filter, especially for edge regions. A test implementation of the method is provided as a MATLAB script at the first author's website.

A semi-analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using Buongiorno's mathematical model together with more realistic boundary conditions

Science.gov (United States)

Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid

2018-06-01

The main aim of the present analysis is to examine the electroconvection phenomenon that takes place in a dielectric nanofluid under the influence of a perpendicularly applied alternating electric field. In this investigation, we assume that the nanofluid has a Newtonian rheological behavior and verifies the Buongiorno's mathematical model, in which the effects of thermophoretic and Brownian diffusions are incorporated explicitly in the governing equations. Moreover, the nanofluid layer is taken to be confined horizontally between two parallel plate electrodes, heated from below and cooled from above. In a fast pulse electric field, the onset of electroconvection is due principally to the buoyancy forces and the dielectrophoretic forces. Within the framework of the Oberbeck-Boussinesq approximation and the linear stability theory, the governing stability equations are solved semi-analytically by means of the power series method for isothermal, no-slip and non-penetrability conditions. In addition, the computational implementation with the impermeability condition implies that there exists no nanoparticles mass flux on the electrodes. On the other hand, the obtained analytical solutions are validated by comparing them to those available in the literature for the limiting case of dielectric fluids. In order to check the accuracy of our semi-analytical results obtained for the case of dielectric nanofluids, we perform further numerical and semi-analytical computations by means of the Runge-Kutta-Fehlberg method, the Chebyshev-Gauss-Lobatto spectral method, the Galerkin weighted residuals technique, the polynomial collocation method and the Wakif-Galerkin weighted residuals technique. In this analysis, the electro-thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical AC electric Rayleigh number Rec , whose value depends on several physical parameters. Furthermore, the effects of various pertinent parameters on the electro

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-15

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

International Nuclear Information System (INIS)

Joshi, J.R.

2000-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2008-01-01

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

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.

Spectrally selective glazings

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

Spectrally selective glazing is window glass that permits some portions of the solar spectrum to enter a building while blocking others. This high-performance glazing admits as much daylight as possible while preventing transmission of as much solar heat as possible. By controlling solar heat gains in summer, preventing loss of interior heat in winter, and allowing occupants to reduce electric lighting use by making maximum use of daylight, spectrally selective glazing significantly reduces building energy consumption and peak demand. Because new spectrally selective glazings can have a virtually clear appearance, they admit more daylight and permit much brighter, more open views to the outside while still providing the solar control of the dark, reflective energy-efficient glass of the past. This Federal Technology Alert provides detailed information and procedures for Federal energy managers to consider spectrally selective glazings. The principle of spectrally selective glazings is explained. Benefits related to energy efficiency and other architectural criteria are delineated. Guidelines are provided for appropriate application of spectrally selective glazing, and step-by-step instructions are given for estimating energy savings. Case studies are also presented to illustrate actual costs and energy savings. Current manufacturers, technology users, and references for further reading are included for users who have questions not fully addressed here.

Adaptive Spectral Doppler Estimation

DEFF Research Database (Denmark)

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

2009-01-01

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

Rectangular maximum-volume submatrices and their applications

KAUST Repository

Mikhalev, Aleksandr; Oseledets, I.V.

2017-01-01

We introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online.

Rectangular maximum-volume submatrices and their applications

KAUST Repository

Mikhalev, Aleksandr

2017-10-18

We introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online.

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

Technical Note: Continuity of MIPAS-ENVISAT operational ozone data quality from full- to reduced-spectral-resolution operation mode

Directory of Open Access Journals (Sweden)

S. Ceccherini

2008-04-01

Full Text Available MIPAS (Michelson Interferometer for Passive Atmospheric Sounding is operating on the ENVIronmental SATellite (ENVISAT since March 2002. After two years of nearly continuous limb scanning measurements, at the end of March 2004, the instrument was stopped due to problems with the mirror drive of the interferometer. Operations with reduced maximum path difference, corresponding to both a reduced-spectral-resolution and a shorter measurement time, were resumed on January 2005. In order to exploit the reduction in measurement time, the measurement scenario was changed adopting a finer vertical limb scanning. The change of spectral resolution and of measurement scenario entailed an update of the data processing strategy. The aim of this paper is the assessment of the differences in the quality of the MIPAS ozone data acquired before and after the stop of the operations. Two sets of MIPAS ozone profiles acquired in 2003–2004 (full-resolution measurements and in 2005–2006 (reduced-resolution measurements are compared with collocated ozone profiles obtained by GOMOS (Global Ozone Monitoring by Occultation of Stars, itself also onboard ENVISAT. The continuity of the GOMOS data quality allows to assess a possible discontinuity of the MIPAS performances. The relative bias and precision of MIPAS ozone profiles with respect to the GOMOS ones have been compared for the measurements acquired before and after the stop of the MIPAS operations. The results of the comparison show that, in general, the quality of the MIPAS ozone profiles retrieved from reduced-resolution measurements is comparable or better than that obtained from the full-resolution dataset. The only significant change in MIPAS performances is observed at pressures around 2 unit{hPa}, where the relative bias of the instruments increases by a factor of 2 from the 2003–2004 to 2005–2006 measurements.

Novel Heterongineered Detectors for Multi-Color Infrared Sensing

Science.gov (United States)

2012-01-30

a) Sequential but collocated two-color detection capabilities of type II InAsGaSb SLS detector based on an nBn design and (b) Simultaneous and...captions: Figure 1. Heterostructure Schematic of (a) PbIbN Design, (b) Dual Color Detector Design with flat band energy lineups . Figure 2. (a) Spectral

Spectral multitude and spectral dynamics reflect changing conjugation length in single molecules of oligophenylenevinylenes

KAUST Repository

Kobayashi, Hiroyuki; Tsuchiya, Kousuke; Ogino, Kenji; Vacha, Martin

2012-01-01

Single-molecule study of phenylenevinylene oligomers revealed distinct spectral forms due to different conjugation lengths which are determined by torsional defects. Large spectral jumps between different spectral forms were ascribed to torsional flips of a single phenylene ring. These spectral changes reflect the dynamic nature of electron delocalization in oligophenylenevinylenes and enable estimation of the phenylene torsional barriers. © 2012 The Owner Societies.

[Review of digital ground object spectral library].

Science.gov (United States)

Zhou, Xiao-Hu; Zhou, Ding-Wu

2009-06-01

A higher spectral resolution is the main direction of developing remote sensing technology, and it is quite important to set up the digital ground object reflectance spectral database library, one of fundamental research fields in remote sensing application. Remote sensing application has been increasingly relying on ground object spectral characteristics, and quantitative analysis has been developed to a new stage. The present article summarized and systematically introduced the research status quo and development trend of digital ground object reflectance spectral libraries at home and in the world in recent years. Introducing the spectral libraries has been established, including desertification spectral database library, plants spectral database library, geological spectral database library, soil spectral database library, minerals spectral database library, cloud spectral database library, snow spectral database library, the atmosphere spectral database library, rocks spectral database library, water spectral database library, meteorites spectral database library, moon rock spectral database library, and man-made materials spectral database library, mixture spectral database library, volatile compounds spectral database library, and liquids spectral database library. In the process of establishing spectral database libraries, there have been some problems, such as the lack of uniform national spectral database standard and uniform standards for the ground object features as well as the comparability between different databases. In addition, data sharing mechanism can not be carried out, etc. This article also put forward some suggestions on those problems.

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

International Nuclear Information System (INIS)

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

2017-01-01

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

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

Science.gov (United States)

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

2017-10-01

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

SpectralNET – an application for spectral graph analysis and visualization

Directory of Open Access Journals (Sweden)

Schreiber Stuart L

2005-10-01

Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is

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

Directory of Open Access Journals (Sweden)

E. D. Resende

2007-09-01

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

(LMRG): Microscope Resolution, Objective Quality, Spectral Accuracy and Spectral Un-mixing

Science.gov (United States)

Bayles, Carol J.; Cole, Richard W.; Eason, Brady; Girard, Anne-Marie; Jinadasa, Tushare; Martin, Karen; McNamara, George; Opansky, Cynthia; Schulz, Katherine; Thibault, Marc; Brown, Claire M.

2012-01-01

The second study by the LMRG focuses on measuring confocal laser scanning microscope (CLSM) resolution, objective lens quality, spectral imaging accuracy and spectral un-mixing. Affordable test samples for each aspect of the study were designed, prepared and sent to 116 labs from 23 countries across the globe. Detailed protocols were designed for the three tests and customized for most of the major confocal instruments being used by the study participants. One protocol developed for measuring resolution and objective quality was recently published in Nature Protocols (Cole, R. W., T. Jinadasa, et al. (2011). Nature Protocols 6(12): 1929–1941). The first study involved 3D imaging of sub-resolution fluorescent microspheres to determine the microscope point spread function. Results of the resolution studies as well as point spread function quality (i.e. objective lens quality) from 140 different objective lenses will be presented. The second study of spectral accuracy looked at the reflection of the laser excitation lines into the spectral detection in order to determine the accuracy of these systems to report back the accurate laser emission wavelengths. Results will be presented from 42 different spectral confocal systems. Finally, samples with double orange beads (orange core and orange coating) were imaged spectrally and the imaging software was used to un-mix fluorescence signals from the two orange dyes. Results from 26 different confocal systems will be summarized. Time will be left to discuss possibilities for the next LMRG study.

Characterizing CDOM Spectral Variability Across Diverse Regions and Spectral Ranges

Science.gov (United States)

Grunert, Brice K.; Mouw, Colleen B.; Ciochetto, Audrey B.

2018-01-01

Satellite remote sensing of colored dissolved organic matter (CDOM) has focused on CDOM absorption (aCDOM) at a reference wavelength, as its magnitude provides insight into the underwater light field and large-scale biogeochemical processes. CDOM spectral slope, SCDOM, has been treated as a constant or semiconstant parameter in satellite retrievals of aCDOM despite significant regional and temporal variabilities. SCDOM and other optical metrics provide insights into CDOM composition, processing, food web dynamics, and carbon cycling. To date, much of this work relies on fluorescence techniques or aCDOM in spectral ranges unavailable to current and planned satellite sensors (e.g., global variability in SCDOM and fit deviations in the aCDOM spectra using the recently proposed Gaussian decomposition method. From this, we investigate if global variability in retrieved SCDOM and Gaussian components is significant and regionally distinct. We iteratively decreased the spectral range considered and analyzed the number, location, and magnitude of fitted Gaussian components to understand if a reduced spectral range impacts information obtained within a common spectral window. We compared the fitted slope from the Gaussian decomposition method to absorption-based indices that indicate CDOM composition to determine the ability of satellite-derived slope to inform the analysis and modeling of large-scale biogeochemical processes. Finally, we present implications of the observed variability for remote sensing of CDOM characteristics via SCDOM.

On the collocation between dayside auroral activity and coherent HF radar backscatter

Directory of Open Access Journals (Sweden)

J. Moen

Full Text Available The 2D morphology of coherent HF radar and optical cusp aurora has been studied for conditions of predominantly southward IMF conditions, which favours low-latitude boundary layer reconnection. Despite the variability in shape of radar cusp Doppler spectra, the spectral width criterion of > 220 m s^–1 proves to be a robust cusp discriminator. For extended periods of well-developed radar backscatter echoes, the equatorward boundary of the > 220 m s^–1 spectral width enhancement lines up remarkably well with the equatorward boundary of the optical cusp aurora. The spectral width boundary is however poorly determined during development and fading of radar cusp backscatter. Closer inspection of radar Doppler profile characteristics suggests that a combination of spectral width and shape may advance boundary layer identification by HF radar. For the two December days studied the onset of radar cusp backscatter occurred within pre-existing 630.0 nm cusp auroral activity and appear to be initiated by sunrise, i.e. favourable radio wave propagation conditions had to develop. Better methods are put forward for analysing optical data, and for physical interpretation of HF radar data, and for combining these data, as applied to detection, tracking, and better understanding of dayside aurora. The broader motivation of this work is to develop wider use by the scientific community, of results of these techniques, to accelerate understanding of dynamic high-latitude boundary-processes. The contributions in this work are: (1 improved techniques of analysis of observational data, yielding meaningfully enhanced accuracy for deduced cusp locations; (2 a correspondingly more pronounced validation of correlation of boundary locations derived from the observational data set; and (3 a firmer physical rationale as to why the good correlation observed should theoretically be expected.

Key words: Ionosphere (ionospheric

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.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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

Directory of Open Access Journals (Sweden)

Ruili Wen

2016-08-01

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

Estimation of spectral kurtosis

Science.gov (United States)

Sutawanir

2017-03-01

Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to

Spectral stratigraphy

Science.gov (United States)

Lang, Harold R.

1991-01-01

A new approach to stratigraphic analysis is described which uses photogeologic and spectral interpretation of multispectral remote sensing data combined with topographic information to determine the attitude, thickness, and lithology of strata exposed at the surface. The new stratigraphic procedure is illustrated by examples in the literature. The published results demonstrate the potential of spectral stratigraphy for mapping strata, determining dip and strike, measuring and correlating stratigraphic sequences, defining lithofacies, mapping biofacies, and interpreting geological structures.

Spectral unmixing: estimating partial abundances

CSIR Research Space (South Africa)

Debba, Pravesh

2009-01-01

Full Text Available techniques is complicated when considering very similar spectral signatures. Iron-bearing oxide/hydroxide/sulfate minerals have similar spectral signatures. The study focuses on how could estimates of abundances of spectrally similar iron-bearing oxide...

Monolithic Integrated Ceramic Waveguide Filters

OpenAIRE

Hunter, IC; Sandhu, MY

2014-01-01

Design techniques for a new class of integrated monolithic high permittivity ceramic waveguide filters are presented. These filters enable a size reduction of 50% compared to air-filled TEM filters with the same unloaded Q-Factor. Designs for both chebyshev and asymmetric generalized chebyshev filter are presented, with experimental results for an 1800 MHz chebyshev filter showing excellent agreement with theory.

Space-time spectral collocation algorithm for solving time-fractional Tricomi-type equations

Directory of Open Access Journals (Sweden)

Abdelkawy M.A.

2016-01-01

Full Text Available We introduce a new numerical algorithm for solving one-dimensional time-fractional Tricomi-type equations (T-FTTEs. We used the shifted Jacobi polynomials as basis functions and the derivatives of fractional is evaluated by the Caputo definition. The shifted Jacobi Gauss-Lobatt algorithm is used for the spatial discretization, while the shifted Jacobi Gauss-Radau algorithmis applied for temporal approximation. Substituting these approximations in the problem leads to a system of algebraic equations that greatly simplifies the problem. The proposed algorithm is successfully extended to solve the two-dimensional T-FTTEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Introduction to spectral theory

CERN Document Server

Levitan, B M

1975-01-01

This monograph is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.

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.

[Analysis of sensitive spectral bands for burning status detection using hyper-spectral images of Tiangong-01].

Science.gov (United States)

Qin, Xian-Lin; Zhu, Xi; Yang, Fei; Zhao, Kai-Rui; Pang, Yong; Li, Zeng-Yuan; Li, Xu-Zhi; Zhang, Jiu-Xing

2013-07-01

To obtain the sensitive spectral bands for detection of information on 4 kinds of burning status, i. e. flaming, smoldering, smoke, and fire scar, with satellite data, analysis was conducted to identify suitable satellite spectral bands for detection of information on these 4 kinds of burning status by using hyper-spectrum images of Tiangong-01 (TG-01) and employing a method combining statistics and spectral analysis. The results show that: in the hyper-spectral images of TG-01, the spectral bands differ obviously for detection of these 4 kinds of burning status; in all hyper-spectral short-wave infrared channels, the reflectance of flaming is higher than that of all other 3 kinds of burning status, and the reflectance of smoke is the lowest; the reflectance of smoke is higher than that of all other 3 kinds of burning status in the channels corresponding to hyper-spectral visible near-infrared and panchromatic sensors. For spectral band selection, more suitable spectral bands for flaming detection are 1 000.0-1 956.0 and 2 020.0-2 400.0 nm; the suitable spectral bands for identifying smoldering are 930.0-1 000.0 and 1 084.0-2 400.0 nm; the suitable spectral bands for smoke detection is in 400.0-920.0 nm; for fire scar detection, it is suitable to select bands with central wavelengths of 900.0-930.0 and 1 300.0-2 400.0 nm, and then to combine them to construct a detection model.

Spectral Decomposition Algorithm (SDA)

Data.gov (United States)

National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...

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.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization (II): Solution of Equation

International Nuclear Information System (INIS)

Wang Huaiyu; Long Yao; Chen Nanxian

2006-01-01

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Chebyshev Distance

OpenAIRE

Coghetto Roland

2016-01-01

In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of ℰTn${\\cal E}_T^n $ and in [20] he has formalized that ℰTn${\\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23]) a denumerable base of ℰTn${\\cal E}_T^n $.

Chebyshev Distance

Directory of Open Access Journals (Sweden)

Coghetto Roland

2016-06-01

Full Text Available In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26] of ℰTn${\\cal E}_T^n $ and in [20] he has formalized that ℰTn${\\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23] a denumerable base of ℰTn${\\cal E}_T^n $.

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

Science.gov (United States)

Ophaug, Vegard; Gerlach, Christian

2017-11-01

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

Optimization of spectral printer modeling based on a modified cellular Yule-Nielsen spectral Neugebauer model.

Science.gov (United States)

Liu, Qiang; Wan, Xiaoxia; Xie, Dehong

2014-06-01

The study presented here optimizes several steps in the spectral printer modeling workflow based on a cellular Yule-Nielsen spectral Neugebauer (CYNSN) model. First, a printer subdividing method was developed that reduces the number of sub-models while maintaining the maximum device gamut. Second, the forward spectral prediction accuracy of the CYNSN model for each subspace of the printer was improved using back propagation artificial neural network (BPANN) estimated n values. Third, a sequential gamut judging method, which clearly reduced the complexity of the optimal sub-model and cell searching process during printer backward modeling, was proposed. After that, we further modified the use of the modeling color metric and comprehensively improved the spectral and perceptual accuracy of the spectral printer model. The experimental results show that the proposed optimization approaches provide obvious improvements in aspects of the modeling accuracy or efficiency for each of the corresponding steps, and an overall improvement of the optimized spectral printer modeling workflow was also demonstrated.

Ice particle production in mid-level stratiform mixed-phase clouds observed with collocated A-Train measurements

Directory of Open Access Journals (Sweden)

D. Zhang

2018-03-01

Full Text Available Collocated A-Train CloudSat radar and CALIPSO lidar measurements between 2006 and 2010 are analyzed to study primary ice particle production characteristics in mid-level stratiform mixed-phase clouds on a global scale. For similar clouds in terms of cloud top temperature and liquid water path, Northern Hemisphere latitude bands have layer-maximum radar reflectivity (ZL that is  ∼  1 to 8 dBZ larger than their counterparts in the Southern Hemisphere. The systematically larger ZL under similar cloud conditions suggests larger ice number concentrations in mid-level stratiform mixed-phase clouds over the Northern Hemisphere, which is possibly related to higher background aerosol loadings. Furthermore, we show that springtime northern mid- and high latitudes have ZL that is larger by up to 6 dBZ (a factor of 4 higher ice number concentration than other seasons, which might be related to more dust events that provide effective ice nucleating particles. Our study suggests that aerosol-dependent ice number concentration parameterizations are required in climate models to improve mixed-phase cloud simulations, especially over the Northern Hemisphere.

Spectral radius of graphs

CERN Document Server

Stevanovic, Dragan

2015-01-01

Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the

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

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.

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

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

Directory of Open Access Journals (Sweden)

Seyed Hossein Mahdavi

2015-01-01

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

Spectral L2/L1 norm: A new perspective for spectral kurtosis for characterizing non-stationary signals

Science.gov (United States)

Wang, Dong

2018-05-01

Thanks to the great efforts made by Antoni (2006), spectral kurtosis has been recognized as a milestone for characterizing non-stationary signals, especially bearing fault signals. The main idea of spectral kurtosis is to use the fourth standardized moment, namely kurtosis, as a function of spectral frequency so as to indicate how repetitive transients caused by a bearing defect vary with frequency. Moreover, spectral kurtosis is defined based on an analytic bearing fault signal constructed from either a complex filter or Hilbert transform. On the other hand, another attractive work was reported by Borghesani et al. (2014) to mathematically reveal the relationship between the kurtosis of an analytical bearing fault signal and the square of the squared envelope spectrum of the analytical bearing fault signal for explaining spectral correlation for quantification of bearing fault signals. More interestingly, it was discovered that the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum corresponds to the raw 4th order moment. Inspired by the aforementioned works, in this paper, we mathematically show that: (1) spectral kurtosis can be decomposed into squared envelope and squared L2/L1 norm so that spectral kurtosis can be explained as spectral squared L2/L1 norm; (2) spectral L2/L1 norm is formally defined for characterizing bearing fault signals and its two geometrical explanations are made; (3) spectral L2/L1 norm is proportional to the square root of the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum; (4) some extensions of spectral L2/L1 norm for characterizing bearing fault signals are pointed out.

Spectral methods. Fundamentals in single domains

International Nuclear Information System (INIS)

Canuto, C.

2006-01-01

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

Vowel Inherent Spectral Change

CERN Document Server

Assmann, Peter

2013-01-01

It has been traditional in phonetic research to characterize monophthongs using a set of static formant frequencies, i.e., formant frequencies taken from a single time-point in the vowel or averaged over the time-course of the vowel. However, over the last twenty years a growing body of research has demonstrated that, at least for a number of dialects of North American English, vowels which are traditionally described as monophthongs often have substantial spectral change. Vowel Inherent Spectral Change has been observed in speakers’ productions, and has also been found to have a substantial effect on listeners’ perception. In terms of acoustics, the traditional categorical distinction between monophthongs and diphthongs can be replaced by a gradient description of dynamic spectral patterns. This book includes chapters addressing various aspects of vowel inherent spectral change (VISC), including theoretical and experimental studies of the perceptually relevant aspects of VISC, the relationship between ar...

Spectrally accurate contour dynamics

International Nuclear Information System (INIS)

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

1994-01-01

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

Assessing the role of spectral and intensity cues in spectral ripple detection and discrimination in cochlear-implant users.

Science.gov (United States)

Anderson, Elizabeth S; Oxenham, Andrew J; Nelson, Peggy B; Nelson, David A

2012-12-01

Measures of spectral ripple resolution have become widely used psychophysical tools for assessing spectral resolution in cochlear-implant (CI) listeners. The objective of this study was to compare spectral ripple discrimination and detection in the same group of CI listeners. Ripple detection thresholds were measured over a range of ripple frequencies and were compared to spectral ripple discrimination thresholds previously obtained from the same CI listeners. The data showed that performance on the two measures was correlated, but that individual subjects' thresholds (at a constant spectral modulation depth) for the two tasks were not equivalent. In addition, spectral ripple detection was often found to be possible at higher rates than expected based on the available spectral cues, making it likely that temporal-envelope cues played a role at higher ripple rates. Finally, spectral ripple detection thresholds were compared to previously obtained speech-perception measures. Results confirmed earlier reports of a robust relationship between detection of widely spaced ripples and measures of speech recognition. In contrast, intensity difference limens for broadband noise did not correlate with spectral ripple detection measures, suggesting a dissociation between the ability to detect small changes in intensity across frequency and across time.

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

Science.gov (United States)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

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

Intersection numbers of spectral curves

CERN Document Server

Eynard, B.

2011-01-01

We compute the symplectic invariants of an arbitrary spectral curve with only 1 branchpoint in terms of integrals of characteristic classes in the moduli space of curves. Our formula associates to any spectral curve, a characteristic class, which is determined by the laplace transform of the spectral curve. This is a hint to the key role of Laplace transform in mirror symmetry. When the spectral curve is y=\\sqrt{x}, the formula gives Kontsevich--Witten intersection numbers, when the spectral curve is chosen to be the Lambert function \\exp{x}=y\\exp{-y}, the formula gives the ELSV formula for Hurwitz numbers, and when one chooses the mirror of C^3 with framing f, i.e. \\exp{-x}=\\exp{-yf}(1-\\exp{-y}), the formula gives the Marino-Vafa formula, i.e. the generating function of Gromov-Witten invariants of C^3. In some sense this formula generalizes ELSV, Marino-Vafa formula, and Mumford formula.

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.

Underground collocation of nuclear power plant reactors and repository to facilitate the post-renaissance expansion of nuclear power

Energy Technology Data Exchange (ETDEWEB)

Myers, Carl W [Los Alamos National Laboratory; Elkins, Ned Z [Los Alamos National Laboratory

2008-01-01

Underground collocation of nuclear power reactors and the nuclear waste management facilities supporting those reactors, termed an underground nuclear park (UNP), appears to have several advantages compared to the conventional approach to siting reactors and waste management facilities. These advantages include the potential to lower reactor capital and operating cost, lower nuclear waste management cost, and increase margins of physical security and safety. Envirorunental impacts related to worker health, facility accidents, waste transportation, and sabotage and terrorism appear to be lower for UNPs compared to the current approach. In-place decommissioning ofUNP reactors appears to have cost, safety, envirorunental and waste disposal advantages. The UNP approach has the potential to lead to greater public acceptance for the deployment of new power reactors. Use of the UNP during the post-nuclear renaissance time frame has the potential to enable a greater expansion of U.S. nuclear power generation than might otherwise result. Technical and economic aspects of the UNP concept need more study to determine the viability of the concept.

Atmospheric parameters, spectral indexes and their relation to CPV spectral performance

Energy Technology Data Exchange (ETDEWEB)

Núñez, Rubén, E-mail: ruben.nunez@ies-def.upm.es; Antón, Ignacio, E-mail: ruben.nunez@ies-def.upm.es; Askins, Steve, E-mail: ruben.nunez@ies-def.upm.es; Sala, Gabriel, E-mail: ruben.nunez@ies-def.upm.es [Instituto de Energía Solar - Universidad Politécnica de Madrid, Instituto de Energía Solar, ETSI Telecomunicación, Ciudad Universitaria 28040 Madrid (Spain)

2014-09-26

Air Mass and atmosphere components (basically aerosol (AOD) and precipitable water (PW)) define the absorption of the sunlight that arrive to Earth. Radiative models such as SMARTS or MODTRAN use these parameters to generate an equivalent spectrum. However, complex and expensive instruments (as AERONET network devices) are needed to obtain AOD and PW. On the other hand, the use of isotype cells is a convenient way to characterize spectrally a place for CPV considering that they provide the photocurrent of the different internal subcells individually. Crossing data from AERONET station and a Tri-band Spectroheliometer, a model that correlates Spectral Mismatch Ratios and atmospheric parameters is proposed. Considering the amount of stations of AERONET network, this model may be used to estimate the spectral influence on energy performance of CPV systems close to all the stations worldwide.

Calibration with near-continuous spectral measurements

DEFF Research Database (Denmark)

Nielsen, Henrik Aalborg; Rasmussen, Michael; Madsen, Henrik

2001-01-01

In chemometrics traditional calibration in case of spectral measurements express a quantity of interest (e.g. a concentration) as a linear combination of the spectral measurements at a number of wavelengths. Often the spectral measurements are performed at a large number of wavelengths and in thi...... by an example in which the octane number of gasoline is related to near infrared spectral measurements. The performance is found to be much better that for the traditional calibration methods....

Calibrating spectral images using penalized likelihood

NARCIS (Netherlands)

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

2003-01-01

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

Spectral Learning for Supervised Topic Models.

Science.gov (United States)

Ren, Yong; Wang, Yining; Zhu, Jun

2018-03-01

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

Metallicity and the spectral energy distribution and spectral types of dwarf O-stars

NARCIS (Netherlands)

Mokiem, MR; Martin-Hernandez, NL; Lenorzer, A; de Koter, A; Tielens, AGGA

We present a systematic study of the effect of metallicity on the stellar spectral energy distribution (SED) of 0 main sequence (dwarf) stars, focussing on the hydrogen and helium ionizing continua, and on the optical and near-IR lines used for spectral classification. The spectra are based on

Metallicity and the spectral energy distribution and spectral types of dwarf O-stars

NARCIS (Netherlands)

Mokiem, M.R.; Martín-Hernández, N.L.; Lenorzer, A.; de Koter, A.; Tielens, A.G.G.M.

2004-01-01

We present a systematic study of the effect of metallicity on the stellar spectral energy distribution (SED) of O main sequence (dwarf) stars, focussing on the hydrogen and helium ionizing continua, and on the optical and near-IR lines used for spectral classification. The spectra are based on

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

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

Directory of Open Access Journals (Sweden)

WANG Yupu

2016-06-01

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

Spectral filtering for plant production

Energy Technology Data Exchange (ETDEWEB)

Young, R.E.; McMahon, M.J.; Rajapakse, N.C.; Becoteau, D.R.

1994-12-31

Research to date suggests that spectral filtering can be an effective alternative to chemical growth regulators for altering plant development. If properly implemented, it can be nonchemical and environmentally friendly. The aqueous CuSO{sub 4}, and CuCl{sub 2} solutions in channelled plastic panels have been shown to be effective filters, but they can be highly toxic if the solutions contact plants. Some studies suggest that spectral filtration limited to short EOD intervals can also alter plant development. Future research should be directed toward confirmation of the influence of spectral filters and exposure times on a broader range of plant species and cultivars. Efforts should also be made to identify non-noxious alternatives to aqueous copper solutions and/or to incorporate these chemicals permanently into plastic films and panels that can be used in greenhouse construction. It would also be informative to study the impacts of spectral filters on insect and microbal populations in plant growth facilities. The economic impacts of spectral filtering techniques should be assessed for each delivery methodology.

Evaluating the capabilities of vegetation spectral indices on chlorophyll content estimation at Sentinel-2 spectral resolutions

Science.gov (United States)

Sun, Qi; Jiao, Quanjun; Dai, Huayang

2018-03-01

Chlorophyll is an important pigment in green plants for photosynthesis and obtaining the energy for growth and development. The rapid, nondestructive and accurate estimation of chlorophyll content is significant for understanding the crops growth, monitoring the disease and insect, and assessing the yield of crops. Sentinel-2 equipped with the Multi-Spectral Instrument (MSI), which will provide images with high spatial, spectral and temporal resolution. It covers the VNIR/SWIR spectral region in 13 bands and incorporates two new spectral bands in the red-edge region and a spatial resolution of 20nm, which can be used to derive vegetation indices using red-edge bands. In this paper, we will focus on assessing the potential of vegetation spectral indices for retrieving chlorophyll content from Sentinel-2 at different angles. Subsequently, we used in-situ spectral data and Sentinel-2 data to test the relationship between VIs and chlorophyll content. The REP, MTCI, CIred-edge, CIgreen, Macc01, TCARI/OSAVI [705,750], NDRE1 and NDRE2 were calculated. NDRE2 index displays a strongly similar result for hyperspectral and simulated Sentinel-2 spectral bands (R2 =0.53, R2 =0.51, for hyperspectral and Sentinel-2, respectively). At different observation angles, NDRE2 has the smallest difference in performance (R2 = 0.51, R2 =0.64, at 0° and 15° , respectively).

On Longitudinal Spectral Coherence

DEFF Research Database (Denmark)

Kristensen, Leif

1979-01-01

It is demonstrated that the longitudinal spectral coherence differs significantly from the transversal spectral coherence in its dependence on displacement and frequency. An expression for the longitudinal coherence is derived and it is shown how the scale of turbulence, the displacement between ...... observation sites and the turbulence intensity influence the results. The limitations of the theory are discussed....

Speech recognition from spectral dynamics

Indian Academy of Sciences (India)

Carrier nature of speech; modulation spectrum; spectral dynamics ... the relationships between phonetic values of sounds and their short-term spectral envelopes .... the number of free parameters that need to be estimated from training data.

Meson spectral functions at finite temperature

International Nuclear Information System (INIS)

Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S.

2001-10-01

The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T c . The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64) 3 x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature. (orig.)

Meson spectral functions at finite temperature

International Nuclear Information System (INIS)

Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S.

2002-01-01

The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T c . The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64) 3 x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature

Meson spectral functions at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S

2002-03-01

The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T{sub c}. The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64){sup 3} x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature.

Meson spectral functions at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S. [Bielefeld Univ. (Germany). Fakultaet fuer Physik

2001-10-01

The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T{sub c}. The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64){sup 3} x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature. (orig.)

The development of a modified spectral ripple test.

Science.gov (United States)

Aronoff, Justin M; Landsberger, David M

2013-08-01

Poor spectral resolution can be a limiting factor for hearing impaired listeners, particularly for complex listening tasks such as speech understanding in noise. Spectral ripple tests are commonly used to measure spectral resolution, but these tests contain a number of potential confounds that can make interpretation of the results difficult. To measure spectral resolution while avoiding those confounds, a modified spectral ripple test with dynamically changing ripples was created, referred to as the spectral-temporally modulated ripple test (SMRT). This paper describes the SMRT and provides evidence that it is sensitive to changes in spectral resolution.

Comparing auditory filter bandwidths, spectral ripple modulation detection, spectral ripple discrimination, and speech recognition: Normal and impaired hearing.

Science.gov (United States)

Davies-Venn, Evelyn; Nelson, Peggy; Souza, Pamela

2015-07-01

Some listeners with hearing loss show poor speech recognition scores in spite of using amplification that optimizes audibility. Beyond audibility, studies have suggested that suprathreshold abilities such as spectral and temporal processing may explain differences in amplified speech recognition scores. A variety of different methods has been used to measure spectral processing. However, the relationship between spectral processing and speech recognition is still inconclusive. This study evaluated the relationship between spectral processing and speech recognition in listeners with normal hearing and with hearing loss. Narrowband spectral resolution was assessed using auditory filter bandwidths estimated from simultaneous notched-noise masking. Broadband spectral processing was measured using the spectral ripple discrimination (SRD) task and the spectral ripple depth detection (SMD) task. Three different measures were used to assess unamplified and amplified speech recognition in quiet and noise. Stepwise multiple linear regression revealed that SMD at 2.0 cycles per octave (cpo) significantly predicted speech scores for amplified and unamplified speech in quiet and noise. Commonality analyses revealed that SMD at 2.0 cpo combined with SRD and equivalent rectangular bandwidth measures to explain most of the variance captured by the regression model. Results suggest that SMD and SRD may be promising clinical tools for diagnostic evaluation and predicting amplification outcomes.

Comparing auditory filter bandwidths, spectral ripple modulation detection, spectral ripple discrimination, and speech recognition: Normal and impaired hearinga)

Science.gov (United States)

Davies-Venn, Evelyn; Nelson, Peggy; Souza, Pamela

2015-01-01

Some listeners with hearing loss show poor speech recognition scores in spite of using amplification that optimizes audibility. Beyond audibility, studies have suggested that suprathreshold abilities such as spectral and temporal processing may explain differences in amplified speech recognition scores. A variety of different methods has been used to measure spectral processing. However, the relationship between spectral processing and speech recognition is still inconclusive. This study evaluated the relationship between spectral processing and speech recognition in listeners with normal hearing and with hearing loss. Narrowband spectral resolution was assessed using auditory filter bandwidths estimated from simultaneous notched-noise masking. Broadband spectral processing was measured using the spectral ripple discrimination (SRD) task and the spectral ripple depth detection (SMD) task. Three different measures were used to assess unamplified and amplified speech recognition in quiet and noise. Stepwise multiple linear regression revealed that SMD at 2.0 cycles per octave (cpo) significantly predicted speech scores for amplified and unamplified speech in quiet and noise. Commonality analyses revealed that SMD at 2.0 cpo combined with SRD and equivalent rectangular bandwidth measures to explain most of the variance captured by the regression model. Results suggest that SMD and SRD may be promising clinical tools for diagnostic evaluation and predicting amplification outcomes. PMID:26233047

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

Science.gov (United States)

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

2014-05-01

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

Reduction of Linear Programming to Linear Approximation

OpenAIRE

Vaserstein, Leonid N.

2006-01-01

It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

Spectral properties of generalized eigenparameter dependent ...

African Journals Online (AJOL)

Jost function, spectrum, the spectral singularities, and the properties of the principal vectors corresponding to the spectral singularities of L, if. ∞Σn=1 n(∣1 - an∣ + ∣bnl) < ∞. Mathematics Subject Classication (2010): 34L05, 34L40, 39A70, 47A10, 47A75. Key words: Discrete equations, eigenparameter, spectral analysis, ...

Planck 2013 results. IX. HFI spectral response

CERN Document Server

Ade, P A R; Armitage-Caplan, C; Arnaud, M; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Battaner, E; Benabed, K; Benoît, A; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bobin, J; Bock, J J; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bridges, M; Bucher, M; Burigana, C; Cardoso, J -F; Catalano, A; Challinor, A; Chamballu, A; Chary, R -R; Chen, X; Chiang, L -Y; Chiang, H C; Christensen, P R; Church, S; Clements, D L; Colombi, S; Colombo, L P L; Combet, C; Comis, B; Couchot, F; Coulais, A; Crill, B P; Curto, A; Cuttaia, F; Danese, L; Davies, R D; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Delouis, J -M; Désert, F -X; Dickinson, C; Diego, J M; Dole, H; Donzelli, S; Doré, O; Douspis, M; Dupac, X; Efstathiou, G; Enßlin, T A; Eriksen, H K; Falgarone, E; Finelli, F; Forni, O; Frailis, M; Franceschi, E; Galeotta, S; Ganga, K; Giard, M; Giraud-Héraud, Y; González-Nuevo, J; Górski, K M; Gratton, S; Gregorio, A; Gruppuso, A; Hansen, F K; Hanson, D; Harrison, D; Henrot-Versillé, S; Hernández-Monteagudo, C; Herranz, D; Hildebrandt, S R; Hivon, E; Hobson, M; Holmes, W A; Hornstrup, A; Hovest, W; Huffenberger, K M; Hurier, G; Jaffe, T R; Jaffe, A H; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Kneissl, R; Knoche, J; Knox, L; Kunz, M; Kurki-Suonio, H; Lagache, G; Lamarre, J -M; Lasenby, A; Laureijs, R J; Lawrence, C R; Leahy, J P; Leonardi, R; Leroy, C; Lesgourgues, J; Liguori, M; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maffei, B; Mandolesi, N; Maris, M; Marshall, D J; Martin, P G; Martínez-González, E; Masi, S; Matarrese, S; Matthai, F; Mazzotta, P; McGehee, P; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Mitra, S; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Netterfield, C B; Nørgaard-Nielsen, H U; North, C; Noviello, F; Novikov, D; Novikov, I; Osborne, S; Oxborrow, C A; Paci, F; Pagano, L; Pajot, F; Paoletti, D; Pasian, F; Patanchon, G; Perdereau, O; Perotto, L; Perrotta, F; Piacentini, F; Piat, M; Pierpaoli, E; Pietrobon, D; Plaszczynski, S; Pointecouteau, E; Polenta, G; Ponthieu, N; Popa, L; Poutanen, T; Pratt, G W; Prézeau, G; Prunet, S; Puget, J -L; Rachen, J P; Reinecke, M; Remazeilles, M; Renault, C; Ricciardi, S; Riller, T; Ristorcelli, I; Rocha, G; Rosset, C; Roudier, G; Rusholme, B; Santos, D; Savini, G; Shellard, E P S; Spencer, L D; Starck, J -L; Stolyarov, V; Stompor, R; Sudiwala, R; Sureau, F; Sutton, D; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Tavagnacco, D; Terenzi, L; Tomasi, M; Tristram, M; Tucci, M; Umana, G; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Vittorio, N; Wade, L A; Wandelt, B D; Yvon, D; Zacchei, A; Zonca, A

2014-01-01

The Planck High Frequency Instrument (HFI) spectral response was determined through a series of ground based tests conducted with the HFI focal plane in a cryogenic environment prior to launch. The main goal of the spectral transmission tests was to measure the relative spectral response (including out-of-band signal rejection) of all HFI detectors. This was determined by measuring the output of a continuously scanned Fourier transform spectrometer coupled with all HFI detectors. As there is no on-board spectrometer within HFI, the ground-based spectral response experiments provide the definitive data set for the relative spectral calibration of the HFI. The spectral response of the HFI is used in Planck data analysis and component separation, this includes extraction of CO emission observed within Planck bands, dust emission, Sunyaev-Zeldovich sources, and intensity to polarization leakage. The HFI spectral response data have also been used to provide unit conversion and colour correction analysis tools. Ver...

CRISS power spectral density

International Nuclear Information System (INIS)

Vaeth, W.

1979-04-01

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

Onboard spectral imager data processor

Science.gov (United States)

Otten, Leonard J.; Meigs, Andrew D.; Franklin, Abraham J.; Sears, Robert D.; Robison, Mark W.; Rafert, J. Bruce; Fronterhouse, Donald C.; Grotbeck, Ronald L.

1999-10-01

Previous papers have described the concept behind the MightySat II.1 program, the satellite's Fourier Transform imaging spectrometer's optical design, the design for the spectral imaging payload, and its initial qualification testing. This paper discusses the on board data processing designed to reduce the amount of downloaded data by an order of magnitude and provide a demonstration of a smart spaceborne spectral imaging sensor. Two custom components, a spectral imager interface 6U VME card that moves data at over 30 MByte/sec, and four TI C-40 processors mounted to a second 6U VME and daughter card, are used to adapt the sensor to the spacecraft and provide the necessary high speed processing. A system architecture that offers both on board real time image processing and high-speed post data collection analysis of the spectral data has been developed. In addition to the on board processing of the raw data into a usable spectral data volume, one feature extraction technique has been incorporated. This algorithm operates on the basic interferometric data. The algorithm is integrated within the data compression process to search for uploadable feature descriptions.

Using GIS servers and interactive maps in spectral data sharing and administration: Case study of Ahvaz Spectral Geodatabase Platform (ASGP)

Science.gov (United States)

Karami, Mojtaba; Rangzan, Kazem; Saberi, Azim

2013-10-01

With emergence of air-borne and space-borne hyperspectral sensors, spectroscopic measurements are gaining more importance in remote sensing. Therefore, the number of available spectral reference data is constantly increasing. This rapid increase often exhibits a poor data management, which leads to ultimate isolation of data on disk storages. Spectral data without precise description of the target, methods, environment, and sampling geometry cannot be used by other researchers. Moreover, existing spectral data (in case it accompanied with good documentation) become virtually invisible or unreachable for researchers. Providing documentation and a data-sharing framework for spectral data, in which researchers are able to search for or share spectral data and documentation, would definitely improve the data lifetime. Relational Database Management Systems (RDBMS) are main candidates for spectral data management and their efficiency is proven by many studies and applications to date. In this study, a new approach to spectral data administration is presented based on spatial identity of spectral samples. This method benefits from scalability and performance of RDBMS for storage of spectral data, but uses GIS servers to provide users with interactive maps as an interface to the system. The spectral files, photographs and descriptive data are considered as belongings of a geospatial object. A spectral processing unit is responsible for evaluation of metadata quality and performing routine spectral processing tasks for newly-added data. As a result, by using internet browser software the users would be able to visually examine availability of data and/or search for data based on descriptive attributes associated to it. The proposed system is scalable and besides giving the users good sense of what data are available in the database, it facilitates participation of spectral reference data in producing geoinformation.

Precise Multi-Spectral Dermatological Imaging

DEFF Research Database (Denmark)

Gomez, David Delgado; Carstensen, Jens Michael; Ersbøll, Bjarne Kjær

2004-01-01

In this work, an integrated imaging system to obtain accurate and reproducible multi-spectral dermatological images is proposed. The system is made up of an integrating sphere, light emitting diodes and a generic monochromatic camera. The system can collect up to 10 different spectral bands....... These spectral bands vary from ultraviolet to near infrared. The welldefined and diffuse illumination of the optically closed scene aims to avoid shadows and specular reflections. Furthermore, the system has been developed to guarantee the reproducibility of the collected images. This allows for comparative...

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.

SPAM- SPECTRAL ANALYSIS MANAGER (UNIX VERSION)

Science.gov (United States)

Solomon, J. E.

1994-01-01

The Spectral Analysis Manager (SPAM) was developed to allow easy qualitative analysis of multi-dimensional imaging spectrometer data. Imaging spectrometers provide sufficient spectral sampling to define unique spectral signatures on a per pixel basis. Thus direct material identification becomes possible for geologic studies. SPAM provides a variety of capabilities for carrying out interactive analysis of the massive and complex datasets associated with multispectral remote sensing observations. In addition to normal image processing functions, SPAM provides multiple levels of on-line help, a flexible command interpretation, graceful error recovery, and a program structure which can be implemented in a variety of environments. SPAM was designed to be visually oriented and user friendly with the liberal employment of graphics for rapid and efficient exploratory analysis of imaging spectrometry data. SPAM provides functions to enable arithmetic manipulations of the data, such as normalization, linear mixing, band ratio discrimination, and low-pass filtering. SPAM can be used to examine the spectra of an individual pixel or the average spectra over a number of pixels. SPAM also supports image segmentation, fast spectral signature matching, spectral library usage, mixture analysis, and feature extraction. High speed spectral signature matching is performed by using a binary spectral encoding algorithm to separate and identify mineral components present in the scene. The same binary encoding allows automatic spectral clustering. Spectral data may be entered from a digitizing tablet, stored in a user library, compared to the master library containing mineral standards, and then displayed as a timesequence spectral movie. The output plots, histograms, and stretched histograms produced by SPAM can be sent to a lineprinter, stored as separate RGB disk files, or sent to a Quick Color Recorder. SPAM is written in C for interactive execution and is available for two different

Curvature Effect and the Spectral Softening Phenomenon Detected ...

Indian Academy of Sciences (India)

soft spectral evolution, indicating that this spectral softening is not a rare phenomenon .... of time, there exists a temporal steep decay phase accompanied by spectral softening. (d) In most cases, the temporal power law index α and the spectral.

Comparison of matrix exponential methods for fuel burnup calculations

International Nuclear Information System (INIS)

Oh, Hyung Suk; Yang, Won Sik

1999-01-01

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

Spectral properties of 441 radio pulsars

Science.gov (United States)

Jankowski, F.; van Straten, W.; Keane, E. F.; Bailes, M.; Barr, E. D.; Johnston, S.; Kerr, M.

2018-02-01

We present a study of the spectral properties of 441 pulsars observed with the Parkes radio telescope near the centre frequencies of 728, 1382 and 3100 MHz. The observations at 728 and 3100 MHz were conducted simultaneously using the dual-band 10-50 cm receiver. These high-sensitivity, multifrequency observations provide a systematic and uniform sample of pulsar flux densities. We combine our measurements with spectral data from the literature in order to derive the spectral properties of these pulsars. Using techniques from robust regression and information theory, we classify the observed spectra in an objective, robust and unbiased way into five morphological classes: simple or broken power law, power law with either low- or high-frequency cut-off and log-parabolic spectrum. While about 79 per cent of the pulsars that could be classified have simple power-law spectra, we find significant deviations in 73 pulsars, 35 of which have curved spectra, 25 with a spectral break and 10 with a low-frequency turn-over. We identify 11 gigahertz-peaked spectrum (GPS) pulsars, with 3 newly identified in this work and 8 confirmations of known GPS pulsars; 3 others show tentative evidence of GPS, but require further low-frequency measurements to support this classification. The weighted mean spectral index of all pulsars with simple power-law spectra is -1.60 ± 0.03. The observed spectral indices are well described by a shifted log-normal distribution. The strongest correlations of spectral index are with spin-down luminosity, magnetic field at the light-cylinder and spin-down rate. We also investigate the physical origin of the observed spectral features and determine emission altitudes for three pulsars.

Spectral emissivity of tungsten: analytic expressions for the 340-nm to 2.6-μm spectral region

International Nuclear Information System (INIS)

Pon, R.M.; Hessler, J.P.

1984-01-01

To correct emission spectra a standard radiance source is often used to determine the spectral responsivity of the detection system. In the near-UV, visible, and near-IR spectral regions the most common radiance standard is a tungsten strip lamp calibrated by a standards laboratory. For day-to-day experiments where slightly less accuracy is acceptable, a less expensive uncalibrated lamp is useful. In this case, the radiant temperature T/sub r/ of the lamp is measured with an optical pyrometer, generally at a single wavelength such as 650 nm, and the source spectral radiance L(λ) is calculated from L(λ) = tau(λ)epsilon(λ,T)L/sub B/(λ,T). The transmittance of the source is tau(λ), the spectral emissivity is epsilon(λ,T), and L/sub B/(λ,T) is the spectral distribution of blackbody radiation, Planck's radiation law. To obtain the true temperature T, Wien's approximation is employed. To conveniently calibrate a system, especially one which utilizes a microcomputer, it is advantageous to have analytic expressions for the spectral emissivity of tungsten. Although Larrabee has published such expressions, they are limited to the 450-800-nm spectral region. To obtain analytic expressions from 340 nm to 2.6 μm they have used the measurements of DeVos. Although DeVos's results differ by 2% from those of Larrabee, this difference is assumed to be acceptable

The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter

Directory of Open Access Journals (Sweden)

Cornelis van der Mee

2005-01-01

Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian

Spectrally-engineered solar thermal photovoltaic devices

Science.gov (United States)

Lenert, Andrej; Bierman, David; Chan, Walker; Celanovic, Ivan; Soljacic, Marin; Wang, Evelyn N.; Nam, Young Suk; McEnaney, Kenneth; Kraemer, Daniel; Chen, Gang

2018-03-27

A solar thermal photovoltaic device, and method of forming same, includes a solar absorber and a spectrally selective emitter formed on either side of a thermally conductive substrate. The solar absorber is configured to absorb incident solar radiation. The solar absorber and the spectrally selective emitter are configured with an optimized emitter-to-absorber area ratio. The solar thermal photovoltaic device also includes a photovoltaic cell in thermal communication with the spectrally selective emitter. The spectrally selective emitter is configured to permit high emittance for energies above a bandgap of the photovoltaic cell and configured to permit low emittance for energies below the bandgap.

Spacetime Discontinuous Galerkin FEM: Spectral Response

International Nuclear Information System (INIS)

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

2014-01-01

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

Spectral quality requirements for effluent identification

Science.gov (United States)

Czerwinski, R. N.; Seeley, J. A.; Wack, E. C.

2005-11-01

We consider the problem of remotely identifying gaseous materials using passive sensing of long-wave infrared (LWIR) spectral features at hyperspectral resolution. Gaseous materials are distinguishable in the LWIR because of their unique spectral fingerprints. A sensor degraded in capability by noise or limited spectral resolution, however, may be unable to positively identify contaminants, especially if they are present in low concentrations or if the spectral library used for comparisons includes materials with similar spectral signatures. This paper will quantify the relative importance of these parameters and express the relationships between them in a functional form which can be used as a rule of thumb in sensor design or in assessing sensor capability for a specific task. This paper describes the simulation of remote sensing datacontaining a gas cloud.In each simulation, the spectra are degraded in spectral resolution and through the addition of noise to simulate spectra collected by sensors of varying design and capability. We form a trade space by systematically varying the number of sensor spectral channels and signal-to-noise ratio over a range of values. For each scenario, we evaluate the capability of the sensor for gas identification by computing the ratio of the F-statistic for the truth gas tothe same statistic computed over the rest of the library.The effect of the scope of the library is investigated as well, by computing statistics on the variability of the identification capability as the library composition is varied randomly.

Information-efficient spectral imaging sensor

Science.gov (United States)

Sweatt, William C.; Gentry, Stephen M.; Boye, Clinton A.; Grotbeck, Carter L.; Stallard, Brian R.; Descour, Michael R.

2003-01-01

A programmable optical filter for use in multispectral and hyperspectral imaging. The filter splits the light collected by an optical telescope into two channels for each of the pixels in a row in a scanned image, one channel to handle the positive elements of a spectral basis filter and one for the negative elements of the spectral basis filter. Each channel for each pixel disperses its light into n spectral bins, with the light in each bin being attenuated in accordance with the value of the associated positive or negative element of the spectral basis vector. The spectral basis vector is constructed so that its positive elements emphasize the presence of a target and its negative elements emphasize the presence of the constituents of the background of the imaged scene. The attenuated light in the channels is re-imaged onto separate detectors for each pixel and then the signals from the detectors are combined to give an indication of the presence or not of the target in each pixel of the scanned scene. This system provides for a very efficient optical determination of the presence of the target, as opposed to the very data intensive data manipulations that are required in conventional hyperspectral imaging systems.

Spectral theory of linear operators and spectral systems in Banach algebras

CERN Document Server

Müller, Vladimir

2003-01-01

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

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.

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

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-10-15

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

Cochlear implant users' spectral ripple resolution.

Science.gov (United States)

Jeon, Eun Kyung; Turner, Christopher W; Karsten, Sue A; Henry, Belinda A; Gantz, Bruce J

2015-10-01

This study revisits the issue of the spectral ripple resolution abilities of cochlear implant (CI) users. The spectral ripple resolution of recently implanted CI recipients (implanted during the last 10 years) were compared to those of CI recipients implanted 15 to 20 years ago, as well as those of normal-hearing and hearing-impaired listeners from previously published data from Henry, Turner, and Behrens [J. Acoust. Soc. Am. 118, 1111-1121 (2005)]. More recently, implanted CI recipients showed significantly better spectral ripple resolution. There is no significant difference in spectral ripple resolution for these recently implanted subjects compared to hearing-impaired (acoustic) listeners. The more recently implanted CI users had significantly better pre-operative speech perception than previously reported CI users. These better pre-operative speech perception scores in CI users from the current study may be related to better performance on the spectral ripple discrimination task; however, other possible factors such as improvements in internal and external devices cannot be excluded.

Spectral dimension in causal set quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Mizera, Sebastian

2014-01-01

We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can be connected to the nonlocality of causal set theory that is deeply rooted in its fundamentally Lorentzian nature. Based on its large-scale behaviour, we conjecture that the spectral dimension can serve as a tool to distinguish causal sets that approximate manifolds from those that do not. As a new tool to probe quantum spacetime in different quantum gravity approaches, we introduce a novel dimensional estimator, the causal spectral dimension, based on the meeting probability of two random walkers, which respect the causal structure of the quantum spacetime. We discuss a causal-set example, where the spectral dimension and the causal spectral dimension differ, due to the existence of a preferred foliation. (paper)

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

Science.gov (United States)

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

2018-01-01

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

A Simple Spectral Observer

Directory of Open Access Journals (Sweden)

Lizeth Torres

2018-05-01

Full Text Available The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1 the reconstruction of a simple periodical signal, (2 the approximation of both a square and a triangular signal, (3 the edge detection in signals by using the Fourier coefficients, (4 the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5 the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT, which is a well-known method for time-frequency analysis.

Spectral characterization of natural backgrounds

Science.gov (United States)

Winkelmann, Max

2017-10-01

As the distribution and use of hyperspectral sensors is constantly increasing, the exploitation of spectral features is a threat for camouflaged objects. To improve camouflage materials at first the spectral behavior of backgrounds has to be known to adjust and optimize the spectral reflectance of camouflage materials. In an international effort, the NATO CSO working group SCI-295 "Development of Methods for Measurements and Evaluation of Natural Background EO Signatures" is developing a method how this characterization of backgrounds has to be done. It is obvious that the spectral characterization of a background will be quite an effort. To compare and exchange data internationally the measurements will have to be done in a similar way. To test and further improve this method an international field trial has been performed in Storkow, Germany. In the following we present first impressions and lessons learned from this field campaign and describe the data that has been measured.

Substitution dynamical systems spectral analysis

CERN Document Server

Queffélec, Martine

2010-01-01

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many...

Camouflage in thermal IR: spectral design

Science.gov (United States)

Pohl, Anna; Fagerström, Jan; Kariis, Hans; Lindell, Roland; Hallberg, Tomas; Högström, Herman

2016-10-01

In this work a spectral designed coating from SPECTROGON is evaluated. Spectral design in this case means that the coating has a reflectivity equal to one at 3-5 and 8-12 microns were sensors operate and a much lower reflectivity in the other wave length regions. Three boxes are evaluated: one metallic, one black-body and one with a spectral designed surface, all with a 15 W radiator inside the box. It is shown that the box with the spectral designed surface can combine the two good characteristics of the other boxes: low signature from the metallic box and reasonable inside temperature from the black-body box. The measurements were verified with calculations using RadThermIR.

Light distribution system comprising spectral conversion means

DEFF Research Database (Denmark)

2012-01-01

, longer wavelength,a spectral conversion characteristics of the spectral conversion fibre being essentially determined by the spectral absorption and emission properties of the photoluminescent agent, the amount of photo- luminescent agent,and the distribution of the photoluminescent agent in the spectral......System (200, 300) for the distribution of white light, having a supply side (201, 301, 401) and a delivery side (202, 302, 402), the system being configured for guiding light with a multitude of visible wavelengths in a propagation direction P from the supply side to the distribution side...... of providing a light distribution system and a method of correcting the spectral transmission characteristics of a light distribution system are disclosed....

Parametric Explosion Spectral Model

Energy Technology Data Exchange (ETDEWEB)

Ford, S R; Walter, W R

2012-01-19

Small underground nuclear explosions need to be confidently detected, identified, and characterized in regions of the world where they have never before occurred. We develop a parametric model of the nuclear explosion seismic source spectrum derived from regional phases that is compatible with earthquake-based geometrical spreading and attenuation. Earthquake spectra are fit with a generalized version of the Brune spectrum, which is a three-parameter model that describes the long-period level, corner-frequency, and spectral slope at high-frequencies. Explosion spectra can be fit with similar spectral models whose parameters are then correlated with near-source geology and containment conditions. We observe a correlation of high gas-porosity (low-strength) with increased spectral slope. The relationship between the parametric equations and the geologic and containment conditions will assist in our physical understanding of the nuclear explosion source.

[Modeling and Simulation of Spectral Polarimetric BRDF].

Science.gov (United States)

Ling, Jin-jiang; Li, Gang; Zhang, Ren-bin; Tang, Qian; Ye, Qiu

2016-01-01

Under the conditions of the polarized light, The reflective surface of the object is affected by many factors, refractive index, surface roughness, and so the angle of incidence. For the rough surface in the different wavelengths of light exhibit different reflection characteristics of polarization, a spectral polarimetric BRDF based on Kirchhof theory is proposee. The spectral model of complex refraction index is combined with refraction index and extinction coefficient spectral model which were got by using the known complex refraction index at different value. Then get the spectral model of surface roughness derived from the classical surface roughness measuring method combined with the Fresnel reflection function. Take the spectral model of refraction index and roughness into the BRDF model, then the spectral polarimetirc BRDF model is proposed. Compare the simulation results of the refractive index varies with wavelength, roughness is constant, the refraction index and roughness both vary with wavelength and origin model with other papers, it shows that, the spectral polarimetric BRDF model can show the polarization characteristics of the surface accurately, and can provide a reliable basis for the application of polarization remote sensing, and other aspects of the classification of substances.

Spectral Line Shapes in Plasmas and Gases

International Nuclear Information System (INIS)

Oks, E.; Dalimier, D.; Stamm, R.; Stehle, CH.; Gonzalez, M.A.

2011-01-01

The subject of spectral line shapes (SLS), a.k.a. spectral line broadening, which embraces both shapes and shifts of spectral lines, is of both fundamental and practical importance. On the fundamental side, the study of the spectral line profiles reveals the underlying atomic and molecular interactions. On the practical side, the spectral line profiles are employed as powerful diagnostic tools for various media, such as neutral gases, technological gas discharges, magnetically confined plasmas for fusion, laser- and Z-pinch-produced plasmas (for fusion and other purposes), astrophysical plasmas (most importantly, solar plasmas), and planetary atmospheres. The research area covered by this special issue includes both the SLS dominated by various electric fields (including electron and ion micro fields in strongly ionized plasmas) and the SLS controlled by neutral particles. In the physical slang, the former is called plasma broadening while the latter is called neutral broadening (of course, the results of neutral broadening apply also to the spectral line broadening in neutral gases)

Local and global statistical dynamical properties of chaotic Markov analytic maps and repellers: A coarse grained and spectral perspective

International Nuclear Information System (INIS)

MacKernan, Donal; Basios, Vasileios

2009-01-01

The statistical properties of chaotic Markov analytic maps and equivalent repellers are investigated through matrix representations of the Frobenius-Perron operator (U). The associated basis sets are constructed using Chebyshev functions and Markov partitions which can be tailored to examine statistical dynamical properties associated with observables having support over local regions or for example, about periodic orbits. The decay properties of corresponding time correlations functions are given by a analytic expression of the spectra of U which is expected to be valid for a much larger class of systems than that studied here. An explicit and general expression is also derived for the correction factor to the dynamical zeta functions occurring when analytic function spaces are not invariant under U.

SPECTRAL SMILE CORRECTION IN CRISM HYPERSPECTRAL IMAGES

Science.gov (United States)

Ceamanos, X.; Doute, S.

2009-12-01

The Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) is affected by a common artifact in "push-broom" sensors, the so-called "spectral smile". As a consequence, both central wavelength and spectral width of the spectral response vary along the across-track dimension, thus giving rise to a shifting and smoothing of spectra (see Fig. 1 (left)). In fact, both effects are greater for spectra on the edges, while they are minimum for data acquired by central detectors, the so-called "sweet spot". The prior artifacts become particularly critical for Martian observations which contain steep spectra such as CO2 ice-rich polar images. Fig. 1 (right) shows the horizontal brightness gradient which appears in every band corresponding to a steep portion of spectra. The correction of CRISM spectral smile is addressed using a two-step method which aims at modifying data sensibly in order to mimic the optimal CRISM response. First, all spectra, which are previously interpolated by cubic splines, are resampled to the "sweet spot" wavelengths in order to overcome the spectra shift. Secondly, the non-uniform spectral width is overcome by mimicking an increase of spectral resolution thanks to a spectral sharpening. In order to minimize noise, only bands particularly suffering from smile are selected. First, bands corresponding to the outliers of the Minimum Noise Transformation (MNF) eigenvector, which corresponds to the MNF band related to smile (MNF-smile), are selected. Then, a spectral neighborhood Θi, which takes into account the local spectral convexity or concavity, is defined for every selected band in order to maximize spectral shape preservation. The proposed sharpening technique takes into account both the instrument parameters and the observed spectra. First, every reflectance value belonging to a Θi is reevaluated by a sharpening which depends on a ratio of the spectral width of the current detector and the "sweet spot" one. Then, the optimal degree of

Buckling feedback of the spectral calculations

International Nuclear Information System (INIS)

Jing Xingqing; Shan Wenzhi; Luo Jingyu

1992-01-01

This paper studies the problems about buckling feedback of spectral calculations in physical calculations of the reactor and presents a useful method by which the buckling feedback of spectral calculations is implemented. The effect of the buckling feedback in spectra and the broad group cross section, convergence of buckling feedback iteration and the effect of the spectral zones dividing are discussed in the calculations. This method has been used for the physical design of HTR-10 MW Test Module

Spectral Slope as an Indicator of Pasture Quality

Directory of Open Access Journals (Sweden)

Rachel Lugassi

2014-12-01

Full Text Available In this study, we develop a spectral method for assessment of pasture quality based only on the spectral information obtained with a small number of wavelengths. First, differences in spectral behavior were identified across the near infrared–shortwave infrared spectral range that were indicative of changes in chemical properties. Then, slopes across different spectral ranges were calculated and correlated with the changes in crude protein (CP, neutral detergent fiber (NDF and metabolic energy concentration (MEC. Finally, partial least squares (PLS regression analysis was applied to identify the optimal spectral ranges for accurate assessment of CP, NDF and MEC. Six spectral domains and a set of slope criteria for real-time evaluation of pasture quality were suggested. The evaluation of three level categories (low, medium, high for these three parameters showed a success rate of: 73%–96% for CP, 72%–87% for NDF and 60%–85% for MEC. Moreover, only one spectral range, 1748–1764 nm, was needed to provide a good estimation of CP, NDF and MEC. Importantly, five of the six selected spectral regions were not affected by water absorbance. With some modifications, this rationale can be applied to further analyses of pasture quality from airborne sensors.

Spectrally-Selective Photonic Structures for PV Applications

Directory of Open Access Journals (Sweden)

Benedikt Bläsi

2010-01-01

Full Text Available We review several examples of how spectrally-selective photonic structures may be used to improve solar cell systems. Firstly, we introduce different spectrally-selective structures that are based on interference effects. Examples shown include Rugate filter, edge filter and 3D photonic crystals such as artificial opals. In the second part, we discuss several examples of photovoltaic (PV concepts that utilize spectral selectivity such as fluorescence collectors, upconversion systems, spectrum splitting concepts and the intermediate reflector concept. The potential of spectrally selective filters in the context of solar cells is discussed.

Multi-Configuration Matched Spectral Filter Core, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — OPTRA proposes an open-architecture spectral gas sensor based on compressive sensing concepts employed for both spatial and spectral domains. Our matched spectral...

Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples

OpenAIRE

Marcolli, Matilde; Zolman, Nick

2016-01-01

We investigate the spectral geometry and spectral action functionals associated to 1D Supersymmetry Algebras, using the classification of these superalgebras in terms of Adinkra graphs and the construction of associated dessin d'enfant and origami curves. The resulting spectral action functionals are computed in terms of the Selberg (super) trace formula.

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

Science.gov (United States)

2016-10-17

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

The X-Shooter spectral library

NARCIS (Netherlands)

Chen, Y. P.; Trager, S. C.; Peletier, R. F.; Lançon, A.; Prugniel, Ph.; Koleva, M.

2012-01-01

We are building a new spectral library with the X-Shooter instrument on ESO's VLT: XSL, the X-Shooter Spectral Library. We present our progress in building XSL, which covers the wavelength range from the near-UV to the near-IR with a resolution of R˜10000. As of now we have collected spectra for

A New Measurement of the Spectral Lag of Gamma-Ray Bursts and its Implications for Spectral Evolution Behaviors

Energy Technology Data Exchange (ETDEWEB)

Shao, Lang; Wang, Fu-Ri; Cheng, Ye-Hao; Zhang, Xi; Yu, Bang-Yao; Xi, Bao-Jia; Wang, Xue; Feng, Huan-Xue; Zhang, Meng, E-mail: lshao@hebtu.edu.cn [Department of Space Sciences and Astronomy, Hebei Normal University, Shijiazhuang 050024 (China); Zhang, Bin-Bin [Instituto de Astrofísica de Andalucá (IAA-CSIC), P.O. Box 03004, E-18080 Granada (Spain); Wu, Xue-Feng [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China); Xu, Dong [Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China)

2017-08-01

We carry out a systematical study of the spectral lag properties of 50 single-pulsed gamma-ray bursts (GRBs) detected by the Fermi Gamma-Ray Burst Monitor. By dividing the light curves into multiple consecutive energy channels, we provide a new measurement of the spectral lag that is independent of energy channel selections. We perform a detailed statistical study of our new measurements. We find two similar power-law energy dependencies of both the pulse arrival time and pulse width. Our new results on the power-law indices would favor the relativistic geometric effects for the origin of spectral lag. However, a complete theoretical framework that can fully account for the diverse energy dependencies of both arrival time and pulse width revealed in this work is still lacking. We also study the spectral evolution behaviors of the GRB pulses. We find that a GRB pulse with negligible spectral lag would usually have a shorter pulse duration and would appear to have a “hardness-intensity tracking” behavior, and a GRB pulse with a significant spectral lag would usually have a longer pulse duration and would appear to have a “hard-to-soft” behavior.

Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

Energy Technology Data Exchange (ETDEWEB)

Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico

2014-12-15

In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.

Learning theory of distributed spectral algorithms

International Nuclear Information System (INIS)

Guo, Zheng-Chu; Lin, Shao-Bo; Zhou, Ding-Xuan

2017-01-01

Spectral algorithms have been widely used and studied in learning theory and inverse problems. This paper is concerned with distributed spectral algorithms, for handling big data, based on a divide-and-conquer approach. We present a learning theory for these distributed kernel-based learning algorithms in a regression framework including nice error bounds and optimal minimax learning rates achieved by means of a novel integral operator approach and a second order decomposition of inverse operators. Our quantitative estimates are given in terms of regularity of the regression function, effective dimension of the reproducing kernel Hilbert space, and qualification of the filter function of the spectral algorithm. They do not need any eigenfunction or noise conditions and are better than the existing results even for the classical family of spectral algorithms. (paper)