Rectangular spectral collocation
Driscoll, Tobin A.; Hale, Nicholas
2015-01-01
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon
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
Rectangular spectral collocation
Driscoll, Tobin A.
2015-02-06
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.
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.
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.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
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
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.
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.
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).
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Crosstalk statistics via collocation method
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
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.
Modified Chebyshev Collocation Method for Solving Differential Equations
Directory of Open Access Journals (Sweden)
M Ziaul Arif
2015-05-01
Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.
Recent advances in radial basis function collocation methods
Chen, Wen; Chen, C S
2014-01-01
This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s ...
A Line-Tau Collocation Method for Partial Differential Equations ...
African Journals Online (AJOL)
This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...
Sinc-collocation method for solving the Blasius equation
International Nuclear Information System (INIS)
Parand, K.; Dehghan, Mehdi; Pirkhedri, A.
2009-01-01
Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.
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.
Numerical simulation of GEW equation using RBF collocation method
Directory of Open Access Journals (Sweden)
Hamid Panahipour
2012-08-01
Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.
Application of 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)
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.
B-spline Collocation with Domain Decomposition Method
International Nuclear Information System (INIS)
Hidayat, M I P; Parman, S; Ariwahjoedi, B
2013-01-01
A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C 0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.
A 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.)
Pseudospectral collocation methods for fourth order differential equations
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.
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).
Simulation of electrically driven jet using Chebyshev collocation method
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with invariants.Then the implicit differential equations solver "ddaskr" is used to solve the ODEs and ...
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.
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
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.
Block Hybrid Collocation Method with Application to Fourth Order Differential Equations
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Lee Ken Yap
2015-01-01
Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.
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
A stochastic collocation method for the second order wave equation with a discontinuous random speed
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
A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method
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Changqing Yang
2012-01-01
Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
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.
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method
Directory of Open Access Journals (Sweden)
Olumuyiwa A. Agbolade
2017-01-01
Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
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.
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
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
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.
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).
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.
A stochastic collocation method for the second order wave equation with a discontinuous random speed
Motamed, Mohammad
2012-08-31
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.
The Application of the Probabilistic Collocation Method to a Transonic Axial Flow Compressor
Loeven, G.J.A.; Bijl, H.
2010-01-01
In this paper the Probabilistic Collocation method is used for uncertainty quantification of operational uncertainties in a transonic axial flow compressor (i.e. NASA Rotor 37). Compressor rotors are components of a gas turbine that are highly sensitive to operational and geometrical uncertainties.
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
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.
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
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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.
Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation
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...
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Salih Yalcinbas
2016-01-01
Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.
An adaptive multi-element probabilistic collocation method for statistical EMC/EMI characterization
Yücel, Abdulkadir C.
2013-12-01
An adaptive multi-element probabilistic collocation (ME-PC) method for quantifying uncertainties in electromagnetic compatibility and interference phenomena involving electrically large, multi-scale, and complex platforms is presented. The method permits the efficient and accurate statistical characterization of observables (i.e., quantities of interest such as coupled voltages) that potentially vary rapidly and/or are discontinuous in the random variables (i.e., parameters that characterize uncertainty in a system\\'s geometry, configuration, or excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the domain of the random variables into subdomains using as a guide the decay rate of relative error in a polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation/integration points determined by the adaptive ME-PC scheme. The adaptive ME-PC scheme requires far fewer (computationally costly) deterministic simulations than traditional polynomial chaos collocation and Monte Carlo methods for computing averages, standard deviations, and probability density functions of rapidly varying observables. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of voltages in shielded/unshielded microwave amplifiers and magnetic fields induced on car tire pressure sensors. © 2013 IEEE.
A pseudospectral collocation time-domain method for diffractive optics
DEFF Research Database (Denmark)
Dinesen, P.G.; Hesthaven, J.S.; Lynov, Jens-Peter
2000-01-01
We present a pseudospectral method for the analysis of diffractive optical elements. The method computes a direct time-domain solution of Maxwell's equations and is applied to solving wave propagation in 2D diffractive optical elements. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights...
Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
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.
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
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Qinghai Zhao
2015-01-01
Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.
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
Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method
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Ishfaq Ahmad Ganaie
2013-01-01
Full Text Available A convenient computational approach for solving mathematical model related to diffusion dispersion during flow through packed bed is presented. The algorithm is based on the mixed collocation method. The method is particularly useful for solving stiff system arising in chemical and process engineering. The convergence of the method is found to be of order 2 using the roots of shifted Chebyshev polynomial. Model is verified using the literature data. This method has provided a convenient check on the accuracy of the results for wide range of parameters, namely, Peclet numbers. Breakthrough curves are plotted to check the effect of Peclet number on average and exit solute concentrations.
A fractional spline collocation-Galerkin method for the time-fractional diffusion equation
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Pezza L.
2018-03-01
Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.
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.
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
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems
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.
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.
An embedded formula of the Chebyshev collocation method for stiff problems
Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu
2017-12-01
In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.
An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis
Yücel, Abdulkadir C.
2010-07-01
The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a system\\'s excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.). To bound the probability of system malfunction, fast and accurate techniques to quantify the uncertainty in system observables (e.g., voltages across mission-critical circuit elements) are called for. Recently proposed stochastic frameworks [1-2] combine deterministic electromagnetic (EM) simulators with stochastic collocation (SC) methods that approximate system observables using generalized polynomial chaos expansion (gPC) [3] (viz. orthogonal polynomials spanning the entire random domain) to estimate their statistical moments and probability density functions (pdfs). When constructing gPC expansions, the EM simulator is used solely to evaluate system observables at collocation points prescribed by the SC-gPC scheme. The frameworks in [1-2] therefore are non-intrusive and straightforward to implement. That said, they become inefficient and inaccurate for system observables that vary rapidly or are discontinuous in the random variables (as their representations may require very high-order polynomials). © 2010 IEEE.
A fast collocation method for a variable-coefficient nonlocal diffusion model
Wang, Che; Wang, Hong
2017-02-01
We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N3) required by a commonly used direct solver to O (Nlog N) per iteration and the memory requirement from O (N2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N2) to O (N). Numerical results are presented to show the utility of the fast method.
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Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
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.
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
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
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)
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...
An adaptive multi-element probabilistic collocation method for statistical EMC/EMI characterization
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 Least Squares Collocation Method for Accuracy Improvement of Mobile LiDAR Systems
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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.
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
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.
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...
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.
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
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
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Winfried Auzinger
2006-01-01
Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Zhang, D.; Liao, Q.
2016-12-01
The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of
Geostationary satellites collocation
Li, Hengnian
2014-01-01
Geostationary Satellites Collocation aims to find solutions for deploying a safe and reliable collocation control. Focusing on the orbital perturbation analysis, the mathematical foundations for orbit and control of the geostationary satellite are summarized. The mathematical and physical principle of orbital maneuver and collocation strategies for multi geostationary satellites sharing with the same dead band is also stressed. Moreover, the book presents some applications using the above algorithms and mathematical models to help readers master the corrective method for planning station keeping maneuvers. Engineers and scientists in the fields of aerospace technology and space science can benefit from this book. Hengnian Li is the Deputy Director of State Key Laboratory of Astronautic Dynamics, China.
Multi-Index Monte Carlo and stochastic collocation methods for random PDEs
Nobile, Fabio
2016-01-09
In this talk we consider the problem of computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a finite or countable sequence of terms in a suitable expansion. We describe and analyze a Multi-Index Monte Carlo (MIMC) and a Multi-Index Stochastic Collocation method (MISC). the former is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Instead of using firstorder differences as in MLMC, MIMC uses mixed differences to reduce the variance of the hierarchical differences dramatically. This in turn yields new and improved complexity results, which are natural generalizations of Giles s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence, O(TOL-2). On the same vein, MISC is a deterministic combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. Provided enough mixed regularity, MISC can achieve better complexity than MIMC. Moreover, we show that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one-dimensional spatial problem. We propose optimization procedures to select the most effective mixed differences to include in MIMC and MISC. Such optimization is a crucial step that allows us to make MIMC and MISC computationally effective. We finally show the effectiveness of MIMC and MISC with some computational tests, including tests with a infinite countable number of random parameters.
Multi-Index Monte Carlo and stochastic collocation methods for random PDEs
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.
Collocation methods for uncertainty quanti cation in PDE models with random data
Nobile, Fabio
2014-01-06
In this talk we consider Partial Differential Equations (PDEs) whose input data are modeled as random fields to account for their intrinsic variability or our lack of knowledge. After parametrizing the input random fields by finitely many independent random variables, we exploit the high regularity of the solution of the PDE as a function of the input random variables and consider sparse polynomial approximations in probability (Polynomial Chaos expansion) by collocation methods. We first address interpolatory approximations where the PDE is solved on a sparse grid of Gauss points in the probability space and the solutions thus obtained interpolated by multivariate polynomials. We present recent results on optimized sparse grids in which the selection of points is based on a knapsack approach and relies on sharp estimates of the decay of the coefficients of the polynomial chaos expansion of the solution. Secondly, we consider regression approaches where the PDE is evaluated on randomly chosen points in the probability space and a polynomial approximation constructed by the least square method. We present recent theoretical results on the stability and optimality of the approximation under suitable conditions between the number of sampling points and the dimension of the polynomial space. In particular, we show that for uniform random variables, the number of sampling point has to scale quadratically with the dimension of the polynomial space to maintain the stability and optimality of the approximation. Numerical results show that such condition is sharp in the monovariate case but seems to be over-constraining in higher dimensions. The regression technique seems therefore to be attractive in higher dimensions.
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
Chebyshev and Fourier spectral methods
Boyd, John P
2001-01-01
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
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.
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.
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.
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
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.)
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...
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.
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.
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.
Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation
Im, Dong Kyun; Kim, Hyun Soon; Choi, Seongim
2018-05-01
A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev-Gauss-Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass-spring-damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments.
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.
Spectral Methods in Numerical Plasma Simulation
DEFF Research Database (Denmark)
Coutsias, E.A.; Hansen, F.R.; Huld, T.
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...
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.
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
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.
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.
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.
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....
CSIR Research Space (South Africa)
Napier, JAL
2002-09-01
Full Text Available The numerical solution of problems relating to crack fracture and failure can be accomplished using the displacement discontinuity boundary element method. This paper presents an extension to the normal formulation of this method to enable stress...
Dehghan, Mehdi; Mohammadi, Vahid
2017-03-01
As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.
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.
Multi-fidelity stochastic collocation method for computation of statistical moments
Energy Technology Data Exchange (ETDEWEB)
Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu [Department of Mathematics, University of Iowa, Iowa City, IA 52242 (United States); Linebarger, Erin M., E-mail: aerinline@sci.utah.edu [Department of Mathematics, University of Utah, Salt Lake City, UT 84112 (United States); Xiu, Dongbin, E-mail: xiu.16@osu.edu [Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)
2017-07-15
We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.
Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
A Collocation Method by Moving Least Squares Applicable to European Option Pricing
Directory of Open Access Journals (Sweden)
M. Amirfakhrian
2016-05-01
Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.
Spectral shift reactor control method
International Nuclear Information System (INIS)
Impink, A.J. Jr.
1981-01-01
A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core wherein is established a reator coolant temperature set point at which it is desired to operate said reactor and first reactor coolant temperature band limits are provided within which said set point is located and it is desired to operate said reactor charactrized in that said reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in said core as said reactor coolant temperature approaches said first band limits thereby to maintain said reactor coolant temperature near said set point and within said first band limits
Spectral shift reactor control method
International Nuclear Information System (INIS)
Impink, A.J.
1982-01-01
A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core where there is established a reactor coolant temperature set point at which it is desired to operate the reactor and first reactor coolant temperature band limits within which the set point is characterized. The reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in the core as the reactor coolant temperature approaches the first band limits to maintain the reactor coolant temperature near the set point and within the first band limits. The reactivity charges associated with movement of respective coolant displacer element clusters is calculated and compared with a calculated derived reactivity charge in order to select the cluster to be moved. (author)
A spectral element-FCT method for the compressible Euler equations
International Nuclear Information System (INIS)
Giannakouros, J.; Karniadakis, G.E.
1994-01-01
A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements
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.)
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)
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....
Logarithmic compression methods for spectral data
Dunham, Mark E.
2003-01-01
A method is provided for logarithmic compression, transmission, and expansion of spectral data. A log Gabor transformation is made of incoming time series data to output spectral phase and logarithmic magnitude values. The output phase and logarithmic magnitude values are compressed by selecting only magnitude values above a selected threshold and corresponding phase values to transmit compressed phase and logarithmic magnitude values. A reverse log Gabor transformation is then performed on the transmitted phase and logarithmic magnitude values to output transmitted time series data to a user.
Stochastic Spectral and Conjugate Descent Methods
Kovalev, Dmitry
2018-02-11
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.
Stochastic Spectral and Conjugate Descent Methods
Kovalev, Dmitry; Gorbunov, Eduard; Gasanov, Elnur; Richtarik, Peter
2018-01-01
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.
Evolutionary Computing Methods for Spectral Retrieval
Terrile, Richard; Fink, Wolfgang; Huntsberger, Terrance; Lee, Seugwon; Tisdale, Edwin; VonAllmen, Paul; Tinetti, Geivanna
2009-01-01
A methodology for processing spectral images to retrieve information on underlying physical, chemical, and/or biological phenomena is based on evolutionary and related computational methods implemented in software. In a typical case, the solution (the information that one seeks to retrieve) consists of parameters of a mathematical model that represents one or more of the phenomena of interest. The methodology was developed for the initial purpose of retrieving the desired information from spectral image data acquired by remote-sensing instruments aimed at planets (including the Earth). Examples of information desired in such applications include trace gas concentrations, temperature profiles, surface types, day/night fractions, cloud/aerosol fractions, seasons, and viewing angles. The methodology is also potentially useful for retrieving information on chemical and/or biological hazards in terrestrial settings. In this methodology, one utilizes an iterative process that minimizes a fitness function indicative of the degree of dissimilarity between observed and synthetic spectral and angular data. The evolutionary computing methods that lie at the heart of this process yield a population of solutions (sets of the desired parameters) within an accuracy represented by a fitness-function value specified by the user. The evolutionary computing methods (ECM) used in this methodology are Genetic Algorithms and Simulated Annealing, both of which are well-established optimization techniques and have also been described in previous NASA Tech Briefs articles. These are embedded in a conceptual framework, represented in the architecture of the implementing software, that enables automatic retrieval of spectral and angular data and analysis of the retrieved solutions for uniqueness.
Spectral Analysis Methods of Social Networks
Directory of Open Access Journals (Sweden)
P. G. Klyucharev
2017-01-01
Full Text Available Online social networks (such as Facebook, Twitter, VKontakte, etc. being an important channel for disseminating information are often used to arrange an impact on the social consciousness for various purposes - from advertising products or services to the full-scale information war thereby making them to be a very relevant object of research. The paper reviewed the analysis methods of social networks (primarily, online, based on the spectral theory of graphs. Such methods use the spectrum of the social graph, i.e. a set of eigenvalues of its adjacency matrix, and also the eigenvectors of the adjacency matrix.Described measures of centrality (in particular, centrality based on the eigenvector and PageRank, which reflect a degree of impact one or another user of the social network has. A very popular PageRank measure uses, as a measure of centrality, the graph vertices, the final probabilities of the Markov chain, whose matrix of transition probabilities is calculated on the basis of the adjacency matrix of the social graph. The vector of final probabilities is an eigenvector of the matrix of transition probabilities.Presented a method of dividing the graph vertices into two groups. It is based on maximizing the network modularity by computing the eigenvector of the modularity matrix.Considered a method for detecting bots based on the non-randomness measure of a graph to be computed using the spectral coordinates of vertices - sets of eigenvector components of the adjacency matrix of a social graph.In general, there are a number of algorithms to analyse social networks based on the spectral theory of graphs. These algorithms show very good results, but their disadvantage is the relatively high (albeit polynomial computational complexity for large graphs.At the same time it is obvious that the practical application capacity of the spectral graph theory methods is still underestimated, and it may be used as a basis to develop new methods.The work
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.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Collocations in Marine Engineering English
Directory of Open Access Journals (Sweden)
Mirjana Borucinsky
2016-05-01
Full Text Available Collocations are very frequent in the English language (Hill, 2000, and they are probably the most common and most representative of English multi-word expressions (Lewis, 2000. Furthermore, as a subset of formulaic sequences, collocations are considered to be a central aspect of communicative competence (Nation, 2001. Hence, the importance of teaching collocations in General English (GE as well as in English for Specific Purposes (ESP is undeniable. Understanding and determining the relevant collocations and their mastery are of “utmost importance to a ME instructor” (Cole et al., 2007, p. 137, and collocations are one of the most productive ways of enriching vocabulary and terminology in modern ME. Vişan & Georgescu (2011 have undertaken a relevant study on collocations and “collocational competence” on board ships, including mostly nautical terminology. However, no substantial work on collocations in Marine Engineering English as a sub-register of ME has been carried out. Hence, this paper tries to determine the most important collocations in Marine Engineering English, based on a small corpus of collected e-mails. After determining the most relevant collocations, we suggest how to implement these in the language classroom and how to improve the collocational competence of marine engineering students.
Varlamova, Elena V.; Naciscione, Anita; Tulusina, Elena A.
2016-01-01
Relevance of the issue stated in the article is determined by the fact that there is a lack of research devoted to the methods of teaching English and German collocations. The aim of our work is to determine methods of teaching English and German collocations to Russian university students studying foreign languages through experimental testing.…
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.
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)
Numerical Methods for Stochastic Computations A Spectral Method Approach
Xiu, Dongbin
2010-01-01
The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth
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)
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.
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...
Directory of Open Access Journals (Sweden)
V. P. Shapeev
2014-01-01
Full Text Available The method of collocations and least residuals (CLR, which was proposed previously for the numerical solution of two-dimensional Navier–Stokes equations governing the stationary flows of a viscous incompressible fluid, is extended here for the three-dimensional case. The solution is sought in the implemented version of the method in the form of an expansion in the basis solenoidal functions. At all stages of the CLR method construction, a computer algebra system (CAS is applied for the derivation and verification of the formulas of the method and for their translation into arithmetic operators of the Fortran language. For accelerating the convergence of iterations a sufficiently universal algorithm is proposed, which is simple in its implementation and is based on the use of the Krylov’s subspaces. The obtained computational formulas of the CLR method were verified on the exact analytic solution of a test problem. Comparisons with the published numerical results of solving the benchmark problem of the 3D driven cubic cavity flow show that the accuracy of the results obtained by the CLR method corresponds to the known high-accuracy solutions.
Chebyshev super spectral viscosity method for water hammer analysis
Directory of Open Access Journals (Sweden)
Hongyu Chen
2013-09-01
Full Text Available In this paper, a new fast and efficient algorithm, Chebyshev super spectral viscosity (SSV method, is introduced to solve the water hammer equations. Compared with standard spectral method, the method's advantage essentially consists in adding a super spectral viscosity to the equations for the high wave numbers of the numerical solution. It can stabilize the numerical oscillation (Gibbs phenomenon and improve the computational efficiency while discontinuities appear in the solution. Results obtained from the Chebyshev super spectral viscosity method exhibit greater consistency with conventional water hammer calculations. It shows that this new numerical method offers an alternative way to investigate the behavior of the water hammer in propellant pipelines.
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.
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
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 ...
Orthogonal feature selection method. [For preprocessing of man spectral data
Energy Technology Data Exchange (ETDEWEB)
Kowalski, B R [Univ. of Washington, Seattle; Bender, C F
1976-01-01
A new method of preprocessing spectral data for extraction of molecular structural information is desired. This SELECT method generates orthogonal features that are important for classification purposes and that also retain their identity to the original measurements. A brief introduction to chemical pattern recognition is presented. A brief description of the method and an application to mass spectral data analysis follow. (BLM)
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 ...
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.
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...
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.
Directory of Open Access Journals (Sweden)
Jun Zhang
2018-01-01
Full Text Available The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i the total scattering cross section (SCS is almost symmetric about the axis α=π/2 with respect to the location (α of the imperfect interface, (ii imperfect interfaces located at α=0 and α=π highly reduce the total SCS under a P-wave incidence and imperfect interfaces located at α=π/2 reduce the total SCS most significantly under SV-incidence, and (iii under a P-wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV-wave incidence.
Parsani, Matteo; Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.
2016-01-01
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
Digital spectral analysis parametric, non-parametric and advanced methods
Castanié, Francis
2013-01-01
Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.An entire chapter is devoted to the non-parametric methods most widely used in industry.High resolution methods a
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
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
International Nuclear Information System (INIS)
Basta, C.
1982-01-01
Using the method of orthogonal colocation the boundary problem for a fix bed with cylindrical geometry was solved. The axial disposal term was despicable and the results were compared with those the explicit finite difference method. (E.G.) [pt
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.
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.
Stability estimates for hp spectral element methods for general ...
Indian Academy of Sciences (India)
We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are ...
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
The spectral volume method as applied to transport problems
International Nuclear Information System (INIS)
McClarren, Ryan G.
2011-01-01
We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)
Performance of spectral fitting methods for vegetation fluorescence quantification
Meroni, M.; Busetto, D.; Colombo, R.; Guanter, L.; Moreno, J.; Verhoef, W.
2010-01-01
The Fraunhofer Line Discriminator (FLD) principle has long been considered as the reference method to quantify solar-induced chlorophyll fluorescence (F) from passive remote sensing measurements. Recently, alternative retrieval algorithms based on the spectral fitting of hyperspectral radiance
Spectral Methods for Immunization of Large Networks
Directory of Open Access Journals (Sweden)
Muhammad Ahmad
2017-11-01
Full Text Available Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbour nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint that are immunized (vaccinated, screened, filtered so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic and efficiency (runtime and space complexity.
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
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.
A divisive spectral method for network community detection
International Nuclear Information System (INIS)
Cheng, Jianjun; Li, Longjie; Yao, Yukai; Chen, Xiaoyun; Leng, Mingwei; Lu, Weiguo
2016-01-01
Community detection is a fundamental problem in the domain of complex network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive spectral method for identifying community structures from networks which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities. The sparsification operation makes the community boundaries clearer and sharper, so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks. Experiments show that the combination of network sparsification and a spectral bisection algorithm is highly successful, the proposed method is more effective in detecting community structures from networks than the others. (paper: interdisciplinary statistical mechanics)
Chebyshev super spectral viscosity method for a fluidized bed model
International Nuclear Information System (INIS)
Sarra, Scott A.
2003-01-01
A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the solution. A modified Gegenbauer postprocessing procedure is used to obtain a solution which is free of oscillations caused by the Gibbs-Wilbraham phenomenon in the spectral viscosity solution. Conservation is maintained by working with unphysical negative particle concentrations
A Spectral Conjugate Gradient Method for Unconstrained Optimization
International Nuclear Information System (INIS)
Birgin, E. G.; Martinez, J. M.
2001-01-01
A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribiere and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented
Spectral method and its high performance implementation
Wu, Zedong
2014-01-01
We have presented a new method that can be dispersion free and unconditionally stable. Thus the computational cost and memory requirement will be reduced a lot. Based on this feature, we have implemented this algorithm on GPU based CUDA for the anisotropic Reverse time migration. There is almost no communication between CPU and GPU. For the prestack wavefield extrapolation, it can combine all the shots together to migration. However, it requires to solve a bigger dimensional problem and more meory which can\\'t fit into one GPU cards. In this situation, we implement it based on domain decomposition method and MPI for distributed memory system.
Analysis of spectral methods for the homogeneous Boltzmann equation
Filbet, Francis
2011-04-01
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.
Analysis of spectral methods for the homogeneous Boltzmann equation
Filbet, Francis; Mouhot, Clé ment
2011-01-01
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.
Spectral/ hp element methods: Recent developments, applications, and perspectives
Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.
2018-02-01
The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.
Spectral methods for quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods in quantum field theory
International Nuclear Information System (INIS)
Graham, Noah; Quandt, Markus; Weigel, Herbert
2009-01-01
This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum in particular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology. The method introduced and applied in this book is shown to give an unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, for example illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many of the subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics. While addressed primarily at young researchers entering the field and nonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoretical aspects of the method make the book self-contained and thus suitable for advanced graduate students. (orig.)
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Spectral radiative property control method based on filling solution
International Nuclear Information System (INIS)
Jiao, Y.; Liu, L.H.; Hsu, P.-F.
2014-01-01
Controlling thermal radiation by tailoring spectral properties of microstructure is a promising method, can be applied in many industrial systems and have been widely researched recently. Among various property tailoring schemes, geometry design of microstructures is a commonly used method. However, the existing radiation property tailoring is limited by adjustability of processed microstructures. In other words, the spectral radiative properties of microscale structures are not possible to change after the gratings are fabricated. In this paper, we propose a method that adjusts the grating spectral properties by means of injecting filling solution, which could modify the thermal radiation in a fabricated microstructure. Therefore, this method overcomes the limitation mentioned above. Both mercury and water are adopted as the filling solution in this study. Aluminum and silver are selected as the grating materials to investigate the generality and limitation of this control method. The rigorous coupled-wave analysis is used to investigate the spectral radiative properties of these filling solution grating structures. A magnetic polaritons mechanism identification method is proposed based on LC circuit model principle. It is found that this control method could be used by different grating materials. Different filling solutions would enable the high absorption peak to move to longer or shorter wavelength band. The results show that the filling solution grating structures are promising for active control of spectral radiative properties. -- Highlights: • A filling solution grating structure is designed to adjust spectral radiative properties. • The mechanism of radiative property control is studied for engineering utilization. • Different grating materials are studied to find multi-functions for grating
Convergence analysis of spectral element method for electromechanical devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2017-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with the
Convergence analysis of spectral element method for magnetic devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2018-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for modeling a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with
A conjugate gradient method for the spectral partitioning of graphs
Kruyt, Nicolaas P.
1997-01-01
The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and
Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs
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
Haji Ali, Abdul Lateef
2016-01-06
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.
Multi-Index Stochastic Collocation for random PDEs
Haji Ali, Abdul Lateef
2016-03-28
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.
Multi-Index Stochastic Collocation for random PDEs
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.
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
Li, Weidong
2017-09-01
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.
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.
The spectral cell method in nonlinear earthquake modeling
Giraldo, Daniel; Restrepo, Doriam
2017-12-01
This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.
Spectral anomaly methods for aerial detection using KUT nuisance rejection
International Nuclear Information System (INIS)
Detwiler, R.S.; Pfund, D.M.; Myjak, M.J.; Kulisek, J.A.; Seifert, C.E.
2015-01-01
This work discusses the application and optimization of a spectral anomaly method for the real-time detection of gamma radiation sources from an aerial helicopter platform. Aerial detection presents several key challenges over ground-based detection. For one, larger and more rapid background fluctuations are typical due to higher speeds, larger field of view, and geographically induced background changes. As well, the possible large altitude or stand-off distance variations cause significant steps in background count rate as well as spectral changes due to increased gamma-ray scatter with detection at higher altitudes. The work here details the adaptation and optimization of the PNNL-developed algorithm Nuisance-Rejecting Spectral Comparison Ratios for Anomaly Detection (NSCRAD), a spectral anomaly method previously developed for ground-based applications, for an aerial platform. The algorithm has been optimized for two multi-detector systems; a NaI(Tl)-detector-based system and a CsI detector array. The optimization here details the adaptation of the spectral windows for a particular set of target sources to aerial detection and the tailoring for the specific detectors. As well, the methodology and results for background rejection methods optimized for the aerial gamma-ray detection using Potassium, Uranium and Thorium (KUT) nuisance rejection are shown. Results indicate that use of a realistic KUT nuisance rejection may eliminate metric rises due to background magnitude and spectral steps encountered in aerial detection due to altitude changes and geographically induced steps such as at land–water interfaces
A modified sliding spectral method and its application to COSMIC ...
Indian Academy of Sciences (India)
A modified sliding spectral method and its application to COSMIC radio occultation data 1751. The window length with 300 samples is supposed to provide a reasonable resolution. In a spherically symmetric atmosphere, the refractive index n as a function of tangent radius r0 can be computed from the bending angle α as.
Deconvolution of EPR spectral lines with an approximate method
International Nuclear Information System (INIS)
Jimenez D, H.; Cabral P, A.
1990-10-01
A recently reported approximation expression to deconvolution Lorentzian-Gaussian spectral lines. with small Gaussian contribution, is applied to study an EPR line shape. The potassium-ammonium solution line reported in the literature by other authors was used and the results are compared with those obtained by employing a precise method. (Author)
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.
Spectral calculations in magnetohydrodynamics using the Jacobi-Davidson method
Belien, A. J. C.; van der Holst, B.; Nool, M.; van der Ploeg, A.; Goedbloed, J. P.
2001-01-01
For the solution of the generalized complex non-Hermitian eigenvalue problems Ax = lambda Bx occurring in the spectral study of linearized resistive magnetohydrodynamics (MHD) a new parallel solver based on the recently developed Jacobi-Davidson [SIAM J. Matrix Anal. Appl. 17 (1996) 401] method has
[An improved low spectral distortion PCA fusion method].
Peng, Shi; Zhang, Ai-Wu; Li, Han-Lun; Hu, Shao-Xing; Meng, Xian-Gang; Sun, Wei-Dong
2013-10-01
Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance.
Convergence of spectral methods for nonlinear conservation laws. Final report
International Nuclear Information System (INIS)
Tadmor, E.
1987-08-01
The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows
INTEGRATED FUSION METHOD FOR MULTIPLE TEMPORAL-SPATIAL-SPECTRAL IMAGES
Directory of Open Access Journals (Sweden)
H. Shen
2012-08-01
Full Text Available Data fusion techniques have been widely researched and applied in remote sensing field. In this paper, an integrated fusion method for remotely sensed images is presented. Differently from the existed methods, the proposed method has the performance to integrate the complementary information in multiple temporal-spatial-spectral images. In order to represent and process the images in one unified framework, two general image observation models are firstly presented, and then the maximum a posteriori (MAP framework is used to set up the fusion model. The gradient descent method is employed to solve the fused image. The efficacy of the proposed method is validated using simulated images.
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.
High order spectral volume and spectral difference methods on unstructured grids
Kannan, Ravishekar
The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed
International Conference on Spectral and High-Order Methods
Dumont, Ney; Hesthaven, Jan
2017-01-01
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
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.
Spectral analysis of mammographic images using a multitaper method
International Nuclear Information System (INIS)
Wu Gang; Mainprize, James G.; Yaffe, Martin J.
2012-01-01
Purpose: Power spectral analysis in radiographic images is conventionally performed using a windowed overlapping averaging periodogram. This study describes an alternative approach using a multitaper technique and compares its performance with that of the standard method. This tool will be valuable in power spectrum estimation of images, whose content deviates significantly from uniform white noise. The performance of the multitaper approach will be evaluated in terms of spectral stability, variance reduction, bias, and frequency precision. The ultimate goal is the development of a useful tool for image quality assurance. Methods: A multitaper approach uses successive data windows of increasing order. This mitigates spectral leakage allowing one to calculate a reduced-variance power spectrum. The multitaper approach will be compared with the conventional power spectrum method in several typical situations, including the noise power spectra (NPS) measurements of simulated projection images of a uniform phantom, NPS measurement of real detector images of a uniform phantom for two clinical digital mammography systems, and the estimation of the anatomic noise in mammographic images (simulated images and clinical mammograms). Results: Examination of spectrum variance versus frequency resolution and bias indicates that the multitaper approach is superior to the conventional single taper methods in the prevention of spectrum leakage and variance reduction. More than four times finer frequency precision can be achieved with equivalent or less variance and bias. Conclusions: Without any shortening of the image data length, the bias is smaller and the frequency resolution is higher with the multitaper method, and the need to compromise in the choice of regions of interest size to balance between the reduction of variance and the loss of frequency resolution is largely eliminated.
Lexical richness and collocational competence in second-language writing
Vedder, I.; Benigno, V.
2016-01-01
In this article we report on an experiment set up to investigate lexical richness and collocational competence in the written production of 39 low-intermediate and intermediate learners of Italian L2. Lexical richness was assessed by means of a lexical profiling method inspired by Laufer and Nation
Solution of the Schroedinger equation by a spectral method
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.
1982-01-01
A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential
High temperature spectral emissivity measurement using integral blackbody method
Pan, Yijie; Dong, Wei; Lin, Hong; Yuan, Zundong; Bloembergen, Pieter
2016-10-01
Spectral emissivity is a critical material's thermos-physical property for heat design and radiation thermometry. A prototype instrument based upon an integral blackbody method was developed to measure material's spectral emissivity above 1000 °. The system was implemented with an optimized commercial variable-high-temperature blackbody, a high speed linear actuator, a linear pyrometer, and an in-house designed synchronization circuit. A sample was placed in a crucible at the bottom of the blackbody furnace, by which the sample and the tube formed a simulated blackbody which had an effective total emissivity greater than 0.985. During the measurement, the sample was pushed to the end opening of the tube by a graphite rod which was actuated through a pneumatic cylinder. A linear pyrometer was used to monitor the brightness temperature of the sample surface through the measurement. The corresponding opto-converted voltage signal was fed and recorded by a digital multi-meter. A physical model was proposed to numerically evaluate the temperature drop along the process. Tube was discretized as several isothermal cylindrical rings, and the temperature profile of the tube was measurement. View factors between sample and rings were calculated and updated along the whole pushing process. The actual surface temperature of the sample at the end opening was obtained. Taking advantages of the above measured voltage profile and the calculated true temperature, spectral emissivity under this temperature point was calculated.
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.
Spectral/hp element methods: Recent developments, applications, and perspectives
DEFF Research Database (Denmark)
Xu, Hui; Cantwell, Chris; Monteserin, Carlos
2018-01-01
regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral...... is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain...
Terahertz spectral unmixing based method for identifying gastric cancer
Cao, Yuqi; Huang, Pingjie; Li, Xian; Ge, Weiting; Hou, Dibo; Zhang, Guangxin
2018-02-01
At present, many researchers are exploring biological tissue inspection using terahertz time-domain spectroscopy (THz-TDS) techniques. In this study, based on a modified hard modeling factor analysis method, terahertz spectral unmixing was applied to investigate the relationships between the absorption spectra in THz-TDS and certain biomarkers of gastric cancer in order to systematically identify gastric cancer. A probability distribution and box plot were used to extract the distinctive peaks that indicate carcinogenesis, and the corresponding weight distributions were used to discriminate the tissue types. The results of this work indicate that terahertz techniques have the potential to detect different levels of cancer, including benign tumors and polyps.
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
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.
Supporting Collocation Learning with a Digital Library
Wu, Shaoqun; Franken, Margaret; Witten, Ian H.
2010-01-01
Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on…
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 ...
"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 ...
Spectral Element Method for the Simulation of Unsteady Compressible Flows
Diosady, Laslo Tibor; Murman, Scott M.
2013-01-01
This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
Spectral Karyotyping. An new method for chromosome analysis
International Nuclear Information System (INIS)
Zhou Liying; Qian Jianxin; Guo Xiaokui; Dai Hong; Liu Yulong; Zhou Jianying
2006-01-01
Spectral Karyotyping (SKY) can reveal fine changes in Chromosome structure which could not be detected by G, R, Q banding before, has become an accurate, sensitive and reliable method for karyotyping, promoted the development of cell genetics to molecular level and has been used in medicine and radiological injury research. It also has the ability of analyzing 24 chromosomes on its once test run and, find implicated structure of chromosome changes, such as metathesis, depletion, amplification, rearrangement, dikinetochore, equiarm and maker-body, detect the abnormal change of stable Chromosome and calculate the bio-dose curve; The abnormal Chromosome detected by SKY can be adopted as early diagnosis, effective indexes of minor remaining changes for use of monitor of treatment and in the duration of follow up. This technique provides us a more advanced and effective method for relative gene cloning and the study of pathological mechanism of cancer. (authors)
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
Spectral analysis methods for vehicle interior vibro-acoustics identification
Hosseini Fouladi, Mohammad; Nor, Mohd. Jailani Mohd.; Ariffin, Ahmad Kamal
2009-02-01
Noise has various effects on comfort, performance and health of human. Sound are analysed by human brain based on the frequencies and amplitudes. In a dynamic system, transmission of sound and vibrations depend on frequency and direction of the input motion and characteristics of the output. It is imperative that automotive manufacturers invest a lot of effort and money to improve and enhance the vibro-acoustics performance of their products. The enhancement effort may be very difficult and time-consuming if one relies only on 'trial and error' method without prior knowledge about the sources itself. Complex noise inside a vehicle cabin originated from various sources and travel through many pathways. First stage of sound quality refinement is to find the source. It is vital for automotive engineers to identify the dominant noise sources such as engine noise, exhaust noise and noise due to vibration transmission inside of vehicle. The purpose of this paper is to find the vibro-acoustical sources of noise in a passenger vehicle compartment. The implementation of spectral analysis method is much faster than the 'trial and error' methods in which, parts should be separated to measure the transfer functions. Also by using spectral analysis method, signals can be recorded in real operational conditions which conduce to more consistent results. A multi-channel analyser is utilised to measure and record the vibro-acoustical signals. Computational algorithms are also employed to identify contribution of various sources towards the measured interior signal. These achievements can be utilised to detect, control and optimise interior noise performance of road transport vehicles.
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.
Genetic Algorithms: A New Method for Neutron Beam Spectral Characterization
International Nuclear Information System (INIS)
David W. Freeman
2000-01-01
A revolutionary new concept for solving the neutron spectrum unfolding problem using genetic algorithms (GAs) has recently been introduced. GAs are part of a new field of evolutionary solution techniques that mimic living systems with computer-simulated chromosome solutions that mate, mutate, and evolve to create improved solutions. The original motivation for the research was to improve spectral characterization of neutron beams associated with boron neutron capture therapy (BNCT). The GA unfolding technique has been successfully applied to problems with moderate energy resolution (up to 47 energy groups). Initial research indicates that the GA unfolding technique may well be superior to popular unfolding methods in common use. Research now under way at Kansas State University is focused on optimizing the unfolding algorithm and expanding its energy resolution to unfold detailed beam spectra based on multiple foil measurements. Indications are that the final code will significantly outperform current, state-of-the-art codes in use by the scientific community
Methods of total spectral radiant flux realization at VNIIOFI
Ivashin, Evgeniy; Lalek, Jan; Rybczyński, Andrzej; Ogarev, Sergey; Khlevnoy, Boris; Dobroserdov, Dmitry; Sapritsky, Victor
2018-02-01
VNIIOFI carries out works on realization of independent methods for realization of the total spectral radiant flux (TSRF) of incoherent optical radiation sources - reference high-temperature blackbodies (BB), halogen lamps, and LED with quasi-Lambert spatial distribution of radiance. The paper describes three schemes for measuring facilities using photometers, spectroradiometers and computer-controlled high class goniometer. The paper describes different approaches for TSRF realization at the VNIIOFI National radiometric standard on the basis of high-temperature BB and LED sources, and gonio-spectroradiometer. Further, they are planned to be compared, and the use of fixed-point cells (in particular, based on the high-temperature δ(MoC)-C metal-carbon eutectic with a phase transition temperature of 2583 °C corresponding to the metrological optical “source-A”) as an option instead of the BB is considered in order to enhance calibration accuracy.
Standard Test Method for Normal Spectral Emittance at Elevated Temperatures
American Society for Testing and Materials. Philadelphia
1972-01-01
1.1 This test method describes a highly accurate technique for measuring the normal spectral emittance of electrically conducting materials or materials with electrically conducting substrates, in the temperature range from 600 to 1400 K, and at wavelengths from 1 to 35 μm. 1.2 The test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is suitable for research laboratories where the highest precision and accuracy are desired, but is not recommended for routine production or acceptance testing. However, because of its high accuracy this test method can be used as a referee method to be applied to production and acceptance testing in cases of dispute. 1.3 The values stated in SI units are to be regarded as the standard. The values in parentheses are for information only. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this stan...
The use of spectral methods in bidomain studies.
Trayanova, N; Pilkington, T
1992-01-01
A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour
2015-01-07
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.
Spectral-Product Methods for Electronic Structure Calculations (Preprint)
National Research Council Canada - National Science Library
Langhoff, P. W; Mills, J. E; Boatz, J. A
2006-01-01
.... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...
Spectral-Product Methods for Electronic Structure Calculations (Postprint)
National Research Council Canada - National Science Library
Langhoff, P. W; Hinde, R. J; Mills, J. D; Boatz, J. A
2007-01-01
.... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...
Kärhä, Petri; Vaskuri, Anna; Mäntynen, Henrik; Mikkonen, Nikke; Ikonen, Erkki
2017-08-01
Spectral irradiance data are often used to calculate colorimetric properties, such as color coordinates and color temperatures of light sources by integration. The spectral data may contain unknown correlations that should be accounted for in the uncertainty estimation. We propose a new method for estimating uncertainties in such cases. The method goes through all possible scenarios of deviations using Monte Carlo analysis. Varying spectral error functions are produced by combining spectral base functions, and the distorted spectra are used to calculate the colorimetric quantities. Standard deviations of the colorimetric quantities at different scenarios give uncertainties assuming no correlations, uncertainties assuming full correlation, and uncertainties for an unfavorable case of unknown correlations, which turn out to be a significant source of uncertainty. With 1% standard uncertainty in spectral irradiance, the expanded uncertainty of the correlated color temperature of a source corresponding to the CIE Standard Illuminant A may reach as high as 37.2 K in unfavorable conditions, when calculations assuming full correlation give zero uncertainty, and calculations assuming no correlations yield the expanded uncertainties of 5.6 K and 12.1 K, with wavelength steps of 1 nm and 5 nm used in spectral integrations, respectively. We also show that there is an absolute limit of 60.2 K in the error of the correlated color temperature for Standard Illuminant A when assuming 1% standard uncertainty in the spectral irradiance. A comparison of our uncorrelated uncertainties with those obtained using analytical methods by other research groups shows good agreement. We re-estimated the uncertainties for the colorimetric properties of our 1 kW photometric standard lamps using the new method. The revised uncertainty of color temperature is a factor of 2.5 higher than the uncertainty assuming no correlations.
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-.
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.
Use of new spectral analysis methods in gamma spectra deconvolution
International Nuclear Information System (INIS)
Pinault, J.L.
1991-01-01
A general deconvolution method applicable to X and gamma ray spectrometry is proposed. Using new spectral analysis methods, it is applied to an actual case: the accurate on-line analysis of three elements (Ca, Si, Fe) in a cement plant using neutron capture gamma rays. Neutrons are provided by a low activity (5 μg) 252 Cf source; the detector is a BGO 3 in.x8 in. scintillator. The principle of the methods rests on the Fourier transform of the spectrum. The search for peaks and determination of peak areas are worked out in the Fourier representation, which enables separation of background and peaks and very efficiently discriminates peaks, or elements represented by several peaks. First the spectrum is transformed so that in the new representation the full width at half maximum (FWHM) is independent of energy. Thus, the spectrum is arranged symmetrically and transformed into the Fourier representation. The latter is multiplied by a function in order to transform original Gaussian into Lorentzian peaks. An autoregressive filter is calculated, leading to a characteristic polynomial whose complex roots represent both the location and the width of each peak, provided that the absolute value is lower than unit. The amplitude of each component (the area of each peak or the sum of areas of peaks characterizing an element) is fitted by the weighted least squares method, taking into account that errors in spectra are independent and follow a Poisson law. Very accurate results are obtained, which would be hard to achieve by other methods. The DECO FORTRAN code has been developed for compatible PC microcomputers. Some features of the code are given. (orig.)
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…
Martian Radiative Transfer Modeling Using the Optimal Spectral Sampling Method
Eluszkiewicz, J.; Cady-Pereira, K.; Uymin, G.; Moncet, J.-L.
2005-01-01
The large volume of existing and planned infrared observations of Mars have prompted the development of a new martian radiative transfer model that could be used in the retrievals of atmospheric and surface properties. The model is based on the Optimal Spectral Sampling (OSS) method [1]. The method is a fast and accurate monochromatic technique applicable to a wide range of remote sensing platforms (from microwave to UV) and was originally developed for the real-time processing of infrared and microwave data acquired by instruments aboard the satellites forming part of the next-generation global weather satellite system NPOESS (National Polarorbiting Operational Satellite System) [2]. As part of our on-going research related to the radiative properties of the martian polar caps, we have begun the development of a martian OSS model with the goal of using it to perform self-consistent atmospheric corrections necessary to retrieve caps emissivity from the Thermal Emission Spectrometer (TES) spectra. While the caps will provide the initial focus area for applying the new model, it is hoped that the model will be of interest to the wider Mars remote sensing community.
Let's collocate: student generated worksheets as a motivational tool
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.
The use of the spectral method within the fast adaptive composite grid method
Energy Technology Data Exchange (ETDEWEB)
McKay, S.M.
1994-12-31
The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.
An empirical understanding of triple collocation evaluation measure
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
Rapid simulation of spatial epidemics: a spectral method.
Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J
2015-04-07
Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel. Copyright © 2015 Elsevier Ltd. All rights reserved.
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo; Keyes, David E.
2016-01-01
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell
2016-06-14
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
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.
Visual Method for Spectral Energy Distribution Calculation of ...
Indian Academy of Sciences (India)
Abstract. In this work, we propose to use 'The Geometer's Sketchpad' to the fitting of a spectral energy distribution of blazar based on three effective spectral indices, αRO, αOX, and αRX and the flux density in the radio band. It can make us to see the fitting in detail with both the peak frequency and peak luminosity given ...
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
Farrell, Patricio
2013-01-01
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.
Towards spectral geometric methods for Euclidean quantum gravity
Panine, Mikhail; Kempf, Achim
2016-04-01
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.
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.
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
This is the first of a series of papers devoted to the study of h-p spec- .... element functions defined on mesh elements in the new system of variables with a uni- ... the spectral element functions on these elements and give construction of the stability .... By Hm( ), we denote the usual Sobolev space of integer order m ≥ 0 ...
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.
Huang, Z.; Chen, Q.; Shen, Y.; Chen, Q.; Liu, X.
2017-09-01
Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information.
Assessment of modern spectral analysis methods to improve wavenumber resolution of F-K spectra
International Nuclear Information System (INIS)
Shirley, T.E.; Laster, S.J.; Meek, R.A.
1987-01-01
The improvement in wavenumber spectra obtained by using high resolution spectral estimators is examined. Three modern spectral estimators were tested, namely the Autoregressive/Maximum Entropy (AR/ME) method, the Extended Prony method, and an eigenstructure method. They were combined with the conventional Fourier method by first transforming each trace with a Fast Fourier Transform (FFT). A high resolution spectral estimator was applied to the resulting complex spatial sequence for each frequency. The collection of wavenumber spectra thus computed comprises a hybrid f-k spectrum with high wavenumber resolution and less spectral ringing. Synthetic and real data records containing 25 traces were analyzed by using the hybrid f-k method. The results show an FFT-AR/ME f-k spectrum has noticeably better wavenumber resolution and more spectral dynamic range than conventional spectra when the number of channels is small. The observed improvement suggests the hybrid technique is potentially valuable in seismic data analysis
International Nuclear Information System (INIS)
Moore, Travis J.; Jones, Matthew R.; Tree, Dale R.; Daniel Maynes, R.; Baxter, Larry L.
2011-01-01
An experimental procedure has been developed to make spectral emittance and temperature measurements. The spectral emittance of an object is calculated using measurements of the spectral emissive power and of the surface temperature of the object obtained using a Fourier transform infrared (FTIR) spectrometer. A calibration procedure is described in detail which accounts for the temperature dependence of the detector. The methods used to extract the spectral emissive power and surface temperature from measured infrared spectra were validated using a blackbody radiator at known temperatures. The average error in the measured spectral emittance was 2.1% and the average difference between the temperature inferred from the recorded spectra and the temperature indicated on the blackbody radiator was 1.2%. The method was used to measure the spectral emittance of oxidized copper at various temperatures.
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
Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification
Winokur, J.; Kim, D.; Bisetti, Fabrizio; Le Maî tre, O. P.; Knio, Omar
2015-01-01
We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a
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) ...
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.
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 ...
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 ...
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 ...
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.
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 ...
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
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
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.
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
Zou, Peng; Cheng, Jiubing
2017-01-01
-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour; Chá con-Rebollo, Tomas
2015-01-01
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base
Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
Directory of Open Access Journals (Sweden)
Jinkui Liu
2012-01-01
Full Text Available A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995 in contrast to the famous CD method, FR method, and PRP method.
A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results
Larsen, Curtis E.; Irvine, Tom
2013-01-01
A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.
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...
Establishing a method to measure bone structure using spectral CT
Ramyar, M.; Leary, C.; Raja, A.; Butler, A. P. H.; Woodfield, T. B. F.; Anderson, N. G.
2017-03-01
Combining bone structure and density measurement in 3D is required to assess site-specific fracture risk. Spectral molecular imaging can measure bone structure in relation to bone density by measuring macro and microstructure of bone in 3D. This study aimed to optimize spectral CT methodology to measure bone structure in excised bone samples. MARS CT with CdTe Medipix3RX detector was used in multiple energy bins to calibrate bone structure measurements. To calibrate thickness measurement, eight different thicknesses of Aluminium (Al) sheets were scanned one in air and the other around a falcon tube and then analysed. To test if trabecular thickness measurements differed depending on scan plane, a bone sample from sheep proximal tibia was scanned in two orthogonal directions. To assess the effect of air on thickness measurement, two parts of the same human femoral head were scanned in two conditions (in the air and in PBS). The results showed that the MARS scanner (with 90μm voxel size) is able to accurately measure the Al (in air) thicknesses over 200μm but it underestimates the thicknesses below 200μm because of partial volume effect in Al-air interface. The Al thickness measured in the highest energy bin is overestimated at Al-falcon tube interface. Bone scanning in two orthogonal directions gives the same trabecular thickness and air in the bone structure reduced measurement accuracy. We have established a bone structure assessment protocol on MARS scanner. The next step is to combine this with bone densitometry to assess bone strength.
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.
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014-01-01
approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction
An Improved Spectral Analysis Method for Fatigue Damage Assessment of Details in Liquid Cargo Tanks
Zhao, Peng-yuan; Huang, Xiao-ping
2018-03-01
Errors will be caused in calculating the fatigue damages of details in liquid cargo tanks by using the traditional spectral analysis method which is based on linear system, for the nonlinear relationship between the dynamic stress and the ship acceleration. An improved spectral analysis method for the assessment of the fatigue damage in detail of a liquid cargo tank is proposed in this paper. Based on assumptions that the wave process can be simulated by summing the sinusoidal waves in different frequencies and the stress process can be simulated by summing the stress processes induced by these sinusoidal waves, the stress power spectral density (PSD) is calculated by expanding the stress processes induced by the sinusoidal waves into Fourier series and adding the amplitudes of each harmonic component with the same frequency. This analysis method can take the nonlinear relationship into consideration and the fatigue damage is then calculated based on the PSD of stress. Take an independent tank in an LNG carrier for example, the accuracy of the improved spectral analysis method is proved much better than that of the traditional spectral analysis method by comparing the calculated damage results with the results calculated by the time domain method. The proposed spectral analysis method is more accurate in calculating the fatigue damages in detail of ship liquid cargo tanks.
International Nuclear Information System (INIS)
Chen, Q G; Xu, Y; Zhu, H H; Chen, H; Lin, B
2015-01-01
A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565–750 nm. The spectral parameter, defined as the ratio of wavebands at 565–750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as <0.66, 0.66–1.06, 1.06–1.62, and >1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems. (paper)
Chen, Q. G.; Zhu, H. H.; Xu, Y.; Lin, B.; Chen, H.
2015-08-01
A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565-750 nm. The spectral parameter, defined as the ratio of wavebands at 565-750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as 1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems.
Relation work in collocated and distributed collaboration
DEFF Research Database (Denmark)
Christensen, Lars Rune; Jensen, Rasmus Eskild; Bjørn, Pernille
2014-01-01
Creating social ties are important for collaborative work; however, in geographically distributed organizations e.g. global software development, making social ties requires extra work: Relation work. We find that characteristics of relation work as based upon shared history and experiences......, emergent in personal and often humorous situations. Relation work is intertwined with other activities such as articulation work and it is rhythmic by following the work patterns of the participants. By comparing how relation work is conducted in collocated and geographically distributed settings we...... in this paper identify basic differences in relation work. Whereas collocated relation work is spontaneous, place-centric, and yet mobile, relation work in a distributed setting is semi-spontaneous, technology-mediated, and requires extra efforts....
Impact of WhatsApp on Learning and Retention of Collocation Knowledge among Iranian EFL Learners
Directory of Open Access Journals (Sweden)
Zahra Ashiyan
2016-10-01
Full Text Available During the recent technological years, language learning has been attempted to transform its path from the conventional methods to instrumental applications. Mobile phone provides people to reach and exchange information through chats (WhatsApp. It is a tool or mode that means the facilities are used for main purposes. The unique features of the application are its compatibility to exchange information, enhance communication and relationship. A mobile phone provides to download, upload and store learning materials and information files. The purpose of the current study was to investigate the use and effect of mobile applications such as WhatsApp on school work and out of school work. In this way, Oxford Placement Test (OPT was conducted among 80 learners in order to select intermediate EFL learners. In total, 60 participants whose scores were 70 or higher were elected as the intermediate level and were divided into experimental and control groups. In order to control the reliability of the collocation pretest, the test was pilot studied on 15 learners. Then, the pretest was conducted to measure the learner’s collocation knowledge in both of the groups. The experimental group frequently installed WhatsApp application in order to learning and practicing new collocations in order to learning and practicing new collocations, while the control group did not use any tool for learning them. An immediate posttest after the treatment was administered. The results in each group were statistically evaluated and the findings manifested that the experimental group who used WhatsApp application in learning collocation significantly outperformed the control group in posttest. Thus usage of WhatsApp application to acquire collocations can reinforce and enhance the process of collocations acquisition and it can guarantee retention of collocations. This study also prepares pedagogical implications for utilizing mobile application as an influential instrument
Multi-spectral lifetime imaging: methods and applications
Fereidouni, F.
2013-01-01
The aim of this PhD project is to further develop multispectral life time imaging hardware and analyses methods. The hardware system, Lambda-Tau, generates a considerable amount of data at high speed. To fully exploit the power of this new hardware, fast and reliable data analyses methods are
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@In this paper, some image processing methods such as directional template (mask) matching enhancement, pseudocolor or false color enhancement, K-L transform enhancement are used to enhance a geological structure, one of important ore-controlling factors, shown in the remote-sensing images.This geological structure is regarded as image anomaly in the remote-sensing image, since considerable differences, based on the spatial spectral distribution pattern, in gray values (spectral), color tones and texture, are always present between the geological structure and background. Therefore,the enhancement of the geological structure in the remotesensing image is that of the spectral spatial difference.
Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients
Irvine, Tom; Larsen, Curtis
2016-01-01
The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.
Continuous non-invasive blood glucose monitoring by spectral image differencing method
Huang, Hao; Liao, Ningfang; Cheng, Haobo; Liang, Jing
2018-01-01
Currently, the use of implantable enzyme electrode sensor is the main method for continuous blood glucose monitoring. But the effect of electrochemical reactions and the significant drift caused by bioelectricity in body will reduce the accuracy of the glucose measurements. So the enzyme-based glucose sensors need to be calibrated several times each day by the finger-prick blood corrections. This increases the patient's pain. In this paper, we proposed a method for continuous Non-invasive blood glucose monitoring by spectral image differencing method in the near infrared band. The method uses a high-precision CCD detector to switch the filter in a very short period of time, obtains the spectral images. And then by using the morphological method to obtain the spectral image differences, the dynamic change of blood sugar is reflected in the image difference data. Through the experiment proved that this method can be used to monitor blood glucose dynamically to a certain extent.
New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams
Energy Technology Data Exchange (ETDEWEB)
Dorf, Mikhail A.; Davidson, Ronald C.; Startsev, Edward A.
2011-04-27
An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.
Multi-spectral temperature measurement method for gas turbine blade
Gao, Shan; Feng, Chi; Wang, Lixin; Li, Dong
2016-02-01
One of the basic methods to improve both the thermal efficiency and power output of a gas turbine is to increase the firing temperature. However, gas turbine blades are easily damaged in harsh high-temperature and high-pressure environments. Therefore, ensuring that the blade temperature remains within the design limits is very important. There are unsolved problems in blade temperature measurement, relating to the emissivity of the blade surface, influences of the combustion gases, and reflections of radiant energy from the surroundings. In this study, the emissivity of blade surfaces has been measured, with errors reduced by a fitting method, influences of the combustion gases have been calculated for different operational conditions, and a reflection model has been built. An iterative computing method is proposed for calculating blade temperatures, and the experimental results show that this method has high precision.
Methods for deconvoluting and interpreting complex gamma- and x-ray spectral regions
International Nuclear Information System (INIS)
Gunnink, R.
1983-06-01
Germanium and silicon detectors are now widely used for the detection and measurement of x and gamma radiation. However, some analysis situations and spectral regions have heretofore been too complex to deconvolute and interpret by techniques in general use. One example is the L x-ray spectrum of an element taken with a Ge or Si detector. This paper describes some new tools and methods that were developed to analyze complex spectral regions; they are illustrated with examples
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.
Semantic Analysis of Verbal Collocations with Lexical Functions
Gelbukh, Alexander
2013-01-01
This book is written for both linguists and computer scientists working in the field of artificial intelligence as well as to anyone interested in intelligent text processing. Lexical function is a concept that formalizes semantic and syntactic relations between lexical units. Collocational relation is a type of institutionalized lexical relations which holds between the base and its partner in a collocation. Knowledge of collocation is important for natural language processing because collocation comprises the restrictions on how words can be used together. The book shows how collocations can be annotated with lexical functions in a computer readable dictionary - allowing their precise semantic analysis in texts and their effective use in natural language applications including parsers, high quality machine translation, periphrasis system and computer-aided learning of lexica. The books shows how to extract collocations from corpora and annotate them with lexical functions automatically. To train algorithms,...
On Collocations and Their Interaction with Parsing and Translation
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.
Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem
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.
Incompressible spectral-element method: Derivation of equations
Deanna, Russell G.
1993-01-01
A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Spectral methods in chemistry and physics applications to kinetic theory and quantum mechanics
Shizgal, Bernard
2015-01-01
This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficient...
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas
International Nuclear Information System (INIS)
Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.
2013-01-01
Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods
Generalized spectral method for near-field optical microscopy
Energy Technology Data Exchange (ETDEWEB)
Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M. [Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093 (United States); Castro Neto, A. H. [Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States); Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore 117542 (Singapore)
2016-02-07
Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.
Methodes spectrales paralleles et applications aux simulations de couches de melange compressibles
Male , Jean-Michel; Fezoui , Loula ,
1993-01-01
La resolution des equations de Navier-Stokes en methodes spectrales pour des ecoulements compressibles peut etre assez gourmande en temps de calcul. On etudie donc ici la parallelisation d'un tel algorithme et son implantation sur une machine massivement parallele, la connection-machine CM-2. La methode spectrale s'adapte bien aux exigences du parallelisme massif, mais l'un des outils de base de cette methode, la transformee de Fourier rapide (lorsqu'elle doit etre appliquee sur les deux dime...
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
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.
A Spectral-Texture Kernel-Based Classification Method for Hyperspectral Images
Directory of Open Access Journals (Sweden)
Yi Wang
2016-11-01
Full Text Available Classification of hyperspectral images always suffers from high dimensionality and very limited labeled samples. Recently, the spectral-spatial classification has attracted considerable attention and can achieve higher classification accuracy and smoother classification maps. In this paper, a novel spectral-spatial classification method for hyperspectral images by using kernel methods is investigated. For a given hyperspectral image, the principle component analysis (PCA transform is first performed. Then, the first principle component of the input image is segmented into non-overlapping homogeneous regions by using the entropy rate superpixel (ERS algorithm. Next, the local spectral histogram model is applied to each homogeneous region to obtain the corresponding texture features. Because this step is performed within each homogenous region, instead of within a fixed-size image window, the obtained local texture features in the image are more accurate, which can effectively benefit the improvement of classification accuracy. In the following step, a contextual spectral-texture kernel is constructed by combining spectral information in the image and the extracted texture information using the linearity property of the kernel methods. Finally, the classification map is achieved by the support vector machines (SVM classifier using the proposed spectral-texture kernel. Experiments on two benchmark airborne hyperspectral datasets demonstrate that our method can effectively improve classification accuracies, even though only a very limited training sample is available. Specifically, our method can achieve from 8.26% to 15.1% higher in terms of overall accuracy than the traditional SVM classifier. The performance of our method was further compared to several state-of-the-art classification methods of hyperspectral images using objective quantitative measures and a visual qualitative evaluation.
Application of Least-Squares Spectral Element Methods to Polynomial Chaos
Vos, P.E.J.; Gerritsma, M.I.
2006-01-01
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
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...
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.
Application of the spectral correction method to reanalysis data in South Africa
DEFF Research Database (Denmark)
Larsén, Xiaoli Guo; Kruger, Andries C.
2014-01-01
of this study is to evaluate the applicability of the method to the relevant region. The impacts from the two aspects are investigated for interior and coastal locations. Measurements from five stations from South Africa are used to evaluate the results from the spectral model S(f)=af−5/3 together...... with the hourly time series of the Climate Forecast System Reanalysis (CFSR) 10 m wind at 38 km resolution over South Africa. The results show that using the spectral correction method to the CFSR wind data produce extreme wind atlases in acceptable agreement with the atlas made from limited measurements across...
The analysis of toxic connections content in water by spectral methods
Plotnikova, I. V.; Chaikovskaya, O. N.; Sokolova, I. V.; Artyushin, V. R.
2017-08-01
The current state of ecology means the strict observance of measures for the utilization of household and industrial wastes that is connected with very essential expenses of means and time. Thanks to spectroscopic devices usage the spectral methods allow to carry out the express quantitative and qualitative analysis in a workplace and field conditions. In a work the application of spectral methods by studying the degradation of toxic organic compounds after preliminary radiation of various sources is shown. Experimental data of optical density of water at various influences are given.
Optimization of Low-Thrust Spiral Trajectories by Collocation
Falck, Robert D.; Dankanich, John W.
2012-01-01
As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.
Tapia-Herrera, R.; Huerta-Lopez, C. I.; Martinez-Cruzado, J. A.
2009-05-01
Results of site characterization for an experimental site in the metropolitan area of Tijuana, B. C., Mexico are presented as part of the on-going research in which time series of earthquakes, ambient noise, and induced vibrations were processed with three different methods: H/V spectral ratios, Spectral Analysis of Surface Waves (SASW), and the Random Decrement Method, (RDM). Forward modeling using the wave propagation stiffness matrix method (Roësset and Kausel, 1981) was used to compute the theoretical SH/P, SV/P spectral ratios, and the experimental H/V spectral ratios were computed following the conventional concepts of Fourier analysis. The modeling/comparison between the theoretical and experimental H/V spectral ratios was carried out. For the SASW method the theoretical dispersion curves were also computed and compared with the experimental one, and finally the theoretical free vibration decay curve was compared with the experimental one obtained with the RDM. All three methods were tested with ambient noise, induced vibrations, and earthquake signals. Both experimental spectral ratios obtained with ambient noise as well as earthquake signals agree quite well with the theoretical spectral ratios, particularly at the fundamental vibration frequency of the recording site. Differences between the fundamental vibration frequencies are evident for sites located at alluvial fill (~0.6 Hz) and at sites located at conglomerate/sandstones fill (0.75 Hz). Shear wave velocities for the soft soil layers of the 4-layer discrete soil model ranges as low as 100 m/s and up to 280 m/s. The results with the SASW provided information that allows to identify low velocity layers, not seen before with the traditional seismic methods. The damping estimations obtained with the RDM are within the expected values, and the dominant frequency of the system also obtained with the RDM correlates within the range of plus-minus 20 % with the one obtained by means of the H/V spectral
Spectral analysis of an algebraic collapsing acceleration for the characteristics method
International Nuclear Information System (INIS)
Le Tellier, R.; Hebert, A.
2005-01-01
A spectral analysis of a diffusion synthetic acceleration called Algebraic Collapsing Acceleration (ACA) was carried out in the context of the characteristics method to solve the neutron transport equation. Two analysis were performed in order to assess the ACA performances. Both a standard Fourier analysis in a periodic and infinite slab-geometry and a direct spectral analysis for a finite slab-geometry were investigated. In order to evaluate its performance, ACA was compared with two competing techniques used to accelerate the convergence of the characteristics method, the Self-Collision Re-balancing technique and the Asymptotic Synthetic Acceleration. In the restricted framework of 1-dimensional slab-geometries, we conclude that ACA offers a good compromise between the reduction of the spectral radius of the iterative matrix and the resources to construct, store and solve the corrective system. A comparison on a monoenergetic 2-dimensional benchmark was performed and tends to confirm these conclusions. (authors)
International Nuclear Information System (INIS)
Ostachowicz, W; Kudela, P
2010-01-01
A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.
Nobe, Kazuki; Yoshimoto, Kayo; Yamada, Kenji; Takahashi, Hideya
2018-02-01
Functional gastrointestinal disorders (FGID) are the most common gastrointestinal disorders. The term "functional" is generally applied to disorders where there are no structural abnormalities. One of the major factors for FGID is abnormal gastrointestinal motility. We have proposed a system for assessing the function of gastric motility using a 3D endoscope. In this previous study, we established a method for estimating characteristics of contraction wave extracted from a 3D shape include contraction wave obtained from stereo endoscope. Because it is difficult to fix the tip position of the endoscope during the examination, estimation of the 3D position between the endoscope and the gastric wall is necessary for the accurate assessment. Then, we have proposed a motion compensation method using 3D scene flow. However, since mucosa has few feature points, it is difficult to obtain 3D scene flow from RGB images. So, we focused on spectral imaging that can enhance visualization of mucosal structure. Spectral image can be obtained without switching optical filters by using technique to estimate spectral reflectance by image processing. In this paper, we propose registration method of measured 3D shape in time series using estimated spectral image. The spectral image is estimated from the RGB image for each frame. 3D scene flow of feature points, that is, enhanced mucosal structure calculated by spectral images in a time series. The position change between the endoscope and gastric wall is estimated by 3D scene flow. We experimented to confirm the validity of the proposed method using papers with a grid of colors close to the background color.
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.
Learning and Teaching L2 Collocations: Insights from Research
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…
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, ...
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 ...
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.
Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks
Menon, Sujatha; Mukundan, Jayakaran
2012-01-01
This paper analyses the discourse of science through the study of collocational patterns of high frequency noun keywords in science textbooks used by upper secondary students in Malaysia. Research has shown that one of the areas of difficulty in science discourse concerns lexis, especially that of collocations. This paper describes a corpus-based…
Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank
DEFF Research Database (Denmark)
Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter
2013-01-01
A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau...... method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...... wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes....
The next step in coastal numerical models: spectral/hp element methods?
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter; Sherwin, Spencer J.
2005-01-01
In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations....
The application of the Chebyshev-spectral method in transport phenomena
Guo, Weidong; Narayanan, Ranga
2012-01-01
Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interes...
A new approach to passivity preserving model reduction : the dominant spectral zero method
Ionutiu, R.; Rommes, J.; Antoulas, A.C.; Roos, J.; Costa, L.R.J.
2010-01-01
A new model reduction method for circuit simulation is presented, which preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a
Mass anomalous dimension of SU(2) with Nf=8 using the spectral density method
DEFF Research Database (Denmark)
Suorsa, Joni M.; Leino, Viljami; Rantaharju, Jarno
2015-01-01
SU(2) with Nf=8 is believed to have an infrared conformal fixed point. We use the spectral density method to evaluate the coupling constant dependence of the mass anomalous dimension for massless HEX smeared, clover improved Wilson fermions with Schr\\"odinger functional boundary conditions....
Spectral mimetic least-squares method for div-curl systems
Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.
2018-01-01
In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test
Stability Estimates for h-p Spectral Element Methods for Elliptic Problems
Dutt, Pravir; Tomar, S.K.; Kumar, B.V. Rathish
2002-01-01
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which
The spectral method and the central limit theorem for general Markov chains
Nagaev, S. V.
2017-12-01
We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.
Evaluation of methods to determine the spectral variations of aerosol optical thickness
Digital Repository Service at National Institute of Oceanography (India)
Suresh, T.; Talaulikar, M.; Rodrigues, A.; Desa, E.; Chauhan, P.
The methods used to derive spectral variations of aerosol optical thickness, AOT are evaluated. For our analysis we have used the AOT measured using a hand held sunphotometer at the coastal station on the west coast of India, Dona-Paula, Goa...
Testing the accuracy and stability of spectral methods in numerical relativity
International Nuclear Information System (INIS)
Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.
2007-01-01
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test
International Nuclear Information System (INIS)
Fiebig, H. Rudolf
2002-01-01
We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss the practical issues of the approach
A complex guided spectral transform Lanczos method for studying quantum resonance states
International Nuclear Information System (INIS)
Yu, Hua-Gen
2014-01-01
A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO, and compared to previous calculations
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Efendiev, Yalchin
2011-02-01
In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ*)1/2, where Λ* is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings. © 2010.
Development and validation of a new fallout transport method using variable spectral winds
International Nuclear Information System (INIS)
Hopkins, A.T.
1984-01-01
A new method was developed to incorporate variable winds into fallout transport calculations. The method uses spectral coefficients derived by the National Meteorological Center. Wind vector components are computed with the coefficients along the trajectories of falling particles. Spectral winds are used in the two-step method to compute dose rate on the ground, downwind of a nuclear cloud. First, the hotline is located by computing trajectories of particles from an initial, stabilized cloud, through spectral winds to the ground. The connection of particle landing points is the hotline. Second, dose rate on and around the hotline is computed by analytically smearing the falling cloud's activity along the ground. The feasibility of using spectral winds for fallout particle transport was validated by computing Mount St. Helens ashfall locations and comparing calculations to fallout data. In addition, an ashfall equation was derived for computing volcanic ash mass/area on the ground. Ashfall data and the ashfall equation were used to back-calculate an aggregated particle size distribution for the Mount St. Helens eruption cloud
A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA
Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan
2016-11-01
The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.
High-precision solution to the moving load problem using an improved spectral element method
Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li
2018-02-01
In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
Wang, Wei; Song, Wei-Guo; Liu, Shi-Xing; Zhang, Yong-Ming; Zheng, Hong-Yang; Tian, Wei
2011-04-01
An improved method for detecting cloud combining Kmeans clustering and the multi-spectral threshold approach is described. On the basis of landmark spectrum analysis, MODIS data is categorized into two major types initially by Kmeans method. The first class includes clouds, smoke and snow, and the second class includes vegetation, water and land. Then a multi-spectral threshold detection is applied to eliminate interference such as smoke and snow for the first class. The method is tested with MODIS data at different time under different underlying surface conditions. By visual method to test the performance of the algorithm, it was found that the algorithm can effectively detect smaller area of cloud pixels and exclude the interference of underlying surface, which provides a good foundation for the next fire detection approach.
Ultrafast method of calculating the dynamic spectral line shapes for integrated modelling of plasmas
International Nuclear Information System (INIS)
Lisitsa, V.S.
2009-01-01
An ultrafast code for spectral line shape calculations is presented to be used in the integrated modelling of plasmas. The code is based on the close analogy between two mechanisms: (i) Dicke narrowing of the Doppler-broadened spectral lines and (ii) transition from static to impact regime in the Stark broadening. The analogy makes it possible to describe the dynamic Stark broadening in terms of an analytical functional of the static line shape. A comparison of new method with the widely used Frequency Fluctuating Method (FFM) developed by the Marseille University group (B. Talin, R. Stamm, et al.) shows good agreement, with the new method being faster than the standard FFM by nearly two orders of magnitude. The method proposed may significantly simplify the radiation transport modeling and opens new possibilities for integrated modeling of the edge and divertor plasma in tokamaks. (author)
A sparse-mode spectral method for the simulation of turbulent flows
International Nuclear Information System (INIS)
Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.
1996-01-01
We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows
Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
Reduction of Musical Noise in Spectral Subtraction Method Using Subframe Phase Randomization
Energy Technology Data Exchange (ETDEWEB)
Seok, J.W.; Bae, K.S. [Kyungpook National University, Taegu (Korea)
1999-06-01
The Subframe phase randomization method is applied to the spectral subtraction method to reduce the musical noise in nonvoicing region after speech enhancement. The musical noise in the spectral subtraction method is the result of the narrowband tonal components that appearing somewhat periodically in the spectrogram of unvoiced and silence regions. Thus each synthesis frame in nonvoicing region is divided into several subframes to broaden the narrowband spectrum, and then phases of silence and unvoiced regions are randomized to eliminate the tonal components in the spectrum while keeping the shape of the amplitude spectrum. Performance assessments based on visual inspection of spectrogram, objective measure, and informal subjective listening tests demonstrate the superiority of the proposed algorithm. (author). 7 refs., 5 figs.
Funamizu, Hideki; Onodera, Yusei; Aizu, Yoshihisa
2018-05-01
In this study, we report color quality improvement of reconstructed images in color digital holography using the speckle method and the spectral estimation. In this technique, an object is illuminated by a speckle field and then an object wave is produced, while a plane wave is used as a reference wave. For three wavelengths, the interference patterns of two coherent waves are recorded as digital holograms on an image sensor. Speckle fields are changed by moving a ground glass plate in an in-plane direction, and a number of holograms are acquired to average the reconstructed images. After the averaging process of images reconstructed from multiple holograms, we use the Wiener estimation method for obtaining spectral transmittance curves in reconstructed images. The color reproducibility in this method is demonstrated and evaluated using a Macbeth color chart film and staining cells of onion.
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.
Zhao, Li-Ting; Xiang, Yu-Hong; Dai, Yin-Mei; Zhang, Zhuo-Yong
2010-04-01
Near infrared spectroscopy was applied to measure the tissue slice of endometrial tissues for collecting the spectra. A total of 154 spectra were obtained from 154 samples. The number of normal, hyperplasia, and malignant samples was 36, 60, and 58, respectively. Original near infrared spectra are composed of many variables, for example, interference information including instrument errors and physical effects such as particle size and light scatter. In order to reduce these influences, original spectra data should be performed with different spectral preprocessing methods to compress variables and extract useful information. So the methods of spectral preprocessing and wavelength selection have played an important role in near infrared spectroscopy technique. In the present paper the raw spectra were processed using various preprocessing methods including first derivative, multiplication scatter correction, Savitzky-Golay first derivative algorithm, standard normal variate, smoothing, and moving-window median. Standard deviation was used to select the optimal spectral region of 4 000-6 000 cm(-1). Then principal component analysis was used for classification. Principal component analysis results showed that three types of samples could be discriminated completely and the accuracy almost achieved 100%. This study demonstrated that near infrared spectroscopy technology and chemometrics method could be a fast, efficient, and novel means to diagnose cancer. The proposed methods would be a promising and significant diagnosis technique of early stage cancer.
Rapid screening of guar gum using portable Raman spectral identification methods.
Srivastava, Hirsch K; Wolfgang, Steven; Rodriguez, Jason D
2016-01-25
Guar gum is a well-known inactive ingredient (excipient) used in a variety of oral pharmaceutical dosage forms as a thickener and stabilizer of suspensions and as a binder of powders. It is also widely used as a food ingredient in which case alternatives with similar properties, including chemically similar gums, are readily available. Recent supply shortages and price fluctuations have caused guar gum to come under increasing scrutiny for possible adulteration by substitution of cheaper alternatives. One way that the U.S. FDA is attempting to screen pharmaceutical ingredients at risk for adulteration or substitution is through field-deployable spectroscopic screening. Here we report a comprehensive approach to evaluate two field-deployable Raman methods--spectral correlation and principal component analysis--to differentiate guar gum from other gums. We report a comparison of the sensitivity of the spectroscopic screening methods with current compendial identification tests. The ability of the spectroscopic methods to perform unambiguous identification of guar gum compared to other gums makes them an enhanced surveillance alternative to the current compendial identification tests, which are largely subjective in nature. Our findings indicate that Raman spectral identification methods perform better than compendial identification methods and are able to distinguish guar gum from other gums with 100% accuracy for samples tested by spectral correlation and principal component analysis. Published by Elsevier B.V.
Spectral element method for elastic and acoustic waves in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)
2016-12-15
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
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.
Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems
International Nuclear Information System (INIS)
Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da
2001-01-01
Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
International Nuclear Information System (INIS)
Mitsuyasu, T.; Ishii, K.; Hino, T.; Aoyama, M.
2009-01-01
Spectral history methods for pin-by-pin core analysis method using the three-dimensional direct response matrix have been developed. The direct response matrix is formalized by four sub-response matrices in order to respond to a core eigenvalue k and thus can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the burn-up effect related to spectral history. One of the methods is to evaluate the nodal burn-up spectrum obtained using the out-going neutron current. The other is to correct the fuel rod neutron production rates obtained the pin-by-pin correction. These spectral history methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error can be reduced by half during burn-up, the nodal neutron production rates errors can be reduced by 30% or more. The root-mean-square differences between the relative fuel rod neutron production rate distributions can be reduced within 1.1% error. This means that these methods can accurately reflect the effects of intra- and inter-assembly heterogeneities during burn-up and can be used for core analysis. Core analysis with the DRM method was carried out for an ABWR quarter core and it was found that both thermal power and coolant-flow distributions were smoothly converged. (authors)
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2012-11-01
Full Text Available The present work advances the inverse quantum (IQ structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings to more wave behavior (free or covalent bindings. This so-called spectral inverse quantum (Spectral-IQ particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB and cetyltrimethylammonium bromide (CTAB and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature.
International Nuclear Information System (INIS)
Barros, R.C.; Filho, H.A.; Oliveira, F.B.S.; Silva, F.C. da
2004-01-01
Presented here are the advances in spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: (i) the use of the standard discretized spatial balance SN equations; (ii) the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and (iii) the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. Moreover, we describe in this paper the progress of the approximate SN albedo boundary conditions for substituting the non-multiplying regions around the nuclear reactor core. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (Author)
Spectral feature characterization methods for blood stain detection in crime scene backgrounds
Yang, Jie; Mathew, Jobin J.; Dube, Roger R.; Messinger, David W.
2016-05-01
Blood stains are one of the most important types of evidence for forensic investigation. They contain valuable DNA information, and the pattern of the stains can suggest specifics about the nature of the violence that transpired at the scene. Blood spectral signatures containing unique reflectance or absorption features are important both for forensic on-site investigation and laboratory testing. They can be used for target detection and identification applied to crime scene hyperspectral imagery, and also be utilized to analyze the spectral variation of blood on various backgrounds. Non-blood stains often mislead the detection and can generate false alarms at a real crime scene, especially for dark and red backgrounds. This paper measured the reflectance of liquid blood and 9 kinds of non-blood samples in the range of 350 nm - 2500 nm in various crime scene backgrounds, such as pure samples contained in petri dish with various thicknesses, mixed samples with different colors and materials of fabrics, and mixed samples with wood, all of which are examined to provide sub-visual evidence for detecting and recognizing blood from non-blood samples in a realistic crime scene. The spectral difference between blood and non-blood samples are examined and spectral features such as "peaks" and "depths" of reflectance are selected. Two blood stain detection methods are proposed in this paper. The first method uses index to denote the ratio of "depth" minus "peak" over"depth" add"peak" within a wavelength range of the reflectance spectrum. The second method uses relative band depth of the selected wavelength ranges of the reflectance spectrum. Results show that the index method is able to discriminate blood from non-blood samples in most tested crime scene backgrounds, but is not able to detect it from black felt. Whereas the relative band depth method is able to discriminate blood from non-blood samples on all of the tested background material types and colors.
Methods for measuring the spectral reflectivity of advanced materials at high temperature
International Nuclear Information System (INIS)
Salikhov, T.P.; Kan, V.V.
1993-01-01
For investigation in the domain of advanced materials as well as for new technologies there is an urgent need for knowledge of the spectral reflectivity of the materials specially at high temperatures. However the methods available are mostly intended for measuring the model materials with specular or diffuse reflection surface. This is not quite correct since advanced materials have mixed specular diffuse reflection surfaces. New methods for reflectivity measurements of materials in the visible, near and middle infrared range at high temperature, regardless of surface texture, have been developed. The advantages of the methods proposed are as flows: (a) the facility of performing the reflectivity measurements for materials with mixed specular diffuse reflectance; (b) wide spectral range 0,38-8 micro m; (c) wide temperature range 300-3000 K; (d) high accuracy and rapid measurements. The methods are based on the following principals (i) Diffuse irradiation of the sample surface and the use of Helkholtz reciprocity principle to determine the directional hemispherical reflectivity ii) Pulse polychromatic probing of the sample by additional light source. The first principle excludes the influence of the angular reflection distribution of sample surface on data obtained. The second principle gives the possibility of simultaneous measurements of the reflectivity. The second principle gives the possibility of simultaneous measurements of the reflectivity in wide spectral range. On the basis of these principles for high temperature reflectometers have been developed and discussed here. (author)
Spectral decomposition in advection-diffusion analysis by finite element methods
International Nuclear Information System (INIS)
Nickell, R.E.; Gartling, D.K.; Strang, G.
1978-01-01
In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies
A spectral measurement method for determining white OLED average junction temperatures
Zhu, Yiting; Narendran, Nadarajah
2016-09-01
The objective of this study was to investigate an indirect method of measuring the average junction temperature of a white organic light-emitting diode (OLED) based on temperature sensitivity differences in the radiant power emitted by individual emitter materials (i.e., "blue," "green," and "red"). The measured spectral power distributions (SPDs) of the white OLED as a function of temperature showed amplitude decrease as a function of temperature in the different spectral bands, red, green, and blue. Analyzed data showed a good linear correlation between the integrated radiance for each spectral band and the OLED panel temperature, measured at a reference point on the back surface of the panel. The integrated radiance ratio of the spectral band green compared to red, (G/R), correlates linearly with panel temperature. Assuming that the panel reference point temperature is proportional to the average junction temperature of the OLED panel, the G/R ratio can be used for estimating the average junction temperature of an OLED panel.
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
International Nuclear Information System (INIS)
Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.
2003-01-01
Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate time-integration. In particular, interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection. The numerical strategy introduced in this paper is a general procedure to account for this time-scale disparity. The proposed methods are high-order multi-implicit generalizations of spectral deferred correction methods (MISDC methods), constructed for the temporal integration of A-D-R equations. Spectral deferred correction methods compute a high-order approximation to the solution of a differential equation by using a simple, low-order numerical method to solve a series of correction equations, each of which increases the order of accuracy of the approximation. The key feature of MISDC methods is their flexibility in handling several sub-processes implicitly but independently, while avoiding the splitting errors present in traditional operator-splitting methods and also allowing for different time steps for each process. The stability, accuracy, and efficiency of MISDC methods are first analyzed using a linear model problem and the results are compared to semi-implicit spectral deferred correction methods. Furthermore, numerical tests on simplified reacting flows demonstrate the expected convergence rates for MISDC methods of orders three, four, and five. The gain in efficiency by independently controlling the sub-process time steps is illustrated for nonlinear problems, where reaction and diffusion are much stiffer than advection. Although the paper focuses on this specific time-scales ordering, the generalization to any ordering combination is straightforward
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)
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)
A collocation--Galerkin finite element model of cardiac action potential propagation.
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.
International Nuclear Information System (INIS)
Koszykowski, M.L.; Pfeffer, G.A.; Noid, D.W.
1987-01-01
Nonlinear dynamics plays a dominant role in a variety of important problems in chemical physics. Examples are unimolecular reactions, infrared multiphoton decomposition of molecules, the pumping process of the gamma ray laser, dissociation of vibrationally excited state-selected van der Waals's complexes, and many other chemical and atomic processes. The present article discusses recent theoretical studies on the quasi-periodic and chaotic dynamic aspects of vibrational-rotational states of atomic, nuclear, and molecular systems using the semiclassical spectral method (SSM). The authors note that the coordinates, momenta, and so on, are found using classical mechanics in the studies included in this review. They outline the semiclassical spectral method and a wide variety of applications. Although this technique was first developed ten years ago, it has proved to be tremendously successful as a tool used in dynamics problems. Applications include problems in nonlinear dynamics, molecular and atomic spectra, surface science, astronomy and stellar dynamics, nuclear physics, and polymer physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Xu, Qinwu; Hesthaven, Jan S.
2014-01-01
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.
Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers
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…
Corpus-Aided Business English Collocation Pedagogy: An Empirical Study in Chinese EFL Learners
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,…
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1989-01-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
MURILLO, Carol Andrea; THOREL, Luc; CAICEDO, Bernardo
2009-01-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge test...
Application of the spectral-correlation method for diagnostics of cellulose paper
Kiesewetter, D.; Malyugin, V.; Reznik, A.; Yudin, A.; Zhuravleva, N.
2017-11-01
The spectral-correlation method was described for diagnostics of optically inhomogeneous biological objects and materials of natural origin. The interrelation between parameters of the studied objects and parameters of the cross correlation function of speckle patterns produced by scattering of coherent light at different wavelengths is shown for thickness, optical density and internal structure of the material. A detailed study was performed for cellulose electric insulating paper with different parameters.
Perturbation method utilization in the analysis of the Convertible Spectral Shift Reactor (RCVS)
International Nuclear Information System (INIS)
Bruna, G.B; Legendre, J.F.; Porta, J.; Doriath, J.Y.
1988-01-01
In the framework of the preliminary faisability studies on a new core concept, techniques derived from perturbation theory show-up very useful in the calculation and physical analysis of project parameters. We show, in the present work, some applications of these methods to the RCVS (Reacteur Convertible a Variation de Spectre - Convertible Spectral Shift Reactor) Concept studies. Actually, we present here the search of a few group project type energy structure and the splitting of reactivity effects into individual components [fr
The spectral induced polarisation method and its application to hydrogeological problems
International Nuclear Information System (INIS)
Hoerdt, A.
2007-01-01
The spectral induced polarisation (SIP) method is an extension of the DC resistivity technique, where an alternating current is injected and the phase shift between voltage and current is measured in addition to the amplitude. In unconsolidated sediments, the phase shift includes complementary information on the structure of the pore space, and thus it should be possible to estimate hydraulic parameters from SIP measurements. Here, I describe some recent developments and give one example where hydraulic conductivity was estimated at the field scale
Performance Evaluation of the Spectral Centroid Downshift Method for Attenuation Estimation
Samimi, Kayvan; Varghese, Tomy
2015-01-01
Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequency-domain approaches applied to this problem. In this study, a statistical analysis of this method’s performance was carried out based on a parametric m...
Energy Technology Data Exchange (ETDEWEB)
Alchimov, A B; Drobot, S I; Drokov, V G; Zarubin, V P; Kazmirov, A D; Skodaev, Y D; Podrezov, A M [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)
1998-12-31
The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.
Energy Technology Data Exchange (ETDEWEB)
Alchimov, A.B.; Drobot, S.I.; Drokov, V.G.; Zarubin, V.P.; Kazmirov, A.D.; Skodaev, Y.D.; Podrezov, A.M. [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)
1997-12-31
The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.
Detection of the power lines in UAV remote sensed images using spectral-spatial methods.
Bhola, Rishav; Krishna, Nandigam Hari; Ramesh, K N; Senthilnath, J; Anand, Gautham
2018-01-15
In this paper, detection of the power lines on images acquired by Unmanned Aerial Vehicle (UAV) based remote sensing is carried out using spectral-spatial methods. Spectral clustering was performed using Kmeans and Expectation Maximization (EM) algorithm to classify the pixels into the power lines and non-power lines. The spectral clustering methods used in this study are parametric in nature, to automate the number of clusters Davies-Bouldin index (DBI) is used. The UAV remote sensed image is clustered into the number of clusters determined by DBI. The k clustered image is merged into 2 clusters (power lines and non-power lines). Further, spatial segmentation was performed using morphological and geometric operations, to eliminate the non-power line regions. In this study, UAV images acquired at different altitudes and angles were analyzed to validate the robustness of the proposed method. It was observed that the EM with spatial segmentation (EM-Seg) performed better than the Kmeans with spatial segmentation (Kmeans-Seg) on most of the UAV images. Copyright © 2017 Elsevier Ltd. All rights reserved.
Vidyasagar, A.; Tan, W. L.; Kochmann, D. M.
2017-09-01
Understanding the electromechanical response of bulk polycrystalline ferroelectric ceramics requires scale-bridging approaches. Recent advances in fast numerical methods to compute the homogenized mechanical response of materials with heterogeneous microstructure have enabled the solution of hitherto intractable systems. In particular, the use of a Fourier-based spectral method as opposed to the traditional finite element method has gained significant interest in the homogenization of periodic microstructures. Here, we solve the periodic, electro-mechanically-coupled boundary value problem at the mesoscale of polycrystalline ferroelectrics in order to extract the effective response of barium titanate (BaTiO3) and lead zirconate titanate (PZT) under applied electric fields. Results include the effective electric hysteresis and the associated butterfly curve of strain vs. electric field for mean stress-free electric loading. Computational predictions of the 3D polycrystalline response show convincing agreement with our experimental electric cycling and strain hysteresis data for PZT-5A. In addition to microstructure-dependent effective physics, we also show how finite-difference-based approximations in the spectral solution scheme significantly reduce instability and ringing phenomena associated with spectral techniques and lead to spatial convergence with h-refinement, which have been major challenges when modeling high-contrast systems such as polycrystals.
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.
A spectral nodal method for discrete ordinates problems in x,y geometry
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-06-01
A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)
The Use of English Collocations in Reader's Digest
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...
A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
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.
A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
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 spectral analysis of the domain decomposed Monte Carlo method for linear systems
Energy Technology Data Exchange (ETDEWEB)
Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)
2013-07-01
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
International Nuclear Information System (INIS)
Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.
2013-01-01
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
Analysing flow structures around a blade using spectral/hp method and HPIV
International Nuclear Information System (INIS)
Stoevesandt, Bernhard; Steigerwald, Christian; Shishkin, Andrei; Wagner, Claus; Peinke, Joachim
2007-01-01
A still difficult, yet pressing task for blade manufacturers and turbine producers is the correct prediction of the effects of turbulent winds on the blade. Reynolds Averaged Numerical Simulations (RANS) are a limited tool for calculating the effects. For large eddy simulations (LES) boundary layer calculation are still difficult therefore the spectral element method seems to be an approach to improve numerical calculations of flow separation. The flow field around an fx79-w151a airfoil has been calculated by the spectral element code NεκTαrusing a direct numerical simulation (DNS) solver. In a first step a laminar inflow on the airfoil at angle of attack of α = 12 0 and a Reynolds number of Re= 33000 was simulated using the 2D Version of the code. The flow pattern was compared to measurements using holographic particle induced velocimetry (HPIV) in a wind tunnel
Spectral element method for band-structure calculations of 3D phononic crystals
International Nuclear Information System (INIS)
Shi, Linlin; Liu, Na; Zhou, Jianyang; Zhou, Yuanguo; Wang, Jiamin; Liu, Qing Huo
2016-01-01
The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals. (paper)
International Nuclear Information System (INIS)
Jovanovic, S.; Stormark, E.
1966-01-01
Measurements of reactor parameters the Nora reactor by Power Spectral Density (PSD) method are described. In case of critical reactor this method was applied for direct measurement of β/l ratio, β is the effective yield of delayed neutrons and l is the neutron lifetime. In case of subcritical reactor values of α+β-ρ/l were measured, ρ is the negative reactivity. Out coming PSD was measured by a filter or by ISAC. PSD was registered by ISAC as well as the auto-correlation function [sr
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
Murillo, Carol Andrea; Thorel, Luc; Caicedo, Bernardo
2009-06-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge testing is a relevant method to characterize VS near the surface.
Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method
Parsani, Matteo
2012-01-01
Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...
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
A fourth order spline collocation approach for a business cycle model
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.
Dilz, R.J.; van Beurden, M.C.
2016-01-01
We propose a mixed spatial spectral method aimed directly at aperiodic, finite scatterers in a layered medium. By using a Gabor frame to discretize the problem a straightforward and fast way to Fourier transform is available. The poles and branchcuts in the spectral-domain Green function can be
The spectral element method for static neutron transport in AN approximation. Part I
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.
2013-01-01
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
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.
Wang, Zhiheng
2015-01-01
A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.
Validation of spectral methods for the seismic analysis of multi-supported structures
International Nuclear Information System (INIS)
Viola, B.
1999-01-01
There are many methodologies for the seismic analysis of buildings. When a seism occurs, structures such piping systems in nuclear power plants are subjected to motions that may be different at each support point. Therefore it is necessary to develop methods that take into account the multi-supported effect. In a first time, a bibliography analysis on the different methods that exist has been carried out. The aim was to find a particular method applicable to the study of piping systems. The second step of this work consisted in developing a program that may be used to test and make comparisons on different selected methods. So spectral methods have the advantage to give an estimation of the maximum values for strain in the structure, in reduced calculation time. The time history analysis is used as the reference for the tests. (author)
Spectral methods for the detection of network community structure: a comparative analysis
International Nuclear Information System (INIS)
Shen, Hua-Wei; Cheng, Xue-Qi
2010-01-01
Spectral analysis has been successfully applied to the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlation matrix and several other variants of these matrices. However, the comparison between these spectral methods is less reported. More importantly, it is still unclear which matrix is more appropriate for the detection of community structure. This paper answers the question by evaluating the effectiveness of these five matrices against benchmark networks with heterogeneous distributions of node degree and community size. Test results demonstrate that the normalized Laplacian matrix and the correlation matrix significantly outperform the other three matrices at identifying the community structure of networks. This indicates that it is crucial to take into account the heterogeneous distribution of node degree when using spectral analysis for the detection of community structure. In addition, to our surprise, the modularity matrix exhibits very similar performance to the adjacency matrix, which indicates that the modularity matrix does not gain benefits from using the configuration model as a reference network with the consideration of the node degree heterogeneity
A Guide on Spectral Methods Applied to Discrete Data in One Dimension
Directory of Open Access Journals (Sweden)
Martin Seilmayer
2017-01-01
Full Text Available This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment R prior to this article.
American Society for Testing and Materials. Philadelphia
1971-01-01
1.1 This test method describes an accurate technique for measuring the normal spectral emittance of electrically nonconducting materials in the temperature range from 1000 to 1800 K, and at wavelengths from 1 to 35 μm. It is particularly suitable for measuring the normal spectral emittance of materials such as ceramic oxides, which have relatively low thermal conductivity and are translucent to appreciable depths (several millimetres) below the surface, but which become essentially opaque at thicknesses of 10 mm or less. 1.2 This test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is particularly suitable for research laboratories, where the highest precision and accuracy are desired, and is not recommended for routine production or acceptance testing. Because of its high accuracy, this test method may be used as a reference method to be applied to production and acceptance testing in case of dispute. 1.3 This test metho...
International Nuclear Information System (INIS)
Gamba, Irene M.; Haack, Jeffrey R.
2014-01-01
We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation
An Excel‐based implementation of the spectral method of action potential alternans analysis
Pearman, Charles M.
2014-01-01
Abstract Action potential (AP) alternans has been well established as a mechanism of arrhythmogenesis and sudden cardiac death. Proper interpretation of AP alternans requires a robust method of alternans quantification. Traditional methods of alternans analysis neglect higher order periodicities that may have greater pro‐arrhythmic potential than classical 2:1 alternans. The spectral method of alternans analysis, already widely used in the related study of microvolt T‐wave alternans, has also been used to study AP alternans. Software to meet the specific needs of AP alternans analysis is not currently available in the public domain. An AP analysis tool is implemented here, written in Visual Basic for Applications and using Microsoft Excel as a shell. This performs a sophisticated analysis of alternans behavior allowing reliable distinction of alternans from random fluctuations, quantification of alternans magnitude, and identification of which phases of the AP are most affected. In addition, the spectral method has been adapted to allow detection and quantification of higher order regular oscillations. Analysis of action potential morphology is also performed. A simple user interface enables easy import, analysis, and export of collated results. PMID:25501439
An Excel-based implementation of the spectral method of action potential alternans analysis.
Pearman, Charles M
2014-12-01
Action potential (AP) alternans has been well established as a mechanism of arrhythmogenesis and sudden cardiac death. Proper interpretation of AP alternans requires a robust method of alternans quantification. Traditional methods of alternans analysis neglect higher order periodicities that may have greater pro-arrhythmic potential than classical 2:1 alternans. The spectral method of alternans analysis, already widely used in the related study of microvolt T-wave alternans, has also been used to study AP alternans. Software to meet the specific needs of AP alternans analysis is not currently available in the public domain. An AP analysis tool is implemented here, written in Visual Basic for Applications and using Microsoft Excel as a shell. This performs a sophisticated analysis of alternans behavior allowing reliable distinction of alternans from random fluctuations, quantification of alternans magnitude, and identification of which phases of the AP are most affected. In addition, the spectral method has been adapted to allow detection and quantification of higher order regular oscillations. Analysis of action potential morphology is also performed. A simple user interface enables easy import, analysis, and export of collated results. © 2014 The Author. Physiological Reports published by Wiley Periodicals, Inc. on behalf of the American Physiological Society and The Physiological Society.
A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate
Djenidi, L.; Antonia, R. A.
2012-10-01
We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a -5/3 inertial subrange only when the Taylor microscale Reynods number R λ is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30 ≤ R λ ≤ 400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of < \\varepsilon rangle in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.
Spectral-element Method for 3D Marine Controlled-source EM Modeling
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).
Continuous Groundwater Monitoring Collocated at USGS Streamgages
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
Performance evaluation of the spectral centroid downshift method for attenuation estimation.
Samimi, Kayvan; Varghese, Tomy
2015-05-01
Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequencydomain approaches applied to this problem. In this study, a statistical analysis of this method's performance was carried out based on a parametric model of the signal power spectrum in the presence of electronic noise. The parametric model used for the power spectrum of received RF data assumes a Gaussian spectral profile for the transmit pulse, and incorporates effects of attenuation, windowing, and electronic noise. Spectral moments were calculated and used to estimate second-order centroid statistics. A theoretical expression for the variance of a maximum likelihood estimator of attenuation coefficient was derived in terms of the centroid statistics and other model parameters, such as transmit pulse center frequency and bandwidth, RF data window length, SNR, and number of regression points. Theoretically predicted estimation variances were compared with experimentally estimated variances on RF data sets from both computer-simulated and physical tissue-mimicking phantoms. Scan parameter ranges for this study were electronic SNR from 10 to 70 dB, transmit pulse standard deviation from 0.5 to 4.1 MHz, transmit pulse center frequency from 2 to 8 MHz, and data window length from 3 to 17 mm. Acceptable agreement was observed between theoretical predictions and experimentally estimated values with differences smaller than 0.05 dB/cm/MHz across the parameter ranges investigated. This model helps predict the best attenuation estimation variance achievable with the CDS method, in terms of said scan parameters.
A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models
International Nuclear Information System (INIS)
Xu, Jin; Yu, Yaming; Van Dyk, David A.; Kashyap, Vinay L.; Siemiginowska, Aneta; Drake, Jeremy; Ratzlaff, Pete; Connors, Alanna; Meng, Xiao-Li
2014-01-01
Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.
Buican, Tudor N.; Martin, John C.
1990-01-01
An apparatus and method simultaneously measures a plurality of spectral wavelengths present in electromagnetic radiation. A modulatable birefringent optical element is employed to divide a polarized light beam into two components, thereby producing a phase difference in two resulting light beams such that the two beams can be made to interfere with one another when recombined, the interference pattern providing the wavelength information required for the analysis of the incident light. The interferometer thus created performs in a similar manner to a Michelson interferometer, but with no moving parts, and with a resolution dependent on the degree of phase shift introduced by the modulator.
Spectral methods in machine learning and new strategies for very large datasets
Belabbas, Mohamed-Ali; Wolfe, Patrick J.
2009-01-01
Spectral methods are of fundamental importance in statistics and machine learning, because they underlie algorithms from classical principal components analysis to more recent approaches that exploit manifold structure. In most cases, the core technical problem can be reduced to computing a low-rank approximation to a positive-definite kernel. For the growing number of applications dealing with very large or high-dimensional datasets, however, the optimal approximation afforded by an exact spectral decomposition is too costly, because its complexity scales as the cube of either the number of training examples or their dimensionality. Motivated by such applications, we present here 2 new algorithms for the approximation of positive-semidefinite kernels, together with error bounds that improve on results in the literature. We approach this problem by seeking to determine, in an efficient manner, the most informative subset of our data relative to the kernel approximation task at hand. This leads to two new strategies based on the Nyström method that are directly applicable to massive datasets. The first of these—based on sampling—leads to a randomized algorithm whereupon the kernel induces a probability distribution on its set of partitions, whereas the latter approach—based on sorting—provides for the selection of a partition in a deterministic way. We detail their numerical implementation and provide simulation results for a variety of representative problems in statistical data analysis, each of which demonstrates the improved performance of our approach relative to existing methods. PMID:19129490
A New Pansharpening Method Based on Spatial and Spectral Sparsity Priors.
He, Xiyan; Condat, Laurent; Bioucas-Diaz, Jose; Chanussot, Jocelyn; Xia, Junshi
2014-06-27
The development of multisensor systems in recent years has led to great increase in the amount of available remote sensing data. Image fusion techniques aim at inferring high quality images of a given area from degraded versions of the same area obtained by multiple sensors. This paper focuses on pansharpening, which is the inference of a high spatial resolution multispectral image from two degraded versions with complementary spectral and spatial resolution characteristics: a) a low spatial resolution multispectral image; and b) a high spatial resolution panchromatic image. We introduce a new variational model based on spatial and spectral sparsity priors for the fusion. In the spectral domain we encourage low-rank structure, whereas in the spatial domain we promote sparsity on the local differences. Given the fact that both panchromatic and multispectral images are integrations of the underlying continuous spectra using different channel responses, we propose to exploit appropriate regularizations based on both spatial and spectral links between panchromatic and the fused multispectral images. A weighted version of the vector Total Variation (TV) norm of the data matrix is employed to align the spatial information of the fused image with that of the panchromatic image. With regard to spectral information, two different types of regularization are proposed to promote a soft constraint on the linear dependence between the panchromatic and the fused multispectral images. The first one estimates directly the linear coefficients from the observed panchromatic and low resolution multispectral images by Linear Regression (LR) while the second one employs the Principal Component Pursuit (PCP) to obtain a robust recovery of the underlying low-rank structure. We also show that the two regularizers are strongly related. The basic idea of both regularizers is that the fused image should have low-rank and preserve edge locations. We use a variation of the recently proposed
Spectral triangulation: a 3D method for locating single-walled carbon nanotubes in vivo
Lin, Ching-Wei; Bachilo, Sergei M.; Vu, Michael; Beckingham, Kathleen M.; Bruce Weisman, R.
2016-05-01
Nanomaterials with luminescence in the short-wave infrared (SWIR) region are of special interest for biological research and medical diagnostics because of favorable tissue transparency and low autofluorescence backgrounds in that region. Single-walled carbon nanotubes (SWCNTs) show well-known sharp SWIR spectral signatures and therefore have potential for noninvasive detection and imaging of cancer tumours, when linked to selective targeting agents such as antibodies. However, such applications face the challenge of sensitively detecting and localizing the source of SWIR emission from inside tissues. A new method, called spectral triangulation, is presented for three dimensional (3D) localization using sparse optical measurements made at the specimen surface. Structurally unsorted SWCNT samples emitting over a range of wavelengths are excited inside tissue phantoms by an LED matrix. The resulting SWIR emission is sampled at points on the surface by a scanning fibre optic probe leading to an InGaAs spectrometer or a spectrally filtered InGaAs avalanche photodiode detector. Because of water absorption, attenuation of the SWCNT fluorescence in tissues is strongly wavelength-dependent. We therefore gauge the SWCNT-probe distance by analysing differential changes in the measured SWCNT emission spectra. SWCNT fluorescence can be clearly detected through at least 20 mm of tissue phantom, and the 3D locations of embedded SWCNT test samples are found with sub-millimeter accuracy at depths up to 10 mm. Our method can also distinguish and locate two embedded SWCNT sources at distinct positions.Nanomaterials with luminescence in the short-wave infrared (SWIR) region are of special interest for biological research and medical diagnostics because of favorable tissue transparency and low autofluorescence backgrounds in that region. Single-walled carbon nanotubes (SWCNTs) show well-known sharp SWIR spectral signatures and therefore have potential for noninvasive detection and
A practical material decomposition method for x-ray dual spectral computed tomography.
Hu, Jingjing; Zhao, Xing
2016-03-17
X-ray dual spectral CT (DSCT) scans the measured object with two different x-ray spectra, and the acquired rawdata can be used to perform the material decomposition of the object. Direct calibration methods allow a faster material decomposition for DSCT and can be separated in two groups: image-based and rawdata-based. The image-based method is an approximative method, and beam hardening artifacts remain in the resulting material-selective images. The rawdata-based method generally obtains better image quality than the image-based method, but this method requires geometrically consistent rawdata. However, today's clinical dual energy CT scanners usually measure different rays for different energy spectra and acquire geometrically inconsistent rawdata sets, and thus cannot meet the requirement. This paper proposes a practical material decomposition method to perform rawdata-based material decomposition in the case of inconsistent measurement. This method first yields the desired consistent rawdata sets from the measured inconsistent rawdata sets, and then employs rawdata-based technique to perform material decomposition and reconstruct material-selective images. The proposed method was evaluated by use of simulated FORBILD thorax phantom rawdata and dental CT rawdata, and simulation results indicate that this method can produce highly quantitative DSCT images in the case of inconsistent DSCT measurements.
A Method of Particle Swarm Optimized SVM Hyper-spectral Remote Sensing Image Classification
International Nuclear Information System (INIS)
Liu, Q J; Jing, L H; Wang, L M; Lin, Q Z
2014-01-01
Support Vector Machine (SVM) has been proved to be suitable for classification of remote sensing image and proposed to overcome the Hughes phenomenon. Hyper-spectral sensors are intrinsically designed to discriminate among a broad range of land cover classes which may lead to high computational time in SVM mutil-class algorithms. Model selection for SVM involving kernel and the margin parameter values selection which is usually time-consuming, impacts training efficiency of SVM model and final classification accuracies of SVM hyper-spectral remote sensing image classifier greatly. Firstly, based on combinatorial optimization theory and cross-validation method, particle swarm algorithm is introduced to the optimal selection of SVM (PSSVM) kernel parameter σ and margin parameter C to improve the modelling efficiency of SVM model. Then an experiment of classifying AVIRIS in India Pine site of USA was performed for evaluating the novel PSSVM, as well as traditional SVM classifier with general Grid-Search cross-validation method (GSSVM). And then, evaluation indexes including SVM model training time, classification Overall Accuracy (OA) and Kappa index of both PSSVM and GSSVM are all analyzed quantitatively. It is demonstrated that OA of PSSVM on test samples and whole image are 85% and 82%, the differences with that of GSSVM are both within 0.08% respectively. And Kappa indexes reach 0.82 and 0.77, the differences with that of GSSVM are both within 0.001. While the modelling time of PSSVM can be only 1/10 of that of GSSVM, and the modelling. Therefore, PSSVM is an fast and accurate algorithm for hyper-spectral image classification and is superior to GSSVM
Sparse Generalized Fourier Series via Collocation-based Optimization
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
Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications
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
A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation
Terrana, S.; Vilotte, J. P.; Guillot, L.
2018-04-01
We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm
Getting Your Peaks in Line: A Review of Alignment Methods for NMR Spectral Data
Directory of Open Access Journals (Sweden)
Trung Nghia Vu
2013-04-01
Full Text Available One of the most significant challenges in the comparative analysis of Nuclear Magnetic Resonance (NMR metabolome profiles is the occurrence of shifts between peaks across different spectra, for example caused by fluctuations in pH, temperature, instrument factors and ion content. Proper alignment of spectral peaks is therefore often a crucial preprocessing step prior to downstream quantitative analysis. Various alignment methods have been developed specifically for this purpose. Other methods were originally developed to align other data types (GC, LC, SELDI-MS, etc., but can also be applied to NMR data. This review discusses the available methods, as well as related problems such as reference determination or the evaluation of alignment quality. We present a generic alignment framework that allows for comparison and classification of different alignment approaches according to their algorithmic principles, and we discuss their performance.
Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method
International Nuclear Information System (INIS)
Zhang Xu; Tan Duowang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)
A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
Efendiev, Yalchin R.
2015-08-01
We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method
International Nuclear Information System (INIS)
Xu, Zhang; Duo-Wang, Tan
2009-01-01
A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))
A multi-domain spectral method for time-fractional differential equations
Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.
2015-07-01
This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.
Gopalakrishnan, Srinivasan; Roy Mahapatra, Debiprosad
2008-01-01
The use of composites and Functionally Graded Materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and have many uses in structural engineering. However, the behaviour of these structures under high-impact loading is not well understood. This book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. It focuses on some of the problems with this media which were previously thought unmanageable. Types of SFEM for regular and damaged 1-D and 2-D waveguides, solution techniques, methods of detecting the presence of damages and their locations, and methods for controlling the wave propagation responses are discussed. Tables, figures and graphs support the theory and case studies are included. This book is of value to senior undergraduates and postgraduates studying in this field, and researchers and practicing engineers in structural integrity.
A method for spectral DNS of low Rm channel flows based on the least dissipative modes
Kornet, Kacper; Pothérat, Alban
2015-10-01
We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The main idea is to take advantage of the fact that such structures are dissipative and that their presence should reduce the number of degrees of freedom of the flow, when paradoxically, their fine resolution incurs extra computational cost in most current methods. The principle of this method is to use a functional basis with elements that already include these fine structures so as to avoid these extra costs. This leads us to develop an algorithm to implement a spectral method for arbitrary functional bases, and in particular, non-orthogonal ones. We construct a basic implementation of this algorithm to simulate magnetohydrodynamic (MHD) channel flows with an externally imposed, transverse magnetic field, where very thin boundary layers are known to develop along the channel walls. In this case, the sought functional basis can be built out of the eigenfunctions of the dissipation operator, which incorporate these boundary layers, and it turns out to be non-orthogonal. We validate this new scheme against numerical simulations of freely decaying MHD turbulence based on a finite volume code and it is found to provide accurate results. Its ability to fully resolve wall-bounded turbulence with a number of modes close to that required by the dynamics is demonstrated on a simple example. This opens the way to full-blown simulations of MHD turbulence under very high magnetic fields. Until now such simulations were too computationally expensive. In contrast to traditional methods the computational cost of the proposed method, does not depend on the intensity of the magnetic field.
A spectral nudging method for the ACCESS1.3 atmospheric model
Uhe, P.; Thatcher, M.
2015-06-01
A convolution-based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS) version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow for flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10-30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.
International Nuclear Information System (INIS)
Haaland, D.M.; Easterling, R.G.; Vopicka, D.A.
1985-01-01
In an extension of earlier work, weighted multivariate least-squares methods of quantitative FT-IR analysis have been developed. A linear least-squares approximation to nonlinearities in the Beer-Lambert law is made by allowing the reference spectra to be a set of known mixtures, The incorporation of nonzero intercepts in the relation between absorbance and concentration further improves the approximation of nonlinearities while simultaneously accounting for nonzero spectra baselines. Pathlength variations are also accommodated in the analysis, and under certain conditions, unknown sample pathlengths can be determined. All spectral data are used to improve the precision and accuracy of the estimated concentrations. During the calibration phase of the analysis, pure component spectra are estimated from the standard mixture spectra. These can be compared with the measured pure component spectra to determine which vibrations experience nonlinear behavior. In the predictive phase of the analysis, the calculated spectra are used in our previous least-squares analysis to estimate sample component concentrations. These methods were applied to the analysis of the IR spectra of binary mixtures of esters. Even with severely overlapping spectral bands and nonlinearities in the Beer-Lambert law, the average relative error in the estimated concentration was <1%
Research on the strong optical feedback effects based on spectral analysis method
Zeng, Zhaoli; Qu, XueMin; Li, Weina; Zhang, Min; Wang, Hao; Li, Tuo
2018-01-01
The strong optical feedback has the advantage of generating high resolution fringes. However, these feedback fringes usually seem like the noise signal when the feedback level is high. This defect severely limits its practical application. In this paper, the generation mechanism of noise fringes with strong optical feedback is studied by using spectral analysis method. The spectral analysis results show that, in most cases, the noise-like fringes are observed owing to the strong multiple high-order feedback. However, at certain feedback cavity condition, there may be only one high-order feedback beam goes back to the laser cavity, the noise-like fringes can change to the cosine-like fringes. And the resolution of this fringe is dozens times than that of the weak optical feedback. This research provides a method to obtain high resolution cosine-like fringes rather than noise signal in the strong optical feedback, which makes it possible to be used in nanoscale displacement measurements.
A spectral nudging method for the ACCESS1.3 atmospheric model
Directory of Open Access Journals (Sweden)
P. Uhe
2015-06-01
Full Text Available A convolution-based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow for flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10–30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.
Zou, Peng
2017-05-10
Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.
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
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
A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate
Energy Technology Data Exchange (ETDEWEB)
Djenidi, L.; Antonia, R.A. [The University of Newcastle, School of Engineering, Newcastle, NSW (Australia)
2012-10-15
We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate left angle {epsilon}right angle in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301-305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity {nu} and left angle {epsilon}right angle at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a -5/3 inertial subrange only when the Taylor microscale Reynolds number R{sub {lambda}} is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30 {<=} R{sub {lambda}}{<=} 400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of left angle {epsilon}right angle in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall. (orig.)
Frequency-dependant homogenized properties of composite using spectral analysis method
International Nuclear Information System (INIS)
Ben Amor, M; Ben Ghozlen, M H; Lanceleur, P
2010-01-01
An inverse procedure is proposed to determine the material constants of multilayered composites using a spectral analysis homogenization method. Recursive process gives interfacial displacement perpendicular to layers in term of deepness. A fast-Fourier transform (FFT) procedure has been used in order to extract the wave numbers propagating in the multilayer. The upper frequency bound of this homogenization domain is estimated. Inside the homogenization domain, we discover a maximum of three planes waves susceptible to propagate in the medium. A consistent algorithm is adopted to develop an inverse procedure for the determination of the materials constants of multidirectional composite. The extracted wave numbers are used as the inputs for the procedure. The outputs are the elastic constants of multidirectional composite. Using this method, the frequency dependent effective elastic constants are obtained and example for [0/90] composites is given.
Parallelizing the spectral transform method: A comparison of alternative parallel algorithms
International Nuclear Information System (INIS)
Foster, I.; Worley, P.H.
1993-01-01
The spectral transform method is a standard numerical technique for solving partial differential equations on the sphere and is widely used in global climate modeling. In this paper, we outline different approaches to parallelizing the method and describe experiments that we are conducting to evaluate the efficiency of these approaches on parallel computers. The experiments are conducted using a testbed code that solves the nonlinear shallow water equations on a sphere, but are designed to permit evaluation in the context of a global model. They allow us to evaluate the relative merits of the approaches as a function of problem size and number of processors. The results of this study are guiding ongoing work on PCCM2, a parallel implementation of the Community Climate Model developed at the National Center for Atmospheric Research
Application of spectral Lanczos decomposition method to large scale problems arising geophysics
Energy Technology Data Exchange (ETDEWEB)
Tamarchenko, T. [Western Atlas Logging Services, Houston, TX (United States)
1996-12-31
This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.
Membership determination of open clusters based on a spectral clustering method
Gao, Xin-Hua
2018-06-01
We present a spectral clustering (SC) method aimed at segregating reliable members of open clusters in multi-dimensional space. The SC method is a non-parametric clustering technique that performs cluster division using eigenvectors of the similarity matrix; no prior knowledge of the clusters is required. This method is more flexible in dealing with multi-dimensional data compared to other methods of membership determination. We use this method to segregate the cluster members of five open clusters (Hyades, Coma Ber, Pleiades, Praesepe, and NGC 188) in five-dimensional space; fairly clean cluster members are obtained. We find that the SC method can capture a small number of cluster members (weak signal) from a large number of field stars (heavy noise). Based on these cluster members, we compute the mean proper motions and distances for the Hyades, Coma Ber, Pleiades, and Praesepe clusters, and our results are in general quite consistent with the results derived by other authors. The test results indicate that the SC method is highly suitable for segregating cluster members of open clusters based on high-precision multi-dimensional astrometric data such as Gaia data.
American Society for Testing and Materials. Philadelphia
2010-01-01
1.1 This test method covers a procedure for the determination of a spectral mismatch parameter used in performance testing of photovoltaic devices. 1.2 The spectral mismatch parameter is a measure of the error, introduced in the testing of a photovoltaic device, caused by mismatch between the spectral responses of the photovoltaic device and the photovoltaic reference cell, as well as mismatch between the test light source and the reference spectral irradiance distribution to which the photovoltaic reference cell was calibrated. Examples of reference spectral irradiance distributions are Tables E490 or G173. 1.3 The spectral mismatch parameter can be used to correct photovoltaic performance data for spectral mismatch error. 1.4 This test method is intended for use with linear photovoltaic devices. 1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. 1.6 This standard does not purport to address all of the safety concerns, if any, a...
MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions
Novosad, Philip; Reader, Andrew J.
2016-06-01
Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [18F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral
Chakraborty, Somsubhra; Das, Bhabani S; Ali, Md Nasim; Li, Bin; Sarathjith, M C; Majumdar, K; Ray, D P
2014-03-01
The aim of this study was to investigate the feasibility of using visible near-infrared (VisNIR) diffuse reflectance spectroscopy (DRS) as an easy, inexpensive, and rapid method to predict compost enzymatic activity, which traditionally measured by fluorescein diacetate hydrolysis (FDA-HR) assay. Compost samples representative of five different compost facilities were scanned by DRS, and the raw reflectance spectra were preprocessed using seven spectral transformations for predicting compost FDA-HR with six multivariate algorithms. Although principal component analysis for all spectral pretreatments satisfactorily identified the clusters by compost types, it could not separate different FDA contents. Furthermore, the artificial neural network multilayer perceptron (residual prediction deviation=3.2, validation r(2)=0.91 and RMSE=13.38 μg g(-1) h(-1)) outperformed other multivariate models to capture the highly non-linear relationships between compost enzymatic activity and VisNIR reflectance spectra after Savitzky-Golay first derivative pretreatment. This work demonstrates the efficiency of VisNIR DRS for predicting compost enzymatic as well as microbial activity. Copyright © 2013 Elsevier Ltd. All rights reserved.
Making of a solar spectral irradiance dataset I: observations, uncertainties, and methods
Directory of Open Access Journals (Sweden)
Schöll Micha
2016-01-01
Full Text Available Context. Changes in the spectral solar irradiance (SSI are a key driver of the variability of the Earth’s environment, strongly affecting the upper atmosphere, but also impacting climate. However, its measurements have been sparse and of different quality. The “First European Comprehensive Solar Irradiance Data Exploitation project” (SOLID aims at merging the complete set of European irradiance data, complemented by archive data that include data from non-European missions. Aims. As part of SOLID, we present all available space-based SSI measurements, reference spectra, and relevant proxies in a unified format with regular temporal re-gridding, interpolation, gap-filling as well as associated uncertainty estimations. Methods. We apply a coherent methodology to all available SSI datasets. Our pipeline approach consists of the pre-processing of the data, the interpolation of missing data by utilizing the spectral coherency of SSI, the temporal re-gridding of the data, an instrumental outlier detection routine, and a proxy-based interpolation for missing and flagged values. In particular, to detect instrumental outliers, we combine an autoregressive model with proxy data. We independently estimate the precision and stability of each individual dataset and flag all changes due to processing in an accompanying quality mask. Results. We present a unified database of solar activity records with accompanying meta-data and uncertainties. Conclusions. This dataset can be used for further investigations of the long-term trend of solar activity and the construction of a homogeneous SSI record.
Energy Technology Data Exchange (ETDEWEB)
Duckwitz, Hannah [Institut fuer Kernphysik, Koeln Univ. (Germany); Petkov, Pavel [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)
2016-07-01
In this new approach to lifetime measurements via Doppler attenuated line shapes, the spectra of a feeding f and a deexciting transition d of the level of interest are used to determine the lifetime without any lineshape analysis of the feeding transition (direct or indirect). Similarly to the DDC method, the decay function λ{sub d}n{sub d}(t) of the deexciting transition is determined. The feeding of the level is included via the spectral difference of the two successive decays. Consequently, the determined lifetime is the real lifetime. After transforming both transitions into the same energy region, their spectral difference D(v{sub θ}) = S{sub d}(v{sub θ})-S{sub f}(v{sub θ}) = ∫{sub 0}{sup ∞}(∂P{sub θ}(t,v{sub θ}))/(∂t)n{sub d}(t) dt, is solved for n{sub d}(t). Dividing n{sub d}(t) by the decay function λ{sub d}n{sub d}(t) should yield a constant τ value for the level lifetime as a function of the time t. After the development and test of the procedure in 2015, it is now applied for the first time. Two level lifetimes are determined in {sup 86}Sr for the 2{sup +}{sub 2} and the 2{sup +}{sub 3} levels.
Vanel, Florence O.; Baysal, Oktay
1995-01-01
Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.
Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method
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.
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-06
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-01
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
A numerical study of viscous vortex rings using a spectral method
Stanaway, S. K.; Cantwell, B. J.; Spalart, Philippe R.
1988-01-01
Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.
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...
Struts, A. V.; Barmasov, A. V.; Brown, M. F.
2016-02-01
This article continues our review of spectroscopic studies of G-protein-coupled receptors. Magnetic resonance methods including electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) provide specific structural and dynamical data for the protein in conjunction with optical methods (vibrational, electronic spectroscopy) as discussed in the accompanying article. An additional advantage is the opportunity to explore the receptor proteins in the natural membrane lipid environment. Solid-state 2H and 13C NMR methods yield information about both the local structure and dynamics of the cofactor bound to the protein and its light-induced changes. Complementary site-directed spin-labeling studies monitor the structural alterations over larger distances and correspondingly longer time scales. A multiscale reaction mechanism describes how local changes of the retinal cofactor unlock the receptor to initiate large-scale conformational changes of rhodopsin. Activation of the G-protein-coupled receptor involves an ensemble of conformational substates within the rhodopsin manifold that characterize the dynamically active receptor.
International Nuclear Information System (INIS)
Arvieu, R.
The assumptions and principles of the spectral distribution method are reviewed. The object of the method is to deduce information on the nuclear spectra by constructing a frequency function which has the same first few moments, as the exact frequency function, these moments being then exactly calculated. The method is applied to subspaces containing a large number of quasi particles [fr
International Nuclear Information System (INIS)
Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.
2015-01-01
Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks
A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems
Liu, X.; Banerjee, J. R.
2017-03-01
A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.
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....
Using spectral element method to solve variational inequalities with applications in finance
International Nuclear Information System (INIS)
Moradipour, M.; Yousefi, S.A.
2015-01-01
Under the Black–Scholes model, the value of an American option solves a time dependent variational inequality problem (VIP). In this paper, first we discretize the variational inequality of American option in temporal direction by applying the Rannacher time stepping and achieve a sequence of elliptic variational inequalities. Second we discretize the spatial domain of variational inequalities by using spectral element methods with high order Lagrangian polynomials introduced on Gauss–Legendre–Lobatto points. Also by computing integrals by the Gauss–Legendre–Lobatto quadrature rule we derive a sequence of the linear complementarity problems (LCPs) having a positive definite sparse coefficient matrix. To find the unique solutions of the LCPs, we use the projected successive over-relaxation (PSOR) algorithm. Furthermore we present some existence and uniqueness theorems for the variational inequalities and LCPs. Finally, theoretical results are verified on the relevant numerical examples.
Statistical learning method in regression analysis of simulated positron spectral data
International Nuclear Information System (INIS)
Avdic, S. Dz.
2005-01-01
Positron lifetime spectroscopy is a non-destructive tool for detection of radiation induced defects in nuclear reactor materials. This work concerns the applicability of the support vector machines method for the input data compression in the neural network analysis of positron lifetime spectra. It has been demonstrated that the SVM technique can be successfully applied to regression analysis of positron spectra. A substantial data compression of about 50 % and 8 % of the whole training set with two and three spectral components respectively has been achieved including a high accuracy of the spectra approximation. However, some parameters in the SVM approach such as the insensitivity zone e and the penalty parameter C have to be chosen carefully to obtain a good performance. (author)
Energy Technology Data Exchange (ETDEWEB)
Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
International Nuclear Information System (INIS)
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-01-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
3D airborne EM modeling based on the spectral-element time-domain (SETD) method
Cao, X.; Yin, C.; Huang, X.; Liu, Y.; Zhang, B., Sr.; Cai, J.; Liu, L.
2017-12-01
In the field of 3D airborne electromagnetic (AEM) modeling, both finite-difference time-domain (FDTD) method and finite-element time-domain (FETD) method have limitations that FDTD method depends too much on the grids and time steps, while FETD requires large number of grids for complex structures. We propose a time-domain spectral-element (SETD) method based on GLL interpolation basis functions for spatial discretization and Backward Euler (BE) technique for time discretization. The spectral-element method is based on a weighted residual technique with polynomials as vector basis functions. It can contribute to an accurate result by increasing the order of polynomials and suppressing spurious solution. BE method is a stable tine discretization technique that has no limitation on time steps and can guarantee a higher accuracy during the iteration process. To minimize the non-zero number of sparse matrix and obtain a diagonal mass matrix, we apply the reduced order integral technique. A direct solver with its speed independent of the condition number is adopted for quickly solving the large-scale sparse linear equations system. To check the accuracy of our SETD algorithm, we compare our results with semi-analytical solutions for a three-layered earth model within the time lapse 10-6-10-2s for different physical meshes and SE orders. The results show that the relative errors for magnetic field B and magnetic induction are both around 3-5%. Further we calculate AEM responses for an AEM system over a 3D earth model in Figure 1. From numerical experiments for both 1D and 3D model, we draw the conclusions that: 1) SETD can deliver an accurate results for both dB/dt and B; 2) increasing SE order improves the modeling accuracy for early to middle time channels when the EM field diffuses fast so the high-order SE can model the detailed variation; 3) at very late time channels, increasing SE order has little improvement on modeling accuracy, but the time interval plays
Energy Technology Data Exchange (ETDEWEB)
Keating, Kristina [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Slater, Lee [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Ntarlagiannis, Dimitris [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Williams, Kenneth H. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Earth Sciences Division
2015-02-24
This documents contains the final report for the project "Integrated Geophysical Measurements for Bioremediation Monitoring: Combining Spectral Induced Polarization, Nuclear Magnetic Resonance and Magnetic Methods" (DE-SC0007049) Executive Summary: Our research aimed to develop borehole measurement techniques capable of monitoring subsurface processes, such as changes in pore geometry and iron/sulfur geochemistry, associated with remediation of heavy metals and radionuclides. Previous work has demonstrated that geophysical method spectral induced polarization (SIP) can be used to assess subsurface contaminant remediation; however, SIP signals can be generated from multiple sources limiting their interpretation value. Integrating multiple geophysical methods, such as nuclear magnetic resonance (NMR) and magnetic susceptibility (MS), with SIP, could reduce the ambiguity of interpretation that might result from a single method. Our research efforts entails combining measurements from these methods, each sensitive to different mineral forms and/or mineral-fluid interfaces, providing better constraints on changes in subsurface biogeochemical processes and pore geometries significantly improving our understanding of processes impacting contaminant remediation. The Rifle Integrated Field Research Challenge (IFRC) site was used as a test location for our measurements. The Rifle IFRC site is located at a former uranium ore-processing facility in Rifle, Colorado. Leachate from spent mill tailings has resulted in residual uranium contamination of both groundwater and sediments within the local aquifer. Studies at the site include an ongoing acetate amendment strategy, native microbial populations are stimulated by introduction of carbon intended to alter redox conditions and immobilize uranium. To test the geophysical methods in the field, NMR and MS logging measurements were collected before, during, and after acetate amendment. Next, laboratory NMR, MS, and SIP measurements
Examining Second Language Receptive Knowledge of Collocation and Factors That Affect Learning
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…
Substructure identification for shear structures: cross-power spectral density method
International Nuclear Information System (INIS)
Zhang, Dongyu; Johnson, Erik A
2012-01-01
In this paper, a substructure identification method for shear structures is proposed. A shear structure is divided into many small substructures; utilizing the dynamic equilibrium of a one-floor substructure, an inductive identification problem is formulated, using the cross-power spectral densities between structural floor accelerations and a reference response, to estimate the parameters of that one story. Repeating this procedure, all story parameters of the shear structure are identified from top to bottom recursively. An identification error analysis is performed for the proposed substructure method, revealing how uncertain factors (e.g. measurement noise) in the identification process affect the identification accuracy. According to the error analysis, a smart reference selection rule is designed to choose the optimal reference response that further enhances the identification accuracy. Moreover, based on the identification error analysis, explicit formulae are developed to calculate the variances of the parameter identification errors. A ten-story shear structure is used to illustrate the effectiveness of the proposed substructure method. The simulation results show that the method, combined with the reference selection rule, can very accurately identify structural parameters despite large measurement noise. Furthermore, the proposed formulae provide good predictions for the variances of the parameter identification errors, which are vital for providing accurate warnings of structural damage. (paper)
A new physics-based method for detecting weak nuclear signals via spectral decomposition
International Nuclear Information System (INIS)
Chan, Kung-Sik; Li, Jinzheng; Eichinger, William; Bai, Erwei
2012-01-01
We propose a new physics-based method to determine the presence of the spectral signature of one or more nuclides from a poorly resolved spectra with weak signatures. The method is different from traditional methods that rely primarily on peak finding algorithms. The new approach considers each of the signatures in the library to be a linear combination of subspectra. These subspectra are obtained by assuming a signature consisting of just one of the unique gamma rays emitted by the nuclei. We propose a Poisson regression model for deducing which nuclei are present in the observed spectrum. In recognition that a radiation source generally comprises few nuclear materials, the underlying Poisson model is sparse, i.e. most of the regression coefficients are zero (positive coefficients correspond to the presence of nuclear materials). We develop an iterative algorithm for a penalized likelihood estimation that prompts sparsity. We illustrate the efficacy of the proposed method by simulations using a variety of poorly resolved, low signal-to-noise ratio (SNR) situations, which show that the proposed approach enjoys excellent empirical performance even with SNR as low as to -15 db.
International Nuclear Information System (INIS)
Gu Yi; Xiong Shengqing; Zhou Jianxin; Fan Zhengguo; Ge Liangquan
2014-01-01
γ-ray released by the radon daughter has severe impact on airborne γ-ray spectrometry. The spectral-ratio method is one of the best mathematical methods for radon background deduction in airborne γ-ray spectrometry. In this paper, an advanced spectral-ratio method was proposed which deducts Compton scattering ray by the fast Fourier transform rather than tripping ratios, the relationship between survey height and correction coefficient of the advanced spectral-ratio radon background correction method was studied, the advanced spectral-ratio radon background correction mathematic model was established, and the ground saturation model calibrating technology for correction coefficient was proposed. As for the advanced spectral-ratio radon background correction method, its applicability and correction efficiency are improved, and the application cost is saved. Furthermore, it can prevent the physical meaning lost and avoid the possible errors caused by matrix computation and mathematical fitting based on spectrum shape which is applied in traditional correction coefficient. (authors)
Multimodal interaction design in collocated mobile phone use
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
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
Spectral map-analysis: a method to analyze gene expression data
Bijnens, Luc J.M.; Lewi, Paul J.; Göhlmann, Hinrich W.; Molenberghs, Geert; Wouters, Luc
2004-01-01
bioinformatics; biplot; correspondence factor analysis; data mining; data visualization; gene expression data; microarray data; multivariate exploratory data analysis; principal component analysis; Spectral map analysis
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
A spectral/B-spline method for the Navier-Stokes equations in unbounded domains
International Nuclear Information System (INIS)
Dufresne, L.; Dumas, G.
2003-01-01
The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r→∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions
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Omar Eldwaik
2018-01-01
Full Text Available Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.
Gilli, L.
2013-01-01
This thesis presents the development and the implementation of an uncertainty propagation algorithm based on the concept of spectral expansion. The first part of the thesis is dedicated to the study of uncertainty propagation methodologies and to the analysis of spectral techniques. The concepts
Czech Academy of Sciences Publication Activity Database
Vojtíšek, Petr; Květoň, M.; Richter, I.
2016-01-01
Roč. 11, February (2016), č. článku 16009. ISSN 1990-2573 R&D Projects: GA MŠk(CZ) LO1206 Institutional support: RVO:61389021 Keywords : Photopolymers * diffraction gratings * angular-spectral maps * spectral selectivity * angular selectivity Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.975, year: 2016
Data preprocessing methods of FT-NIR spectral data for the classification cooking oil
Ruah, Mas Ezatul Nadia Mohd; Rasaruddin, Nor Fazila; Fong, Sim Siong; Jaafar, Mohd Zuli
2014-12-01
This recent work describes the data pre-processing method of FT-NIR spectroscopy datasets of cooking oil and its quality parameters with chemometrics method. Pre-processing of near-infrared (NIR) spectral data has become an integral part of chemometrics modelling. Hence, this work is dedicated to investigate the utility and effectiveness of pre-processing algorithms namely row scaling, column scaling and single scaling process with Standard Normal Variate (SNV). The combinations of these scaling methods have impact on exploratory analysis and classification via Principle Component Analysis plot (PCA). The samples were divided into palm oil and non-palm cooking oil. The classification model was build using FT-NIR cooking oil spectra datasets in absorbance mode at the range of 4000cm-1-14000cm-1. Savitzky Golay derivative was applied before developing the classification model. Then, the data was separated into two sets which were training set and test set by using Duplex method. The number of each class was kept equal to 2/3 of the class that has the minimum number of sample. Then, the sample was employed t-statistic as variable selection method in order to select which variable is significant towards the classification models. The evaluation of data pre-processing were looking at value of modified silhouette width (mSW), PCA and also Percentage Correctly Classified (%CC). The results show that different data processing strategies resulting to substantial amount of model performances quality. The effects of several data pre-processing i.e. row scaling, column standardisation and single scaling process with Standard Normal Variate indicated by mSW and %CC. At two PCs model, all five classifier gave high %CC except Quadratic Distance Analysis.
Parsani, Matteo
2011-09-01
The main goal of this paper is to develop an efficient numerical algorithm to compute the radiated far field noise provided by an unsteady flow field from bodies in arbitrary motion. The method computes a turbulent flow field in the near fields using a high-order spectral difference method coupled with large-eddy simulation approach. The unsteady equations are solved by advancing in time using a second-order backward difference formulae scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lowerupper symmetric GaussSeidel algorithm. In the second step, the method calculates the far field sound pressure based on the acoustic source information provided by the first step simulation. The method is based on the Ffowcs WilliamsHawkings approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10 3 and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional turbulent flow in a muffler at Re = 4.665 × 10 4 and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately. © 2011 IMACS.
Kim, Cheolsun; Lee, Woong-Bi; Ju, Gun Wu; Cho, Jeonghoon; Kim, Seongmin; Oh, Jinkyung; Lim, Dongsung; Lee, Yong Tak; Lee, Heung-No
2017-02-01
In recent years, there has been an increasing interest in miniature spectrometers for research and development. Especially, filter-array-based spectrometers have advantages of low cost and portability, and can be applied in various fields such as biology, chemistry and food industry. Miniaturization in optical filters causes degradation of spectral resolution due to limitations on spectral responses and the number of filters. Nowadays, many studies have been reported that the filter-array-based spectrometers have achieved resolution improvements by using digital signal processing (DSP) techniques. The performance of the DSP-based spectral recovery highly depends on the prior information of transmission functions (TFs) of the filters. The TFs vary with respect to an incident angle of light onto the filter-array. Conventionally, it is assumed that the incident angle of light on the filters is fixed and the TFs are known to the DSP. However, the incident angle is inconstant according to various environments and applications, and thus TFs also vary, which leads to performance degradation of spectral recovery. In this paper, we propose a method of incident angle estimation (IAE) for high resolution spectral recovery in the filter-array-based spectrometers. By exploiting sparse signal reconstruction of the L1- norm minimization, IAE estimates an incident angle among all possible incident angles which minimizes the error of the reconstructed signal. Based on IAE, DSP effectively provides a high resolution spectral recovery in the filter-array-based spectrometers.
A spectral/B-spline method for the Navier-Stokes equations in unbounded domains
Dufresne, L
2003-01-01
The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...
The Sternheimer-GW method and the spectral signatures of plasmonic polarons
Giustino, Feliciano
During the past three decades the GW method has emerged among the most promising electronic structure techniques for predictive calculations of quasiparticle band structures. In order to simplify the GW work-flow while at the same time improving the calculation accuracy, we developed the Sternheimer-GW method. In Sternheimer-GW both the screened Coulomb interaction and the electron Green's function are evaluated by using exclusively occupied Kohn-Sham states, as in density-functional perturbation theory. In this talk I will review the basics of Sternheimer-GW, and I will discuss two recent applications to semiconductors and superconductors. In the case of semiconductors we calculated complete energy- and momentum-resolved spectral functions by combining Sternheimer-GW with the cumulant expansion approach. This study revealed the existence of band structure replicas which arise from electron-plasmon interactions. In the case of superconductors we calculated the Coulomb pseudo-potential from first principles, and combined this approach with the Eliashberg theory of the superconducting critical temperature. This work was supported by the Leverhulme Trust (RL-2012-001), the European Research Council (EU FP7/ERC 239578), the UK Engineering and Physical Sciences Research Council (EP/J009857/1), and the Graphene Flagship (EU FP7/604391).
Directory of Open Access Journals (Sweden)
Tarasenko Alexandr
2016-01-01
Full Text Available The paper is aimed at determining the possibility of applying the simplified method proposed by the authors to calculate the tank seismic resistance in compliance with current regulations and scientific provisions. The authors propose a highly detailed numerical model for a common oil storage tank RVSPK-50000 that enables static operational loads and dynamic action of earthquakes to be calculated. Within the modal analysis the natural oscillation frequencies in the range of 0-10 Hz were calculated; the results are given for the first ten modes. The model takes into account the effect of impulsive and convective components of hydrodynamic pressure during earthquakes. Within the spectral analysis by generalized response spectra was calculated a general stress-strain state of a structure during earthquakes of 7, 8, 9 intensity degrees on the MSK-64 scale for a completely filled up, a half-filled up to the mark of 8.5 m and an empty RVSPK-50000 tank. The developed finite element model can be used to perform calculations of seismic resistance by the direct dynamic method, which will give further consideration to the impact of individual structures (floating roof, support posts, adjoined elements of added stiffness on the general stress-strain state of a tank.
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.
A Wavelet-Modified ESPRIT Hybrid Method for Assessment of Spectral Components from 0 to 150 kHz
Directory of Open Access Journals (Sweden)
Luisa Alfieri
2017-01-01
Full Text Available Waveform distortions are an important issue in distribution systems. In particular, the assessment of very wide spectra, that include also components in the 2–150 kHz range, has recently become an issue of great interest. This is due to the increasing presence of high-spectral emission devices like end-user devices and distributed generation systems. This study proposed a new sliding-window wavelet-modified estimation of signal parameters by rotational invariance technique (ESPRIT method, particularly suitable for the spectral analysis of waveforms that have very wide spectra. The method is very accurate and requires reduced computational effort. It can be applied successfully to detect spectral components in the range of 0–150 kHz introduced both by distributed power plants, such as wind and photovoltaic generation systems, and by end-user equipment connected to grids through static converters, such as fluorescent lamps.
Rosado-Mendez, Ivan M; Nam, Kibo; Hall, Timothy J; Zagzebski, James A
2013-07-01
Reported here is a phantom-based comparison of methods for determining the power spectral density (PSD) of ultrasound backscattered signals. Those power spectral density values are then used to estimate parameters describing α(f), the frequency dependence of the acoustic attenuation coefficient. Phantoms were scanned with a clinical system equipped with a research interface to obtain radiofrequency echo data. Attenuation, modeled as a power law α(f)= α0 f (β), was estimated using a reference phantom method. The power spectral density was estimated using the short-time Fourier transform (STFT), Welch's periodogram, and Thomson's multitaper technique, and performance was analyzed when limiting the size of the parameter-estimation region. Errors were quantified by the bias and standard deviation of the α0 and β estimates, and by the overall power-law fit error (FE). For parameter estimation regions larger than ~34 pulse lengths (~1 cm for this experiment), an overall power-law FE of 4% was achieved with all spectral estimation methods. With smaller parameter estimation regions as in parametric image formation, the bias and standard deviation of the α0 and β estimates depended on the size of the parameter estimation region. Here, the multitaper method reduced the standard deviation of the α0 and β estimates compared with those using the other techniques. The results provide guidance for choosing methods for estimating the power spectral density in quantitative ultrasound methods.
Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification
Winokur, J.
2015-12-19
We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.
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.
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
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Analysis of China's real estate prices and macroeconomy based on evolutionary co-spectral method
Directory of Open Access Journals (Sweden)
Juan Li
2015-04-01
Full Text Available Purpose: This paper investigates the dynamic interaction between the real estate market and the macroeconomic environment of China by use of dynamic coherence function based on co-spectral analysis. Design/methodology/approach: Through a theoretical perspective, the dynamic interrelationship among economic variables at different time intervals (both long and short terms is analyzed. Findings: The empirical results show that China’s real estate market features a high coherence with the change of the long-term interest rate, employment rate and money supply, while there is a moderate coherence between the real estate market and the inflation rate and economic growth rate, and the coherence between the short-term rate of interest and the real estate market is the lowest. Research implications: Previous researches have some shortcomings. They do not consider the dependence between nonlinear series, but the latter is crucial to avoid the deviation of results. In this paper, we proposed a new method of experience to overcome these shortcomings. Originality/value: The paper provides a reasonable explanation accordingly to different coherences between the real estate market and the macroeconomic variables.
Quasiparticle self-consistent GW method for the spectral properties of complex materials.
Bruneval, Fabien; Gatti, Matteo
2014-01-01
The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.
A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method
Energy Technology Data Exchange (ETDEWEB)
Hsu, Li-Chieh; Chen, Chien-Lin; Ye, Jian-Zhi [National Yunlin University of Science and Technology, Taiwan (China)
2017-06-15
This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.
International Nuclear Information System (INIS)
Kwak, Sung-Woo; Yoo, Ho-Sik; Jang, Sung Soon; Kim, Jung-Soo; Yoon, Wan-Ki
2008-01-01
In these days, the threats relating to nuclear or radioactive materials have become a matter of internationally increased grave concern. A plastic scintillation detector in radiation portal monitoring (RPM) application has been used to detect radioactive sources in steel scrap entering reprocessing facilities, and to detect illicit transport of radioactive material across border ports-of-entry. The detection systems for RPM application usually are large and can not easily be moved to a different location. For some situations, an inconspicuous and mobile system for the radioactive or nuclear material during road transport is needed. The mobile radiation detection system has employed a NaI- based radiation detector to detect and identify the material hidden in vehicle. There are some operational constraints - short measuring time, weak activity due to heavy shield of illegal source, long distance - of inspection system in such nuclear security applications. Due to these constraints, large area sensor is required to maximize its sensitivity. Large NaI material, however, is extremely expensive. In designing a radiation detector for prevention of illicit trafficking of nuclear or radioactive materials, the trade-off should be carefully optimized between performance and cost in order to achieve cost-effective inspection system. For the cost-effective mobile radiation detection system, this paper describes new spectral analysis method to use the crude spectroscopic information available from a plastic detector to discriminate other man-made radiation source from NORM
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
Veronese, Mattia; Rizzo, Gaia; Bertoldo, Alessandra; Turkheimer, Federico E
2016-01-01
In Positron Emission Tomography (PET), spectral analysis (SA) allows the quantification of dynamic data by relating the radioactivity measured by the scanner in time to the underlying physiological processes of the system under investigation. Among the different approaches for the quantification of PET data, SA is based on the linear solution of the Laplace transform inversion whereas the measured arterial and tissue time-activity curves of a radiotracer are used to calculate the input response function of the tissue. In the recent years SA has been used with a large number of PET tracers in brain and nonbrain applications, demonstrating that it is a very flexible and robust method for PET data analysis. Differently from the most common PET quantification approaches that adopt standard nonlinear estimation of compartmental models or some linear simplifications, SA can be applied without defining any specific model configuration and has demonstrated very good sensitivity to the underlying kinetics. This characteristic makes it useful as an investigative tool especially for the analysis of novel PET tracers. The purpose of this work is to offer an overview of SA, to discuss advantages and limitations of the methodology, and to inform about its applications in the PET field.
Chacó n Rebollo, Tomá s; Dia, Ben Mansour
2015-01-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Chacón Rebollo, Tomás
2015-03-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Seismoelectric Effects based on Spectral-Element Method for Subsurface Fluid Characterization
Morency, C.
2017-12-01
Present approaches for subsurface imaging rely predominantly on seismic techniques, which alone do not capture fluid properties and related mechanisms. On the other hand, electromagnetic (EM) measurements add constraints on the fluid phase through electrical conductivity and permeability, but EM signals alone do not offer information of the solid structural properties. In the recent years, there have been many efforts to combine both seismic and EM data for exploration geophysics. The most popular approach is based on joint inversion of seismic and EM data, as decoupled phenomena, missing out the coupled nature of seismic and EM phenomena such as seismoeletric effects. Seismoelectric effects are related to pore fluid movements with respect to the solid grains. By analyzing coupled poroelastic seismic and EM signals, one can capture a pore scale behavior and access both structural and fluid properties.Here, we model the seismoelectric response by solving the governing equations derived by Pride and Garambois (1994), which correspond to Biot's poroelastic wave equations and Maxwell's electromagnetic wave equations coupled electrokinetically. We will show that these coupled wave equations can be numerically implemented by taking advantage of viscoelastic-electromagnetic mathematical equivalences. These equations will be solved using a spectral-element method (SEM). The SEM, in contrast to finite-element methods (FEM) uses high degree Lagrange polynomials. Not only does this allow the technique to handle complex geometries similarly to FEM, but it also retains exponential convergence and accuracy due to the use of high degree polynomials. Finally, we will discuss how this is a first step toward full coupled seismic-EM inversion to improve subsurface fluid characterization. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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
Teaching vocabulary using collocations versus using definitions in EFL classes
Altınok, Şerife İper
2000-01-01
Ankara : Institute of Economics and Social Sciences of Bilkent Univ., 2000. Thesis (Master's) -- Bilkent University, 2000. Includes bibliographical references leaves 40-43 Teaching words in collocations is a comparatively new technique and it is accepted as an effective one in vocabulary teaching. The purpose of this study was to find out whether teaching vocabulary would result in better learning and remembering vocabulary items. This study investigated the differences betw...
Ma, Xiaoke; Wang, Bingbo; Yu, Liang
2018-01-01
Community detection is fundamental for revealing the structure-functionality relationship in complex networks, which involves two issues-the quantitative function for community as well as algorithms to discover communities. Despite significant research on either of them, few attempt has been made to establish the connection between the two issues. To attack this problem, a generalized quantification function is proposed for community in weighted networks, which provides a framework that unifies several well-known measures. Then, we prove that the trace optimization of the proposed measure is equivalent with the objective functions of algorithms such as nonnegative matrix factorization, kernel K-means as well as spectral clustering. It serves as the theoretical foundation for designing algorithms for community detection. On the second issue, a semi-supervised spectral clustering algorithm is developed by exploring the equivalence relation via combining the nonnegative matrix factorization and spectral clustering. Different from the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the spectral algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method improves the accuracy of the traditional spectral algorithms in community detection.
International Nuclear Information System (INIS)
Beyer, Florian; Daszuta, Boris; Frauendiener, Jörg; Whale, Ben
2014-01-01
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through the use of integer spin-weighted spherical harmonics, we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2 + 1 Maxwell equations on a deformed sphere. (paper)
A general spectral method for the numerical simulation of one-dimensional interacting fermions
Clason, Christian; von Winckel, Gregory
2012-08-01
This software implements a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient Matlab program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. The new version includes a Python implementation of the presented approach. New version program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 332 No. of bytes in distributed program, including test data, etc.: 5418 Distribution format: tar.gz Programming language: MATLAB/GNU Octave, Python Computer: Any architecture supported by MATLAB, GNU Octave or Python Operating system: Any supported by MATLAB, GNU Octave or Python RAM: Depends on the data Classification: 4.3, 2.2. External routines: Python 2.7+, NumPy 1.3+, SciPy 0.10+ Catalogue identifier of previous version: AEKO_v1_0 Journal reference of previous version: Comput. Phys. Commun. 183 (2012) 405 Does the new version supersede the previous version?: Yes Nature of problem: The direct numerical
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
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.
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
Babu, N Ramesh; Subashchandrabose, S; Ali Padusha, M Syed; Saleem, H; Erdoğdu, Y
2014-01-01
The Spectral Characterization of (E)-1-(Furan-2-yl) methylene)-2-(1-phenylvinyl) hydrazine (FMPVH) were carried out by using FT-IR, FT-Raman and UV-Vis., Spectrometry. The B3LYP/6-311++G(d,p) level of optimization has been performed on the title compound. The conformational analysis was performed for this molecule, in which the cis and trans conformers were studied for spectral characterization. The recorded spectral results were compared with calculated results. The optimized bond parameters of FMPVH molecule was compared with X-ray diffraction data of related molecule. To study the intra-molecular charge transfers within the molecule the Lewis (bonding) and Non-Lewis (anti-bonding) structural calculation was performed. The Non-linear optical behavior of the title compound was measured using first order hyperpolarizability calculation. The atomic charges were calculated and analyzed. Copyright © 2013 Elsevier B.V. All rights reserved.
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 new method of organizing spectral line intensity ratio fluctuations of nightglow emissions
International Nuclear Information System (INIS)
Thelin, B.
1986-02-01
In this paper a new kind of linearization effect between the atmospheric night airglow emissions is presented. The same kind of linearization effect has previously been studied with spectrochemical light sources together with a spectrometer. A linear graph was obtained for atomic spectral lines and vibrational bandspectra when the spectral line intensity ratio fluctuations were plotted versus the photon energies of these emissions. To study this effect data from a number of different photometer investigations of night airglow emissions at different times and places have been used. (author)
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...
Atkinson, Dean B.; Pekour, Mikhail; Chand, Duli; Radney, James G.; Kolesar, Katheryn R.; Zhang, Qi; Setyan, Ari; O'Neill, Norman T.; Cappa, Christopher D.
2018-04-01
Multi-wavelength in situ aerosol extinction, absorption and scattering measurements made at two ground sites during the 2010 Carbonaceous Aerosols and Radiative Effects Study (CARES) are analyzed using a spectral deconvolution method that allows extraction of particle-size-related information, including the fraction of extinction produced by the fine-mode particles and the effective radius of the fine mode. The spectral deconvolution method is typically applied to analysis of remote sensing measurements. Here, its application to in situ measurements allows for comparison with more direct measurement methods and validation of the retrieval approach. Overall, the retrieved fine-mode fraction and effective radius compare well with other in situ measurements, including size distribution measurements and scattering and absorption measurements made separately for PM1 and PM10, although there were some periods during which the different methods yielded different results. One key contributor to differences between the results obtained is the alternative, spectrally based definitions of fine and coarse modes from the optical methods, relative to instruments that use a physically defined cut point. These results indicate that for campaigns where size, composition and multi-wavelength optical property measurements are made, comparison of the results can result in closure or can identify unusual circumstances. The comparison here also demonstrates that in situ multi-wavelength optical property measurements can be used to determine information about particle size distributions in situations where direct size distribution measurements are not available.
Directory of Open Access Journals (Sweden)
D. B. Atkinson
2018-04-01
Full Text Available Multi-wavelength in situ aerosol extinction, absorption and scattering measurements made at two ground sites during the 2010 Carbonaceous Aerosols and Radiative Effects Study (CARES are analyzed using a spectral deconvolution method that allows extraction of particle-size-related information, including the fraction of extinction produced by the fine-mode particles and the effective radius of the fine mode. The spectral deconvolution method is typically applied to analysis of remote sensing measurements. Here, its application to in situ measurements allows for comparison with more direct measurement methods and validation of the retrieval approach. Overall, the retrieved fine-mode fraction and effective radius compare well with other in situ measurements, including size distribution measurements and scattering and absorption measurements made separately for PM1 and PM10, although there were some periods during which the different methods yielded different results. One key contributor to differences between the results obtained is the alternative, spectrally based definitions of fine and coarse modes from the optical methods, relative to instruments that use a physically defined cut point. These results indicate that for campaigns where size, composition and multi-wavelength optical property measurements are made, comparison of the results can result in closure or can identify unusual circumstances. The comparison here also demonstrates that in situ multi-wavelength optical property measurements can be used to determine information about particle size distributions in situations where direct size distribution measurements are not available.
Xie, Xiaoliang Sunney; Freudiger, Christian; Min, Wei
2016-03-15
A microscopy imaging system is disclosed that includes a light source system, a spectral shaper, a modulator system, an optics system, an optical detector and a processor. The light source system is for providing a first train of pulses and a second train of pulses. The spectral shaper is for spectrally modifying an optical property of at least some frequency components of the broadband range of frequency components such that the broadband range of frequency components is shaped producing a shaped first train of pulses to specifically probe a spectral feature of interest from a sample, and to reduce information from features that are not of interest from the sample. The modulator system is for modulating a property of at least one of the shaped first train of pulses and the second train of pulses at a modulation frequency. The optical detector is for detecting an integrated intensity of substantially all optical frequency components of a train of pulses of interest transmitted or reflected through the common focal volume. The processor is for detecting a modulation at the modulation frequency of the integrated intensity of substantially all of the optical frequency components of the train of pulses of interest due to the non-linear interaction of the shaped first train of pulses with the second train of pulses as modulated in the common focal volume, and for providing an output signal for a pixel of an image for the microscopy imaging system.
Tailoring Spectral Properties of Binary PT-Symmetric Gratings by Duty-Cycle Methods
DEFF Research Database (Denmark)
Lupu, Anatole T.; Benisty, Henri; Lavrinenko, Andrei
2016-01-01
We explore the frequency selective functionalities of a nonuniform PT-symmetric Bragg grating with modulated complex index profile. We start by assessing the possibility to achieve an efficient apodization of the PT-symmetric Bragg grating spectral response by using direct adaptations of the conv...
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.
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...
Taneja, Ankur; Higdon, Jonathan
2018-01-01
A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.
Karaoǧlu, Haydar; Romanowicz, Barbara
2018-06-01
We present a global upper-mantle shear wave attenuation model that is built through a hybrid full-waveform inversion algorithm applied to long-period waveforms, using the spectral element method for wavefield computations. Our inversion strategy is based on an iterative approach that involves the inversion for successive updates in the attenuation parameter (δ Q^{-1}_μ) and elastic parameters (isotropic velocity VS, and radial anisotropy parameter ξ) through a Gauss-Newton-type optimization scheme that employs envelope- and waveform-type misfit functionals for the two steps, respectively. We also include source and receiver terms in the inversion steps for attenuation structure. We conducted a total of eight iterations (six for attenuation and two for elastic structure), and one inversion for updates to source parameters. The starting model included the elastic part of the relatively high-resolution 3-D whole mantle seismic velocity model, SEMUCB-WM1, which served to account for elastic focusing effects. The data set is a subset of the three-component surface waveform data set, filtered between 400 and 60 s, that contributed to the construction of the whole-mantle tomographic model SEMUCB-WM1. We applied strict selection criteria to this data set for the attenuation iteration steps, and investigated the effect of attenuation crustal structure on the retrieved mantle attenuation structure. While a constant 1-D Qμ model with a constant value of 165 throughout the upper mantle was used as starting model for attenuation inversion, we were able to recover, in depth extent and strength, the high-attenuation zone present in the depth range 80-200 km. The final 3-D model, SEMUCB-UMQ, shows strong correlation with tectonic features down to 200-250 km depth, with low attenuation beneath the cratons, stable parts of continents and regions of old oceanic crust, and high attenuation along mid-ocean ridges and backarcs. Below 250 km, we observe strong attenuation in the
Directory of Open Access Journals (Sweden)
Angga Yustiawan
2013-09-01
Full Text Available One of the components of the Indonesia Tsunami Early Warning System (InaTEWS is a surface buoy. The surface buoy is exposed to dynamic and random loadings while operating at sea, particularly due to waves. Because of the cyclic nature of the wave load, this may result in a fatigue damage of the keel structure, which connects the mooring line with the buoy hull. The operating location of the buoy is off the Java South Coast at the coordinate (10.3998 S, 108.3417 E. To determine the stress transfer function, model tests were performed, measuring the buoy motions and the stress at the mooring line. A spectral fatigue analysis method is applied for the purpose of estimating the fatigue life of the keel structure. Utilizing the model-test results, the S-N curve obtained in a previous study and the wave data at the buoy location, it is found that the fatigue life of the keel structure is approximately 11 years.
Directory of Open Access Journals (Sweden)
Smejkalová Eva
2017-03-01
Full Text Available The possibilities of remote sensing techniques in the field of the Earth surface monitoring and protection specifically for the problems caused by petroleum contaminations, for the mapping of insufficiently plugged and abandoned old oil wells and for the analysis of onshore oil seeps are described. Explained is the methodology for analyzing and detection of potential hydrocarbon contaminations using the Earth observation in the area of interest in Slovakia (Korňa and in Czech Republic (Nesyt, mainly building and calibrating the spectral library for oil seeps. The acquisition of the in-situ field data (ASD, Cropscan spectroradiometers for this purpose, the successful building and verification of hydrocarbon spectral library, the application of hydrocarbon indexes and use of shift in red-edge part of electromagnetic spectra, the spectral analysis of input data are clarified in the paper. Described is approach which could innovate the routine methods for investigating the occurrence of hydrocarbons and can assist during the mapping and locating the potential oil seep sites. Important outcome is the successful establishment of a spectral library (database with calibration data suitable for further application in data classification for identifying the occurrence of hydrocarbons.
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.
International Nuclear Information System (INIS)
Voronov, G. S.; Berezhetskii, M. S.; Bondar’, Yu. F.; Vafin, I. Yu.; Vasil’kov, D. G.; Voronova, E. V.; Grebenshchikov, S. E.; Grishina, I. A.; Larionova, N. F.; Letunov, A. A.; Logvinenko, V. P.; Meshcheryakov, A. I.; Pleshkov, E. I.; Khol’nov, Yu. V.; Fedyanin, O. I.; Tsygankov, V. A.; Shchepetov, S. V.; Kurnaev, V. A.; Vizgalov, I. V.; Urusov, V. A.
2013-01-01
Results are presented from L-2M stellarator experiments on testing a possible method for detection of water microleakages in the cooling system of the first wall and vacuum chamber of ITER. The method consists in the spectroscopic detection of spectral lines of the OH hydroxyl, which forms via the dissociation of water molecules in plasma. Emission in the spectral band of 305–310 nm can be detected even at water leakage rates less than 10 −4 Pa m 3 /s. Chemical reactions between water and boron compounds on the vacuum chamber wall delay the detection of leakages up to ∼2000 s. A similar phenomenon can be expected when a leakage will occur in ITER, where the materials suggested for the first wall (Be, Li) can also chemically react with water.
Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
International Nuclear Information System (INIS)
Gamba, Irene M.; Tharkabhushanam, Sri Harsha
2009-01-01
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S d-1 . The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ( )]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously
Huang, Xin; Yin, Chang-Chun; Cao, Xiao-Yue; Liu, Yun-He; Zhang, Bo; Cai, Jing
2017-09-01
The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell's equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic
International Nuclear Information System (INIS)
Qiao Haoxue; Cai Qingyu; Rao Jianguo; Li Baiwen
2002-01-01
A spectral fitting method for solving the time-dependent Schroedinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of Δt. Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields
A new method of organizing spectral line intensity ratio fluctuations of auroral emissions
International Nuclear Information System (INIS)
Thelin, B.
1986-02-01
In this paper a new kind of linearization effect between the atmospheric auroral emissions is presented. The same kind of linearization effect has previously been found in nightglow emissions from photometer measurements and in the spectrochemical field from studies of optical light sources. Linear graphs have been obtained for atomic spectral lines and vibrational bandspectra when the spectral line ratio fluctuations were plotted versus the photon energies of these emissions. This new effect has been studied with a spectrophotometer in auroral emissions, where linear graphs have been obtained on different auroral occasions. By doing such studies of auroral light it is possible to see the importance of the inelastic scattering cross section between electrons - atoms and electrons - molecules. In this way it has shown to be possible to determine the mean energy of the interacting thermal electrons that are active in the different auroral phases. (author)
Czech Academy of Sciences Publication Activity Database
Acuna, A.M.; Kaňa, Radek; Gwizdala, M.; Snellenburg, J.J.; van Alphen, P.; van Oort, B.; Kirilovsky, D.; van Grondelle, R.; van Stokkum, I.H.M.
2016-01-01
Roč. 130, 1-3 SI (2016), s. 237-249 ISSN 0166-8595 R&D Projects: GA ČR GBP501/12/G055; GA MŠk(CZ) LO1416; GA MŠk(CZ) ED2.1.00/19.0392 Institutional support: RVO:61388971 Keywords : Cyanobacteria * Spectrally resolved fluorometry * Singular value decomposition Subject RIV: EF - Botanics Impact factor: 3.864, year: 2016
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