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1

VIBRATION ANALYSIS OF PRE-TWISTED BEAMS USING THE SPLINE COLLOCATION METHOD

The variation in the accuracy of the calculated natural fre- quencies of pre-twisted beams solved with spline collocation method is investigated in this study. The spline collocation method is used to formulate the eigenvalue problems of pre-twisted beams. Three types of boundary conditions are considered. Numerical results indicate that the accuracy of the calculated natural frequencies is significantly dependent upon

Ming-Hung Hsu

2009-01-01

2

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Kojima, Fumio

1990-01-01

3

NASA Technical Reports Server (NTRS)

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

4

A fourth order spline collocation approach for a business cycle model

NASA Astrophysics Data System (ADS)

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.

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

2013-10-01

5

Optimization of dynamic systems using collocation methods

NASA Astrophysics Data System (ADS)

The time-based simulation is an important tool for the engineer. Often a time-domain simulation is the most expedient to construct, the most capable of handling complex modeling issues, or the most understandable with an engineer's physical intuition. Aeroelastic systems, for example, are often most easily solved with a nonlinear time-based approach to allow the use of high fidelity models. Simulations of automatic flight control systems can also be easier to model in the time domain, especially when nonlinearities are present. Collocation is an optimization method for systems that incorporate a time-domain simulation. Instead of integrating the equations of motion for each design iteration, the optimizer iteratively solves the simulation as it finds the optimal design. This forms a smooth, well-posed, sparse optimization problem, transforming the numerical integration's sequential calculation into a set of constraints that can be evaluated in any order, or even in parallel. The collocation method used in this thesis has been improved from existing techniques in several ways, in particular with a very simple and computationally inexpensive method of applying dynamic constraints, such as damping, that are more traditionally calculated with linear models in the frequency domain. This thesis applies the collocation method to a range of aircraft design problems, from minimizing the weight of a wing with a flutter constraint, to gain-scheduling the stability augmentation system of a small-scale flight control testbed, to aeroservoelastic design of a large aircraft concept. Collocation methods have not been applied to aeroelastic simulations in the past, although the combination of nonlinear aerodynamic analyses with structural dynamics and stability constraints is well-suited to collocation. The results prove the collocation method's worth as a tool for aircraft design, particularly when applied to the multidisciplinary numerical models used today.

Holden, Michael Eric

6

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

NASA Technical Reports Server (NTRS)

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.

Cai, Wei; Wang, Jian-Zhong

1993-01-01

7

B-spline Method in Fluid Dynamics

NASA Technical Reports Server (NTRS)

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)

2001-01-01

8

An enhanced splined saddle method.

We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)]. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C(60) fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time. PMID:21744889

Ghasemi, S Alireza; Goedecker, Stefan

2011-07-01

9

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

Johnson, Richard Wayne; Landon, Mark Dee

1999-07-01

10

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

M. D. Landon; R. W. Johnson

1999-07-01

11

COLLOCATION METHODS FOR DISTILLATION DESIGN III: FLEXIBLE COLUMN DESIGN

In this third paper on collocation methods for distillation design, we explore the use of the collocation models for design of simple distillation columns as well as flexible columns. Solvent recovery plants must deal with a wide range of feeds and still return pure solvents. The design problem we address is a single flexible column within the overall solvent recovery

Robert S. Huss; Arthur W. Westerberg

12

Aerodynamic influence coefficient method using singularity splines.

NASA Technical Reports Server (NTRS)

A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1973-01-01

13

Numerical Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System

In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing and error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions. PMID:24427270

Abbas, Muhammad; Majid, Ahmad Abd.; Md. Ismail, Ahmad Izani; Rashid, Abdur

2014-01-01

14

Sinc-collocation method for solving the Blasius equation

NASA Astrophysics Data System (ADS)

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.

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

2009-10-01

15

Aerodynamic influence coefficient method using singularity splines

NASA Technical Reports Server (NTRS)

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1974-01-01

16

Stochastic analysis of unsaturated flow with probabilistic collocation method

to study the effect of spatial variability on flow in unsaturated zone [Jury, 1982; Yeh et al., 1985a, 1985Stochastic analysis of unsaturated flow with probabilistic collocation method Weixuan Li,1 Zhiming; published 18 August 2009. [1] In this study, we present an efficient approach, called the probabilistic

Zhang, Dongxiao

17

The Chain Collocation Method: A Spectrally Accurate Calculus of Forms

Calculus (FEEC, [1, 3])) have all proposed discretizations that pre- serve vector calculus identitiesThe Chain Collocation Method: A Spectrally Accurate Calculus of Forms Dzhelil Rufat, Gemma Mason or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting

Desbrun, Mathieu

18

Collocation Methods for Optimization in a Modelica Environment Fredrik Magnussona Johan kessona,b

Collocation Methods for Optimization in a Modelica Environment Fredrik Magnussona Johan ?kessona, code using direct collocation methods is dis- cussed. We start by providing a description of dynamic optimization problems in general and how to solve them by means of direct collocation. Next, an existing

19

Spectral collocation methods for polymer brushes

NASA Astrophysics Data System (ADS)

We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at the grafting surface due to the chain end tethering constraint. We show that this pressure anomaly can be reduced by smearing the grafting points over a narrow zone normal to the surface in an incompressible model, and/or by switching to a compressible model for the molten brush. In both cases, we use results obtained from a source (delta function) distribution of grafting points as a reference. At the grafting surface, we consider both Neumann and Dirichlet conditions, where the latter is paired with a masking method to mimic a confining surface. When only the density profiles and relative free energies of two comparison phases are of interest, either source or smeared distributions of grafting points can be used, but a smeared distribution of grafting points exhibits faster convergence with respect to the number of chain contour steps. Absolute free energies converge only within the smeared model. In addition, when a sine basis is used with the masking method and a smeared distribution, fewer iterations are necessary to converge the SCFT fields for the compressible model. The numerical methods described here and investigated in one-dimension will provide an enabling platform for computationally more demanding three-dimensional SCFT studies of a broad range of mixed polymer brush systems.

Chantawansri, Tanya L.; Hur, Su-Mi; Garca-Cervera, Carlos J.; Ceniceros, Hector D.; Fredrickson, Glenn H.

2011-06-01

20

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

NASA Astrophysics Data System (ADS)

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.

Lee, Wei-Ming

2012-05-01

21

The chain collocation method: A spectrally accurate calculus of forms

NASA Astrophysics Data System (ADS)

Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.

Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu

2014-01-01

22

Evaluation of solid-liquid interface profile during continuous casting by a spline based formalism

A numerical framework has been applied which comprises of a cubic spline based collocation method to determine the solid-liquid\\u000a interface profile (solidification front) during continuous casting process. The basis function chosen for the collocation\\u000a algorithm to be employed in this formalism, is a cubic spline interpolation function. An iterative solution methodology has\\u000a been developed to track the interface profile for

S. K. Das

2001-01-01

23

Multi-element probabilistic collocation method in high dimensions

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 {mu} and the effective dimension {nu}, with {nu}<

Foo, Jasmine [Division of Applied Mathematics, Brown University, 182 George St., Box F, Providence, RI 02912 (United States); Karniadakis, George Em [Division of Applied Mathematics, Brown University, 182 George St., Box F, Providence, RI 02912 (United States)], E-mail: gk@dam.brown.edu

2010-03-01

24

Galerkin methods with splines for singular integral equations over (0, 1)

Summary In this paper a convergence analysis of Galerkin methods with splines for strongly elliptic singular integral equations over the interval (0, 1) is given. As trial functions we utilize smoothest polynomial splines on arbitrary meshes and continuous splines on special nonuniform partitions, multiplied by a weight function. Using inequalities of Grding type for singular integral operators in weightedL2 spaces

J. Elschner

1984-01-01

25

Dynamically Adaptive Wavelet Collocation Method for Shock Computations

NASA Astrophysics Data System (ADS)

Most explicit TVD schemes make use of artificial viscosity to reduce oscillations and avoid the stability requirements that an explicitly written dissipation term would require when solving hyperbolic conservation equations. In this talk an adaptive wavelet collocation method for shock computation is described. The method for determining a shock's location is similar to Harten's multiresolution algorithm, but its implementation is more continuous. The presence of wavelet coefficients on the finest level of resolution indicates that the maximum allowed resolution has been reached and localized artificial viscous terms should be added to smooth the solution. The localized viscosity is constructed by creating a mask of the wavelet coefficients on the finest level that are greater than a given threshold parameter. The mask is smoothed to reduce oscillations that can be induced due to spatial discontinuities in the second derivative. The main advantage of this technique are its generality and zero losses away from shocks. Since the viscosity is written explicitly, sonic points are no longer problematic and there is no need to track wind direction or introduce flux splitting. One- and two-dimensional examples are given and discussed.

Regele, Jonathan

2005-11-01

26

is explained, and then the results of its application to a box model of ocean thermohaline circulation of the probabilistic collocation method, and use its application to a model of ocean thermohaline circulation to show

27

A B-spline Galerkin method for the Dirac equation

NASA Astrophysics Data System (ADS)

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-?y, that can also be written as a pair of first-order equations y=?z, z=-?y. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers ?. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.

Froese Fischer, Charlotte; Zatsarinny, Oleg

2009-06-01

28

NASA Astrophysics Data System (ADS)

A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field.

Morel, J. E.

1981-01-01

29

NASA Astrophysics Data System (ADS)

Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method & nonlinear programming (NLP)) to lunar probe soft-landing trajectory optimization is introduced. Firstly, the model of trajectory optimization control problem to lunar probe soft landing trajectory is established and the equations of motion are simplified respectively based on some reasonable hypotheses. Performance is selected to minimize the fuel consumption. The control variables are thrust attack angle and thrust of engine. Terminal state variable constraints are velocity and altitude constraints. Then, the optimal control problem is transformed into nonlinear programming problem using direct collocation method. The state variables and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem is solved using the SNOPT software package. The simulation results demonstrate that the direct collocation method is not sensitive to lunar soft landing initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the direct collocation method is a viable approach to lunar probe soft landing trajectory optimization problem.

Tu, Lianghui; Yuan, Jianping; Luo, Jianjun; Ning, Xin; Zhou, Ruiwu

2007-11-01

30

NASA Technical Reports Server (NTRS)

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

Zhang, Zhimin; Tomlinson, John; Martin, Clyde

1994-01-01

31

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

32

Multidomain Spectral Collocation Method for the Stokes Problem.

National Technical Information Service (NTIS)

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pr...

G. S. Landriani, H. Vandeven

1989-01-01

33

This paper deals with the developments of mathematical methods for the discretization of continuous models and the solution of nonlinear problems of interest in applied sciences. The contents refer to developments of the differential quadrature method which leads to the so-called generalized collocation methods. The method is developed and applied to the solution of initial-boundary value problems. The computational problems

L. Graziano; A. Romano

2001-01-01

34

Collocation method for the modeling of membrane gas permeation systems A. Feichtingera

Collocation method for the modeling of membrane gas permeation systems A. Feichtingera , A In this work, we describe a numerical method which enables an efficient computation of membrane gas permeation. This is a crucial feature when combining computation of membrane permeation processes with optimization algorithms

Weinmüller, Ewa B.

35

A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field. The method is easily extended to other geometries and higher dimensions. Applications exist in the areas of neutron transport with highly anisotropic scattering (such as that associated with hydrogenous media), charged-particle transport, and particle transport in controlled-fusion plasmas. 23 figures, 6 tables.

Morel, J.E.

1981-01-01

36

The current paper reports on the development and validation of a localized collocation meshless method (LCMM) to model laminar incompressible flows. A high order upwinding scheme was devised to dampen the numerical oscillations arising in convection-dominated flows. Subsequently, the LCMM was analytically validated and demonstrated to yield third-order accurate solutions when compared to a benchmark analytical decaying vortex solution. Numerical

Z. El Zahab; E. Divo; A. J. Kassab

2009-01-01

37

An effective dynamic optimization method based on modified orthogonal collocation and reduced SQP

An effective dynamic optimization solution method based on the modified orthogonal collocation (mOC) and reduced successive quadratic programming (rSQP) is proposed, where the mOC is proposed to decrease the approximation error of the discrete optimal problem while traditional OC method converts the dynamic optimization problem to a regular but discrete nonlinear programming (NLP) problem, and the rSQP method is introduced

Xinggao Liu; Long Chen; Yunqing Hu

2011-01-01

38

A subdivision-based implementation of the hierarchical b-spline finite element method PPZ, U.K. Abstract A novel technique is presented to facilitate the implementation of hierarchical b-splines functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision

Cirak, Fehmi

39

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Quarteroni, Alfio

1989-01-01

40

Numerical solutions of some nonlinear evolution equations by Chebyshev spectral collocation methods

Chebyshev spectral collocation methods (known as El-Gendi methodsas described by El-Gendi in 1969 and Mihaila and Mihaila in 2002) are presented to deal with some nonlinear evolution equations including the Kortewegde Vries (KdV), the modified KdV, the mixed KdV and modified KdV, and the generalized fifth-order KdV equations, which include as special cases some well-known equations. The problem is reduced

A. H. Khater; R. S. Temsah

2007-01-01

41

Global collocation methods for approximation and the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.; Turkel, E.

1986-01-01

42

Numerical approach based on the spectral collocation method has been utilized for analyzing heat convection and conduction\\u000a in eccentric annuli. An eccentric instead of concentric annular duct is sometimes used as a fluid-flow and heat-transfer device\\u000a especially in nuclear power plants. The hydrodynamically and thermally fully developed laminar flow with uniform heat flux\\u000a through the inner and outer walls has

Woo Gun Sim; Jong Min Kim

1996-01-01

43

Higher-order numerical solutions using cubic splines. [for partial differential equations

NASA Technical Reports Server (NTRS)

A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-

Rubin, S. G.; Khosla, P. K.

1975-01-01

44

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

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{sup 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.

Foo, Jasmine; Wan Xiaoliang [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States); Karniadakis, George Em [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States)], E-mail: gk@dam.brown.edu

2008-11-20

45

Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations

This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. PMID:24977177

Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long

2014-01-01

46

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

47

A DOMAIN DECOMPOSITION METHOD FOR COMPUTING BIVARIATE SPLINE FITS OF SCATTERED DATA

A domain decomposition method for solving large bivariate scattered data fitting problems with bivariate minimal energy, discrete least-squares, and penalized least-squares splines is described. The method is based on splitting the domain into smaller domains, solving the associated smaller fitting problems, and combining the coefficients to get a global fit. Explicit error bounds are established for how well our locally

MING-JUN LAI; LARRY L. SCHUMAKER

2008-01-01

48

Interpolation of Superconducting Gravity Observations Using Least-Squares Collocation Method

NASA Astrophysics Data System (ADS)

A pre-processing of the gravity data measured by superconducting gravimeter involves removing of spikes, offsets and gaps. Their presence in observations can limit the data analysis and degrades the quality of obtained results. Short data gaps are filling by theoretical signal in order to get continuous records of gravity. It requires the accurate tidal model and eventually atmospheric pressure at the observed site. The poster presents a design of algorithm for interpolation of gravity observations with a sampling rate of 1 min. Novel approach is based on least-squares collocation which combines adjustment of trend parameters, filtering of noise and prediction. It allows the interpolation of missing data up to a few hours without necessity of any other information. Appropriate parameters for covariance function are found using a Bayes' theorem by modified optimization process. Accuracy of method is improved by the rejection of outliers before interpolation. For filling of longer gaps the collocation model is combined with theoretical tidal signal for the rigid Earth. Finally, the proposed method was tested on the superconducting gravity observations at several selected stations of Global Geodynamics Project. Testing demonstrates its reliability and offers results comparable with the standard approach implemented in ETERNA software package without necessity of an accurate tidal model.

Habel, Branislav; Janak, Juraj

2014-05-01

49

MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA

Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.

Webster, Clayton G [ORNL; Jantsch, Peter A [ORNL; Teckentrup, Aretha L [ORNL; Gunzburger, Max D [ORNL

2013-01-01

50

NASA Technical Reports Server (NTRS)

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

1994-01-01

51

A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme

NASA Astrophysics Data System (ADS)

We present a new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid. The method shares some common aspects with, and it was inspired by, the Box scheme. It uses centered second-order-accurate finite-difference approximations for the spatial derivatives combined with semi-implicit time integration. The proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity-pressure form of the equations. The continuity equation is enforced exactly (to machine accuracy) at the collocated locations, whereas the momentum equations are evaluated in a staggered manner. This formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure. The method shows uniform order of accuracy, both in space and time, for velocity and pressure. In addition, the skew-symmetric form of the non-linear advection term of the Navier-Stokes equations improves discrete conservation of kinetic energy in the inviscid limit, to within the order of the truncation error of the time integrator. The method has been formulated to accommodate different types of boundary conditions; fully periodic, periodic channel, inflow-outflow and lid-driven cavity; always ensuring global mass conservation. A novel aspect of this finite-difference formulation is the derivation of the discretization near boundaries using the weak form of the equations, as in the finite element method. The method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver. To assess the applicability of the new method presented in this paper, four realistic flow problems have been simulated and results are compared with those in the literature. These cases include a lid-driven cavity, backward-facing step, Kovasznay flow, and fully developed turbulent channel.

Ranjan, R.; Pantano, C.

2013-01-01

52

Behaviors of the global and local collocation methods that use multiquadrics as basis functions in solving problems having continuous boundary conditions are well known. In this paper, harmonic and biharmonic problems having discontinuous boundary conditions are solved by these methods. Solutions to two test problems are investigated. The first test problem is a heat conduction problem with discontinuous temperature at

Somchart Chantasiriwan

2007-01-01

53

Behaviors of the global and local collocation methods that use multiquadrics as basis functions in solving problems having continuous boundary conditions are well known. In this paper, harmonic and biharmonic problems having discontinuous boundary conditions are solved by these methods. Solutions to two test problems are investigated. The first test problem is a heat conduction problem with discontinuous temperature at

Somchart Chantasiriwan

2006-01-01

54

Sparse grid collocation schemes for stochastic natural convection problems

Sparse grid collocation schemes for stochastic natural convection problems Baskar case the collocation based approach to efficiently solve natural convection problems involving large-Carlo methods are made. Key words: Collocation methods; Natural convection; Stochastic partial differential

Zabaras, Nicholas J.

55

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

NASA Technical Reports Server (NTRS)

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

1997-01-01

56

Two-dimensional mesh embedding for Galerkin B-spline methods

NASA Technical Reports Server (NTRS)

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Shariff, Karim; Moser, Robert D.

1995-01-01

57

NASA Astrophysics Data System (ADS)

Watershed water quality models are increasingly used in management practices. However, simulations by such complex models often involve significant uncertainty, and observational data for the models to assimilate are usually scarce. In one of our previous studies, a Probabilistic Collocation Method (PCM) based approach was developed to efficiently conduct uncertainty analysis (UA) and global parameter sensitivity analysis (SA), with no data assimilation considered. In this study, the PCM approach was coupled with Shuffled Complex Evolution (SCE-UA) and Markov chain Monte Carlo (MCMC) methods to perform model calibration and UA, respectively, with data assimilation. The PCM-based approaches were applied to a SWAT (Soil and Water Assessment Tool) model of sediment and total nitrogen pollution in the Newport Bay watershed (Southern California). Different error assumptions were tested. The major findings are: 1) under certain error scenarios, the PCM-based approaches can provide adequate calibration and uncertainty results with much less computational cost, compared to traditional methods; 2) the PCM-based global SA can generate critical information on the relative importance of model parameters, which helps accelerate the data assimilation process; and 3) based on a systematic assessment of uncertainty using computationally efficient techniques like the PCM-based approach, cost-effective strategies of water quality data acquisition can be appropriately designed.

Wu, B.; Zheng, Y.

2012-12-01

58

B-spline soliton solution of the fifth order KdV type equations

NASA Astrophysics Data System (ADS)

In this paper, we develop a numerical solution based on sextic B-spline collocation method for solving the generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.

Zahra, W. K.; Ouf, W. A.; El-Azab, M. S.

2013-10-01

59

NASA Astrophysics Data System (ADS)

In order to quantify the reliability of NDE systems, large numbers of experiments are performed to develop a probability of detection (POD) curve for the system. These POD studies require a substantial amount of experimentation which can sometimes be cost prohibitive. To expedite the process of developing these curves, highly precise numerical models are used in conjunction with NDE sensors to understand the uncertainties associated with the inspections. Numerical models are also used in stochastic inversion methods such as Bayesian inversion, which provide a means of characterizing system properties with uncertainties. A strong basis has been developed in the modeling and simulation community for deterministic forward models in NDE, but to fully incorporate these models in model-assisted probability of detection (MAPOD) studies or stochastic inversion schemes, the models must be treated in a stochastic sense. A method of taking random inputs to a "black box" forward model and developing the full probability distribution function (PDF) of the response has been proposed. This method, called the probabilistic collocation method (PCM), takes random inputs to a forward model and uses orthogonal polynomials to construct a surrogate model in the area of the expected values of the inputs which is solved much quicker than the original forward model. In the NDE community, this method has only been used with inputs of known, named distributions. In this work, inputs of arbitrary distribution were used and the orthogonal polynomials for these inputs were developed with a recursion relationship that has been shown to produce orthogonal polynomials with respect to a given, continuous function. A concise code was written to make testing the method and incorporating it into MAPOD studies and inversion schemes relatively easy. The routine was tested with academic problems as well as eddy current problems.

Cherry, M. R.; Knopp, J. S.; Blodgett, M. P.

2012-05-01

60

Numerical simulations entail modeling assumptions that impact outcomes. Therefore, characterizing, in a probabilistic sense, the relationship between the variability of model selection and the variability of outcomes is important. Under certain assumptions, the stochastic collocation method offers a computationally feasible alternative to traditional Monte Carlo approaches for assessing the impact of model and parameter variability. We propose a framework that combines component shape parameterization with the stochastic collocation method to study the effect of drug depot shape variability on the outcome of drug diffusion simulations in a porcine model. We use realistic geometries segmented from MR images and employ level-set techniques to create two alternative univariate shape parameterizations. We demonstrate that once the underlying stochastic process is characterized, quantification of the introduced variability is quite straightforward and provides an important step in the validation and verification process. PMID:19272865

Preston, J Samuel; Tasdizen, Tolga; Terry, Christi M; Cheung, Alfred K; Kirby, Robert M

2009-03-01

61

Accuracy of the collocated transfer standard method for wind instrument auditing

NASA Astrophysics Data System (ADS)

The application of collocated data collection for the purpose of estimating the accuracy of an operating wind instrument requires some baseline demonstrating the best agreement which can be expected. A series of data were carefully taken in 1982 from six different collocated wind instruments. The published reports of these data suggest that the best agreement from averaged wind-speed measurements will be between 0.3 and 0.5 m/s, and for wind direction it will be 4 to 6 degrees. A new analysis of the same data reduces the best expected agreement to about 0.2 m/s and 2 degrees. The several reasons for claiming the better potential accuracy for collocated measurement (auditing) with calibrated transfer standard instruments are discussed.

Lockhart, Thomas J.

1989-08-01

62

GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD

..................................................................................26 1.2.2 Shoal-biased Rule of Nautical Chart Contours..................................................................................................................38 2.1 B-spline Curve...................................................................................................................38 2.1.1 B-spline Curve Definition

New Hampshire, University of

63

NASA Astrophysics Data System (ADS)

The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) [1] and extended by Karkar et al. (2013) [2] now allows to follow the periodic solutions of regularized non-smooth systems (stiff systems). This paper compares its convergence property to a reference method in applied mathematics: orthogonal collocation with piecewise polynomials. A first test is conducted on a nonlinear smooth 2 degree-of-freedom spring mass system, showing better convergence of the HBM. The second test is conducted on a one degree-of-freedom vibro-impact system with a very stiff regularization of the impact law. The HBM continuation of the nonlinear mode was found to be very robust, even with a very large number of harmonics. Surprisingly, the HBM was found to have a better convergence than the collocation method for this vibro-impact system. absolute threshold on the norm of the residue for the Newton-Raphson corrector: ?NR=10-9 (the residue norm is checked at the end of each step, and correction is carried out only if necessary), ANM series threshold used for step length estimation: ?ANM=10-12, ANM series order: Nseries=20. The choice of a small correction threshold ensures that the accuracy of a solution is mainly dependent on the accuracy of the discretization method, and not on that of the solver of the quadratic problem. Similarly, the choice of an even smaller ANM threshold ensures that the approximation at the end of each step is accurate enough so that no correction is usually needed at the beginning of the next step. Finally, the choice of the series order is arbitrary and mainly influences the step length.

Karkar, Sami; Cochelin, Bruno; Vergez, Christophe

2014-06-01

64

NASA Technical Reports Server (NTRS)

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

Mier Muth, A. M.; Willsky, A. S.

1978-01-01

65

Free Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation for the free vibration analysis of slender Kirchoff plates with both mixed and damaged boundaries an important role in applications of mechanical, aerospace and civil engineering. Studying the free vibration

Butcher, Eric A.

66

NASA Astrophysics Data System (ADS)

A collocation spectral domain decomposition method (CSDDM) based on the influence matrix technique is developed to solve radiative transfer problems within a participating medium of 2D partitioned domains. In this numerical approach, the spatial domains of interest are decomposed into rectangular sub-domains. The radiative transfer equation (RTE) in each sub-domain is angularly discretized by the discrete ordinates method (DOM) with the SRAPN quadrature scheme and then is solved by the CSDDM directly. Three test geometries that include square enclosure and two enclosures with one baffle and one centered obstruction are used to validate the accuracy of the developed method and their numerical results are compared to the data obtained by other researchers. These comparisons indicate that the CSDDM has a good accuracy for all solutions. Therefore this method can be considered as a useful approach for the solution of radiative heat transfer problems in 2D partitioned domains.

Chen, Shang-Shang; Li, Ben-Wen

2014-12-01

67

uncertainties in numerical dosimetry M. A. Drissaoui1,2 , S. Lanteri3 , P. Lévêque4 , F. Musy2 , L. Nicolas1 , R with a stochastic problem in a numerical dosimetry application in which the field solutions are computed using--Finite-element methods, numerical analysis, dosimetry. I. INTRODUCTION he lack of knowledge on the electric parameters

Paris-Sud XI, Université de

68

In the present work a theoretical and experimental investigation on the optimization of the molecular weight distribution (MWD) for linear free-radical polymerization systems is presented. The MWD calculations were carried out by two different computational methods, the orthogonal collocation of finite elements (OCFE) method and the fixed pivot (FP) technique. The predictive capabilities of the model were tested against experimental

Apostolos Krallis; Dimitris Meimaroglou; Vassilis Saliakas; Christos Chatzidoukas; Costas Kiparissides

2006-01-01

69

In this paper we develop the Point Collocation-based Method of Finite Spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation, Hankel optimal model and truncated balanced realization techniques for PCMFS. The PCMFS was developed in [1] as a physics-based technique for real time simulation of surgical procedures. It is a meshfree numerical method in which discretization is performed using a set of nodal points with approximation functions compactly supported on spherical subdomains centered at the nodes. The point collocation method is used as the weighted residual technique where the governing differential equations are directly applied at the nodal points. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, truncated balanced realization results in the highest accuracy while modal truncation results in the highest efficiency. PMID:20300494

BaniHani, Suleiman; De, Suvranu

2009-01-01

70

NASA Astrophysics Data System (ADS)

Chatter is a vibrational problem affecting machining operations, which may cause bad surface quality and damages to the machining system. In recent decades, several techniques for avoiding chatter onset were developed. Among other techniques, the continuous modulation of spindle speed during the cutting process (also called Spindle Speed Variation - SSV) has been demonstrated to be very effective for reducing the chance of chatter onset. However, spindle speed modulation parameters should be adequately chosen before machining, in order to effectively increase the material removal rate. In this perspective, chatter prediction algorithms play a crucial role, since they allow a preventive evaluation of process stability for any given spindle speed regime. State of the art algorithms for chatter prediction in milling with SSV are characterized by extremely long computation times, hindering their practical application in industry. In this paper, an innovative and fast algorithm for chatter prediction in milling with SSV, based on the Chebyshev Collocation Method, is presented. The algorithm was successfully compared with a state of the art algorithm - the Semi Discretization Method - in different experimental configurations and cutting conditions. The results showed that the new method is generally more accurate and from ten to one thousand times faster than the Semi Discretization Method.

Totis, G.; Albertelli, P.; Sortino, M.; Monno, M.

2014-02-01

71

NASA Astrophysics Data System (ADS)

This paper presents a semi-analytical approach to solve the eigenproblem of an acoustic cavity with multiple elliptical boundaries. To satisfy the Helmholtz equation in the elliptical coordinate system, the multipole expansion for the acoustic pressure is formulated in terms of angular and radial Mathieu functions. The boundary conditions are satisfied by uniformly collocating points on the boundaries. The acoustic pressure at each point is directly calculated in each elliptical coordinate system. In different coordinate systems, the normal derivative of the acoustic pressure is calculated by using the appropriate directional derivative, an alternative to the addition theorem. By truncating the multipole expansion, a finite linear algebraic system is derived. The direct searching approach is employed to determine the natural frequencies by using the singular value decomposition (SVD). Numerical results are widely discussed for several examples including an elliptical cavity, a confocal elliptical annulus cavity and an elliptical cavity with two elliptical cylinders. The accuracy and numerical convergence of the presented method is validated by comparison with available results from the analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Excellent accuracy and fast rate of convergence are the key features of the present method thanks to its semi-analytical feature.

Lee, W. M.

2011-09-01

72

Multiresolution B-spline Radiosity Yizhou Yu and Qunsheng Peng

--- Multiresolution B-spline Radiosity Yizhou YuÝ and Qunsheng Peng State Key Laboratory of CAD radiosity method called multiresolution B-spline radiosity, which uses B-splines of different scales is rectilinear. Keywords: Computer graphics, Radiosity, Wavelet, B-spline. 1 Introduction In computer graphics

Yu, Yizhou

73

Multivariate Adaptive Regression Splines

A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning

Jerome H. Friedman

1991-01-01

74

NASA Astrophysics Data System (ADS)

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

75

Applications of the Multi-Interval Chebyshev Collocation Method in RF Circuit Simulation

In this paper, we discuss the multi-interval Chebyshev (MIC) method for analog and radio-frequency (RF) circuit simulations. The method has been applied in a wide variety of circuit analyses including periodic steady-state, time-varying small signal, and cyclostationary noise analyses for both driven and autonomous circuits. In contrast to traditional analog\\/RF circuit simulations using either low-order time-domain integration methods or harmonic

Baolin Yang; Yu Zhu; Ali Bouaricha; Joel R. Phillips

2008-01-01

76

Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional MCMC sim- ulations. The computational efficiency is expected to be more beneficial to more computational expensive groundwater problems.

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

2012-09-01

77

Designing of curves and surfaces using cubic splines with geometric characterization

A constructive approach has been adopted to build interpolatory and B-spline like cubic spline curves with a more general continuity than ?-continuity. This method provides not only a large variety of very interesting shape controls like biased, point and interval tensions but, as a special case, also recovers a number of spline methods like ?-spline of G.M. Nielson (1974), ?-splines,

M. Sarfraz

1997-01-01

78

Non-Collocated Flexible Beam Motion Control based on a Delayed Adaptive Inverse Method

The viability of a delayed adaptive inverse method for motion control of the tip of a flexible beam is demonstrated in this paper. This method is based on an adaptive linear FIR filter which provides a stable and close approximation to the inverse plant dynamics. Such FIR filters can be used to control non-minimum phase systems, certain nonlinear systems, or

David S. Wang; Guo-Ben Yang; Max Donath

1993-01-01

79

This paper presents a new approach for time-domain transient simulation of electric power systems with or without power electronic (switching) subsystems. The new methodology has been named quadratic integration method. The method is based on the following two innovations:(a) the nonlinear system model equations (in general differential-algebraic) are reformulated to a fully equivalent system of quadratic equations, by introducing additional

A. P. Meliopoulos; George J. Cokkinides; G. K. Stefopoulos

2005-01-01

80

NASA Technical Reports Server (NTRS)

The geometrical structure of the boundary shape for a two-dimensional boundary value problem is identified. The output least square identification method is considered for estimating partially unknown boundary shapes. A numerical parameter estimation technique using the spline collocation method is proposed.

Kojima, Fumio

1989-01-01

81

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

NASA Astrophysics Data System (ADS)

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts. Existing methods are either computationally unaffordable or with limited application scope. Accordingly, a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed. The fuzziness propagation in the random reliability, which is the focus of the present study, is performed by the proposed method, in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation. First-Order, Second-Moment (FOSM) method which can be replaced by its counterparts is utilized to calculate the structural random reliability. Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.

Xu, MengHui; Qiu, ZhiPing

2014-07-01

82

Numerical simulation of non-linear elastic flows with a general collocated finite-volume method

This paper reports the development and application of a finite-volume based methodology for the calculation of the flow of fluids which follow differential viscoelastic constitutive models. The novelty of the method lies on the use of the non-staggered grid arrangement, in which all dependent variables are located at the center of the control volumes, thus greatly simplifying the adoption of

P. J. Oliveira; F. T. Pinho; G. A. Pinto

1998-01-01

83

SUBMITTED TO: MULTISCALE MODELING AND SIMULATION AN ADAPTIVE WAVELET-COLLOCATION METHOD FOR SHOCK

function . Using this function, an artificial viscous term is explicitly added in the needed regions using, adaptive grid, numerical method, shock locator, artificial viscosity, Riemann problem, shock capturing AMS a major commonality among most of the more traditional schemes and that is the use of artificial viscosity

Vasilyev, Oleg V.

84

NASA Technical Reports Server (NTRS)

A split spline screw type payload fastener assembly, including three identical male and female type split spline sections, is discussed. The male spline sections are formed on the head of a male type spline driver. Each of the split male type spline sections has an outwardly projecting load baring segment including a convex upper surface which is adapted to engage a complementary concave surface of a female spline receptor in the form of a hollow bolt head. Additionally, the male spline section also includes a horizontal spline releasing segment and a spline tightening segment below each load bearing segment. The spline tightening segment consists of a vertical web of constant thickness. The web has at least one flat vertical wall surface which is designed to contact a generally flat vertically extending wall surface tab of the bolt head. Mutual interlocking and unlocking of the male and female splines results upon clockwise and counter clockwise turning of the driver element.

Vranish, John M. (inventor)

1993-01-01

85

Focusing light onto nanostructures thanks to spherical lenses is a first step in enhancing the field and is widely used in applications. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam cannot be described by the simple ray tracing formalism. Here, we present a method for computing the response to a focused beam, based on the B-spline modal method adapted to nanostructures in conical mounting. The eigenmodes are computed in each layer for both polarizations and are then combined for the computation of scattering matrices. The simulation of a Gaussian focused beam is obtained thanks to a truncated decomposition into plane waves computed on a single period, which limits the computation burden. PMID:25121523

Chevalier, Paul; Bouchon, Patrick; Pardo, Fabrice; Hadar, Riad

2014-08-01

86

NASA Astrophysics Data System (ADS)

The basic ideas of the B-spline R-matrix (BSR) approach are reviewed, and the use of the method is illustrated with a variety of applications to atomic structure, electron-atom collisions and photo-induced processes. Special emphasis is placed on complex, open-shell targets, for which the method has proven very successful in reproducing, for example, a wealth of near-threshold resonance structures. Recent extensions to a fully relativistic framework and intermediate energies have allowed for an accurate treatment of heavy targets as well as a fully nonperturbative scheme for electron-impact ionization. Finally, field-free BSR Hamiltonian and electric dipole matrices can be employed in the time-dependent treatment of intense short-pulse laser-atom interactions.

Zatsarinny, Oleg; Bartschat, Klaus

2013-06-01

87

NASA Astrophysics Data System (ADS)

This study develops a wavelet Galerkin method (WGM) that uses B-spline wavelet bases for application to solid mechanics problems. A fictitious domain is often adopted to treat general boundaries in WGMs. In the analysis, the body is extended to its exterior but very low stiffness is applied to the exterior region. The stiffness matrix in the WGM becomes singular without the use of a fictitious domain. The problem arises from the lack of linear independence of the basis functions. A technique to remove basis functions that can be represented by the superposition of the other basis functions is proposed. The basis functions are automatically eliminated in the pre conditioning step. An adaptive strategy is developed using the proposed technique. The solution is refined by superposing finer wavelet functions. Numerical examples of solid mechanics problems are presented to demonstrate the multiresolution properties of the WGM.

Tanaka, Satoyuki; Okada, Hiroshi; Okazawa, Shigenobu

2012-07-01

88

Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method

NASA Astrophysics Data System (ADS)

The Finite Cell Method (FCM) is an embedded domain method, which combines the fictitious domain approach with high-order finite elements, adaptive integration, and weak imposition of unfitted Dirichlet boundary conditions. For smooth problems, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. The present contribution first unhinges the FCM concept from a special high-order basis. Several benchmarks of linear elasticity and a complex proximal femur bone with inhomogeneous material demonstrate that for small deformation analysis, FCM works equally well with basis functions of the p-version of the finite element method or high-order B-splines. Turning to large deformation analysis, it is then illustrated that a straightforward geometrically nonlinear FCM formulation leads to the loss of uniqueness of the deformation map in the fictitious domain. Therefore, a modified FCM formulation is introduced, based on repeated deformation resetting, which assumes for the fictitious domain the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence. Finally, the weak imposition of unfitted Dirichlet boundary conditions via the penalty method, the robustness of FCM under severe mesh distortion, and the large deformation analysis of a complex voxel-based metal foam are addressed.

Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Dster, Alexander; Rank, Ernst

2012-10-01

89

A number of techniques are presented for making conic splines more effective for 2D computer graphics. We give a brief account of the theory of conic splines oriented to computer graphics. We make Pitteway's algorithm exact, and repair an \\

Vaughan R. Pratt

1985-01-01

90

A Fully Relativistic B-Spline R-Matrix Method for Electron and Photon Collisions with Atoms and Ions

NASA Astrophysics Data System (ADS)

We have extended our B-spline R-matrix (close-coupling) method [1] to fully account for relativistic effects in a Dirac-Coulomb formulation. Our numerical implementation of the close-coupling method enables us to construct term-dependent, non-orthogonal sets of one-electron orbitals for the bound and continuum electrons. This is a critical aspect for complex targets, where individually optimized one-electron orbitals can significantly reduce the size of the multi-configuration expansions needed for an accurate target description. Core-valence correlation effets are treated fully ab initio, rather than through semi-empirical model potentials. The method is described in detail and will be illustrated by comparing our theoretical predictions for e-Cs collisions [2] with benchmark experiments for angle-integrated and angle-differential cross sections [3], various spin-dependent scattering asymmetries [4], and Stokes parameters measured in superelastic collisions with laser-excited atoms [5]. [1] O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006). [2] O. Zatsarinny and K. Bartschat, Phys. Rev. A 77, 062701 (2008). [3] W. Gehenn and E. Reichert, J. Phys. B 10, 3105 (1977). [4] G. Baum et al., Phys. Rev. A 66, 022705 (2002) and 70, 012707 (2004). [5] D.S. Slaughter et al., Phys. Rev. A 75, 062717 (2007).

Zatsarinny, Oleg; Bartschat, Klaus

2008-10-01

91

A Full-Relativistic B-Spline R-Matrix Method for Electron and Photon Collisions with Atoms and Ions

NASA Astrophysics Data System (ADS)

We have extended our B-spline R-matrix (close-coupling) method [1] to fully account for relativistic effects in a Dirac-Coulomb formulation. Our numerical implementation of the close-coupling method enables us to construct term-dependent, non-orthogonal sets of one-electron orbitals for the bound and continuum electrons. This is a critical aspect for complex targets, where individually optimized one-electron orbitals can significantly reduce the size of the multi-configuration expansions needed for an accurate target description. Furthermore, core-valence correlation effets are treated fully ab initio, rather than through semi-empirical, and usually local, model potentials. The method will be described in detail and illustrated by comparing our theoretical predictions for e-Cs collisions with benchmark experiments for angle-integrated and angle-differential cross sections [2], various spin-dependent scattering asymmetries [3], and Stokes parameters measured in superelastic collisions with laser-excited atoms [4]. [1] O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006). [2] W. Gehenn and E. Reichert, J. Phys. B 10, 3105 (1977). [3] G. Baum et al., Phys. Rev. A 66, 022705 (2002) and 70, 012707 (2004). [4] D.S. Slaughter et al., Phys. Rev. A 75, 062717 (2007).

Zatsarinny, Oleg; Bartschat, Klaus

2008-05-01

92

CAM PROFILE SMOOTHING BY MODIFIED SPLINE CURVES

High frequency components and\\/or excessive jerks in a cam profile, which are important sources of cam- follower vibration, can be reduced by profile smoothing. Although there are many data smoothing algorithms, the algorithms based on spline curves are most widely used in designing cam profiles. This paper presents a method to smooth cam profiles by using modified spline curves. The

VU-THINH NGUYEN; DOJOONG KIM

2007-01-01

93

Splines and Geometric Modeling Chandrajit L. Bajaj and Susan Evans

. Properties of tensor product B ezier patches include a ne invariance, convex hull property, and the variation elements. Splines are used in applications ranging from image processing, computer aided design shalldwellmainly on spline surface tting methods in IR3 Tensor product splines in Section xx.1,..., triangular

Texas at Austin, University of

94

Improvements in spectral collocation discretization through a multiple domain technique

NASA Technical Reports Server (NTRS)

Spectral collocation methods require that a complicated physical domain must map onto a simple computational domain for discretization. This and other restrictions are presently overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of mesh spacings between regions to be several orders of magnitude higher than allowable in a single domain.

Macaraeg, M. G.; Streett, C. L.

1986-01-01

95

ECS 178 Course Notes SPLITTING A QUADRATIC UNIFORM B-SPLINE CURVE

ECS 178 Course Notes SPLITTING A QUADRATIC UNIFORM B-SPLINE CURVE Kenneth I. Joy Institute for Data Splitting a uniform B-spline curve involves creating two new curves, one that represents the first half on subdivision curves and provide methods that can be applied to splitting B- spline surfaces. In the uniform B-spline

California at Davis, University of

96

On-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT

On-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy subdivision of uniform B-spline curves. The uniform B-spline curves, surfaces and solids have been extensively the refinement method for a quadratic uniform B-spline curve and show that the refinement is exactly

California at Davis, University of

97

ECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT

ECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy Institute for Data of uniform B-spline curves. The uniform B-spline curves, surfaces and solids have been extensively studied method for a quadratic uniform B-spline curve and show that the refinement is exactly that speci- fied

California at Davis, University of

98

NASA Astrophysics Data System (ADS)

Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micro-meteorological (MM) and enclosure measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen-ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and sensitivity to environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R > 0.8, p < 0.05), but the correlation between DFC and MM instantaneous fluxes were from weak to moderate (R = 0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM-techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (< 10% difference). This implicates that the NDFC technique, which accounts for internal friction velocity, effectively bridged the gap in measured Hg0 flux compared to MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.

Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.

2014-09-01

99

Temporal Registration of 2D X-ray Mammogram Using Triangular B-splines Finite Element Method (TBFEM)

of the most common causes for cancer-related death, with annual mortality of over 400, 000 women worldwide). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B. Unfortunately, a temporal pair of mammogram may vary quite significantly due to the spatial disparities caused

Qin, Hong

100

ECT-B-splines defined by generalized divided differences

NASA Astrophysics Data System (ADS)

ECT-spline curves are generated from different local ECT-systems via connection matrices. If they are nonsingular, lower triangular and totally positive there is a basis of the space of ECT-splines consisting of functions having minimal compact supports, normalized either to form a nonnegative partition of unity or to have integral one. In this paper such ECT-B-splines are defined by generalized divided differences. This definition reduces to the classical one in case of a Schoenberg space. Under suitable assumptions it leads to a recursive method for computing the ECT-B-splines that reduces to the de Boor-Mansion-Cox recursion in case of ordinary polynomial splines and to Lyche's recursion in case of Tchebycheff splines [Muhlbach and Tang, Calculation of ECT-B-splines and of ECT-spline curves recursively, in preparation].There is an ECT-spline space naturally adjoint to every ECT-spline space. We also construct B-splines via generalized divided differences for this space and study relations between the two adjoint spaces.

Muhlbach, G.

2006-03-01

101

A numerical method for solving KdV equation with multilevel B-spline quasi-interpolation

In this article, we use a multilevel quartic spline quasi-interpolation scheme to solve the one-dimensional nonlinear Kortewegde Vries (KdV) equation which exhibits a large number of physical phenomena. The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative, and the forward divided difference to approximate the temporal derivative,

Ren-Gui Yu; Ren-Hong Wang; Chun-Gang Zhu

2012-01-01

102

NSDL National Science Digital Library

The Cubic Spline Model displays a cubic spline and its derivatives. The model constructs N third-order piecewise continuous polynomialz (cubic splines) that connect N data points (nodes) with unit separation. Polynomial coefficients are chosen such that the resulting curve and its first derivative are smooth at the nodes. Users can drag the nodes and observe the resulting curve. Radio buttons display first and second derivative curves. Note that the second derivative curve consists of line segments because the second derivative of a piecewise cubic polynomial is a piecewise first order polynomial. The Cubic Spline Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_math_CubicSplineDemo.jar file to run the program if Java is installed.

Christian, Wolfgang

2011-09-17

103

ERIC Educational Resources Information Center

This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates

Webb, Stuart; Kagimoto, Eve

2011-01-01

104

NASA Astrophysics Data System (ADS)

The time domain numerical analysis of sound wave propagation has been performed widely as a result of computer development. The method of characteristics (MOC) is used as a time domain numerical analysis method. In multidimensional MOC sound wave analysis, the so-called automatically absorbing boundary (without additional outer boundary treatment) does not have excellent absorbing performance. To overcome this problem, we introduce the perfectly matched layer (PML) technique into MOC simulation. Through this study, it is clarified that the PML (L = 16) reflection at a vertical incidence is approximately 22 dB lower than the automatically absorbing boundary (without PML) in the simulation by the QUICKEST method.

Adachi, Junpei; Okubo, Kan; Tagawa, Norio; Tsuchiya, Takao; Ishizuka, Takashi

2013-07-01

105

Splines: a perfect fit for medical imaging

NASA Astrophysics Data System (ADS)

Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected in medical imaging applications, mostly as a consequence of what one may call the bad press phenomenon. Thanks to some recent research efforts in signal processing and wavelet-related techniques, the virtues of splines have been revived in our community. There is now compelling evidence (several independent studies) that splines offer the best cost-performance tradeoff among available interpolation methods. In this presentation, we will argue that the spline representation is ideally suited for all processing tasks that require a continuous model of signals or images. We will show that most forms of spline fitting (interpolation, least squares approximation, smoothing splines) can be performed most efficiently using recursive digital filters. We will also have a look at their multiresolution properties which make them prime candidates for constructing wavelet bases and computing image pyramids. Typical application areas where these techniques can be useful are: image reconstruction from projection data, sampling grid conversion, geometric correction, visualization, rigid or elastic image registration, and feature extraction including edge detection and active contour models.

Unser, Michael A.

2002-05-01

106

For many engineers and acousticians, the boundary element method (BEM) provides an invaluable tool in the analysis of complex problems. It is particularly well suited for the examination of acoustical problems within large domains. Unsurprisingly, the widespread application of the BEM continues to produce an academic interest in the methodology. New algorithms and techniques are still being proposed, to extend

B. E. Treeby; J. Panb

2009-01-01

107

Discontinuities in the body force field typically appear at the interface of two fluid systems. Modeled with the volume-of-fluid (VOF) and discretized with the finite volume method, the discontinuous body force fields are represented as abruptly variable. In the present study, gravity and continuum surface force (CSF) are considered. Such strongly variable body forces can produce unphysical spikes in the

Jure Mencinger; Iztok un

2007-01-01

108

NASA Astrophysics Data System (ADS)

The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m2 and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R2), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.

2014-06-01

109

NASA Technical Reports Server (NTRS)

Scientific data often contains random errors that make plotting and curve-fitting difficult. The Rational-Spline Approximation with Automatic Tension Adjustment algorithm lead to a flexible, smooth representation of experimental data. The user sets the conditions for each consecutive pair of knots:(knots are user-defined divisions in the data set) to apply no tension; to apply fixed tension; or to determine tension with a tension adjustment algorithm. The user also selects the number of knots, the knot abscissas, and the allowed maximum deviations from line segments. The selection of these quantities depends on the actual data and on the requirements of a particular application. This program differs from the usual spline under tension in that it allows the user to specify different tension values between each adjacent pair of knots rather than a constant tension over the entire data range. The subroutines use an automatic adjustment scheme that varies the tension parameter for each interval until the maximum deviation of the spline from the line joining the knots is less than or equal to a user-specified amount. This procedure frees the user from the drudgery of adjusting individual tension parameters while still giving control over the local behavior of the spline The Rational Spline program was written completely in FORTRAN for implementation on a CYBER 850 operating under NOS. It has a central memory requirement of approximately 1500 words. The program was released in 1988.

Schiess, J. R.

1994-01-01

110

Local RBF Approximation for Scattered Data Fitting with Bivariate Splines

Local RBF Approximation for Scattered Data Fitting with Bivariate Splines Oleg Davydov, Alessandra at developing efficient meth- ods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used

Davydov, Oleg

111

ECS 178 Course Notes SPLITTING THE CUBIC UNIFORM B-SPLINE CURVE

ECS 178 Course Notes SPLITTING THE CUBIC UNIFORM B-SPLINE CURVE Kenneth I. Joy Institute for Data Splitting a uniform B-spline curve implies creating two new curves, one that represents the first half of the work on subdivision curves and provide methods that can be applied to recursive subdivision of B-spline

California at Davis, University of

112

NASA Astrophysics Data System (ADS)

The methods of Least-Squares Collocation (LSC) and the Reduced Point Mass method (RPM) both uses radial basis-functions for the representation of the anomalous gravity potential (T). LSC uses as many base-functions as the number of observations, while the RPM method uses as many as deemed necessary. Both methods have been evaluated and for some tests compared in the two areas (Central Europe and South-East Pacific). For both areas test data had been generated using EGM2008. As observational data (a) ground gravity disturbances, (b) airborne gravity disturbances, (c) GOCE like Second order radial derivatives and (d) GRACE along-track potential differences were available. The use of these data for the computation of values of (e) T in a grid was the target of the evaluation and comparison investigation. Due to the fact that T in principle can only be computed using global data, the remove-restore procedure was used, with EGM2008 subtracted (and later added to T) up to degree 240 using dataset (a) and (b) and up to degree 36 for datasets (c) and (d). The estimated coefficient error was accounted for when using LSC and in the calculation of error-estimates. The main result is that T was estimated with an error (computed minus control data, (e) from which EGM2008 to degree 240 or 36 had been subtracted ) as found in the table (LSC used): Area Europe Data-set (mgal) (e)-240(a) (b) (e)-36 (c) (d) Mean -0.0 0.0 -0.1 -0.1 -0.3 -1.8 Standard deviation4.1 0.8 2.7 32.6 6.0 19.2 Max. difference 19.9 10.4 16.9 69.9 31.3 47.0 Min.difference -16.2 -3.7 -15.5 -92.1 -27.8 -65.5 Area Pacific Data-set (mgal) (e)-240(a) (b) (e)-36 (c) (d) Mean -0.1 -0.1 -0.1 4.6 -0.2 0.2 Standard deviation4.8 0.2 1.9 49.1 6.7 18.6 Max.difference 22.2 1.8 13.4 115.5 26.9 26.5 Min.difference -28.7 -3.1 -15.7 -106.4 -33.6 22.1 The result using RPM with data-sets (a), (b), (c) gave comparable results. The use of (d) with the RPM method is being implemented. Tests were also done computing dataset (a) from the other datasets. The results here may serve as a bench-mark for other radial basis-function implementations for computing approximations to T. Improvements are certainly possible, e.g. by taking the topography and bathymetry into account.

Tscherning, Carl Christian; Herceg, Matija

2014-05-01

113

Collocations of Complex Nouns: Evidence for Lexicalisation

This paper combines a corpus-based study of noun+verb collocations with an attempt to distinguish compositional, regularly formed compounds from lexicalised ones. We claim that morphologically regular, compositional compounds share most of their collocational preferences with their compound heads, whereas lexicalised compounds have their own collocational preferences, distinct or only marginally overlapping with those of their heads. We test this claim

Heike Zinsmeister; Ulrich Heid

114

{L(1}) Control Theoretic Smoothing Splines

NASA Astrophysics Data System (ADS)

In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.

Nagahara, Masaaki; Martin, Clyde F.

2014-11-01

115

During the last years, spline functions have found widespread application, mainly for the purpose of interpolation []. However, there may be a demand to replace strict interpolation by some kind of smoothing. Usually, such a situation occurs if the values of the ordinates are given only approximately, for example if they stem from experimental data. In the case in which,

Christian H. Reinsch

1967-01-01

116

SURVIVAL ESTIMATION USING SPLINES

A non parametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. t approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. pecial case is that proposed by...

117

Mr. Stockdale's Dictionary of Collocations.

ERIC Educational Resources Information Center

This dictionary of collocations was compiled by an English-as-a-Second-Language (ESL) teacher in Saudi Arabia who teaches adult, native speakers of Arabic. The dictionary is practical in teaching English because it helps to focus on everyday events and situations. The dictionary works as follows: the teacher looks up a word, such as "talk"; next

Stockdale, Joseph Gagen, III

118

Analysis of chromatograph systems using orthogonal collocation

NASA Technical Reports Server (NTRS)

Research is generating fundamental engineering design techniques and concepts for the chromatographic separator of a chemical analysis system for an unmanned, Martian roving vehicle. A chromatograph model is developed which incorporates previously neglected transport mechanisms. The numerical technique of orthogonal collocation is studied. To establish the utility of the method, three models of increasing complexity are considered, the latter two being limiting cases of the derived model: (1) a simple, diffusion-convection model; (2) a rate of adsorption limited, inter-intraparticle model; and (3) an inter-intraparticle model with negligible mass transfer resistance.

Woodrow, P. T.

1974-01-01

119

Splines of complex order: An introduction

NASA Astrophysics Data System (ADS)

We give a short introduction to complex B-splines, highlight their relations to difference operators and Dirichlet means, and introduce complex B-spline surfaces. Finally, we present the new class of splines of complex order.

Massopust, Peter

2012-09-01

120

NASA Technical Reports Server (NTRS)

To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

Fang, Ming; Bowin, Carl

1992-01-01

121

Fitting multidimensional splines using statistical variable selection techniques

NASA Technical Reports Server (NTRS)

This report demonstrates the successful application of statistical variable selection techniques to fit splines. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs using the B-spline basis were developed, and the one for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.

Smith, P. L.

1982-01-01

122

ERIC Educational Resources Information Center

Although it is widely acknowledged that collocations play an important part in second language learning, especially at intermediate-advanced levels, learners' difficulties with collocations have not been investigated in much detail so far. The present study examines ESL learners' use of verb-noun collocations, such as "take notes," "place an

Miyakoshi, Tomoko

2009-01-01

123

Mathematical research on spline functions

NASA Technical Reports Server (NTRS)

One approach in spline functions is to grossly estimate the integrand in J and exactly solve the resulting problem. If the integrand in J is approximated by Y" squared, the resulting problem lends itself to exact solution, the familiar cubic spline. Another approach is to investigate various approximations to the integrand in J and attempt to solve the resulting problems. The results are described.

Horner, J. M.

1973-01-01

124

NASA Technical Reports Server (NTRS)

Ball-bearing carrier includes splined outer surface mating with slightly larger splined inner surface of housing and provides constant deadband, unaffected by movements of other components. Deadband needed to establish radial spring rate and provide for axial movement of bearing for thrust balance. Bearing carrier and bearing intended for use in high-pressure turbopump.

Moore, Jerry H.

1992-01-01

125

C1 Hermite shape preserving polynomial splines in R3

NASA Astrophysics Data System (ADS)

The C 2 variable degree splines1-3 have been proven to be an efficient tool for solving the curve shape-preserving interpolation problem in two and three dimensions. Based on this representation, the current paper proposes a Hermite interpolation scheme, to construct C 1 shape-preserving splines of variable degree. After this, a slight modification of the method leads to a C 1 shape-preserving Hermite cubic spline. Both methods can easily be developed within a CAD system, since they compute directly (without iterations) the B-spline control polygon. They have been implemented and tested within the DNV Software CAD/CAE system GeniE. [Figure not available: see fulltext.

Gabrielides, Nikolaos C.

2012-06-01

126

Adaptive regression splines in the Cox model.

We develop a method for constructing adaptive regression spline models for the exploration of survival data. The method combines Cox's (1972, Journal of the Royal Statistical Society, Series B 34, 187-200) regression model with a weighted least-squares version of the multivariate adaptive regressi on spline (MARS) technique of Friedman (1991, Annals of Statistics 19, 1-141) to adaptively select the knots and covariates. The new technique can automatically fit models with terms that represent nonlinear effects and interactions among covariates. Applications based on simulated data and data from a clinical trial for myeloma are presented. Results from the myeloma application identified several important prognostic variables, including a possible nonmonotone relationship with survival in one laboratory variable. Results are compared to those from the adaptive hazard regression (HARE) method of Kooperberg, Stone, and Truong (1995, Journal of the American Statistical Association 90, 78-94). PMID:11318156

LeBlanc, M; Crowley, J

1999-03-01

127

High-order approximation of conic sections by quadratic splines

Given a segment of a conic section in the form of a rational Bezier curve, a quadratic spline approximation is constructed and an explicit error bound is derived. The convergence order of the error bound is shown to be O(h4) which is optimal, and the spline curve is both C1 and G2. The approximation method is very efficient as it

Michael Floater

1995-01-01

128

NASA Technical Reports Server (NTRS)

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.

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

2013-01-01

129

Error-Bounded B-Spline Curve Approximation Based on Dominant Point Selection

We propose a new method for error-bounded B-spline curve approximation based on dominant point selection. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve

Joo-haeng Lee

2005-01-01

130

Covariance modeling in geodetic applications of collocation

NASA Astrophysics Data System (ADS)

Collocation method is widely applied in geodesy for estimating/interpolating gravity related functionals. The crucial problem of this approach is the correct modeling of the empirical covariance functions of the observations. Different methods for getting reliable covariance models have been proposed in the past by many authors. However, there are still problems in fitting the empirical values, particularly when different functionals of T are used and combined. Through suitable linear combinations of positive degree variances a model function that properly fits the empirical values can be obtained. This kind of condition is commonly handled by solver algorithms in linear programming problems. In this work the problem of modeling covariance functions has been dealt with an innovative method based on the simplex algorithm. This requires the definition of an objective function to be minimized (or maximized) where the unknown variables or their linear combinations are subject to some constraints. The non-standard use of the simplex method consists in defining constraints on model covariance function in order to obtain the best fit on the corresponding empirical values. Further constraints are applied so to have coherence with model degree variances to prevent possible solutions with no physical meaning. The fitting procedure is iterative and, in each iteration, constraints are strengthened until the best possible fit between model and empirical functions is reached. The results obtained during the test phase of this new methodology show remarkable improvements with respect to the software packages available until now. Numerical tests are also presented to check for the impact that improved covariance modeling has on the collocation estimate.

Barzaghi, Riccardo; Cazzaniga, Noemi; De Gaetani, Carlo; Reguzzoni, Mirko

2014-05-01

131

Rapid Software Development through Team Collocation

In a field study conducted at a leading Fortune 100 company, we examined how having development teams reside in their own large room (an arrangement called radical collocation) affected system development. The collocated projects had significantly higher productivity and shorter schedules than both the industry benchmarks and the performance of past similar projects within the firm. The teams reported high

Stephanie D. Teasley; Lisa A. Covi; Mayuram S. Krishnan; Judith S. Olson

2002-01-01

132

Localization of rational B-spline surfaces

Localization of curved surfaces is an important problem in the manufacturing and inspection of mechanical elements and in the simulation of manufacturing processes. The objective of this paper is to provide an efficient method for accurate localization of a single free-form surface of the rational B-spline form. Our approach is based on the following componentsfirst, representation of position tolerances in

N. M. Patrikalakis; L. Bardis

1991-01-01

133

Shape Modification of B-Spline Curves via Constrained Optimization for Multi-target Points

The B-spline curve is one of the most famous curves in computer graphics, computational geometry and CAGD. Developing more convenient techniques for designing and modifying B-spline curves is an important problem, and is also an important research issue. In this study, the shape modification of B-spline curves by geometric constraints is presented. A new method based on changing the control

Qingbiao Wu; Shuyi Tao

2009-01-01

134

Classification of pathological stage of prostate cancer patients using penalized splines

We propose a penalized splines (P-splines) based method to predict the pathological stage of localized prostate cancer. A combination of prostate-specific antigen, Gleason histological score, and clinical stage from a cohort study of 834 prostate cancer patients are used to build the P-splines model. It turns out that the proposed methodology results in improved prediction of pathological stage compared to

Tathagata Banerjee; Tapabrata Maiti; Pushpal Mukhopadhyay

2006-01-01

135

Parametric Curves parametric curves (Splines)

curves (Splines) · polygonal meshes #12;2 Roller coaster · Next programming assignment involves creating a 3D roller coaster animation · We must model the 3D curve describing the roller coaster, but how

Treuille, Adrien

136

Sparse grid collocation schemes for stochastic natural convection problems

In recent years, there has been an interest in analyzing and quantifying the effects of random inputs in the solution of partial differential equations that describe thermal and fluid flow problems. Spectral stochastic methods and Monte-Carlo based sampling methods are two approaches that have been used to analyze these problems. As the complexity of the problem or the number of random variables involved in describing the input uncertainties increases, these approaches become highly impractical from implementation and convergence points-of-view. This is especially true in the context of realistic thermal flow problems, where uncertainties in the topology of the boundary domain, boundary flux conditions and heterogeneous physical properties usually require high-dimensional random descriptors. The sparse grid collocation method based on the Smolyak algorithm offers a viable alternate method for solving high-dimensional stochastic partial differential equations. An extension of the collocation approach to include adaptive refinement in important stochastic dimensions is utilized to further reduce the numerical effort necessary for simulation. We show case the collocation based approach to efficiently solve natural convection problems involving large stochastic dimensions. Equilibrium jumps occurring due to surface roughness and heterogeneous porosity are captured. Comparison of the present method with the generalized polynomial chaos expansion and Monte-Carlo methods are made.

Ganapathysubramanian, Baskar [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 188 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States); Zabaras, Nicholas [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 188 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)]. E-mail: zabaras@cornell.edu

2007-07-01

137

Beamforming with collocated microphone arrays

NASA Astrophysics Data System (ADS)

A collocated microphone array, including three gradient microphones with different orientations and one omnidirectional microphone, was used to acquire data in a sound-treated room and in an outdoor environment. This arrangement of gradient microphones represents an acoustic vector sensor used in air. Beamforming techniques traditionally associated with much larger uniformly spaced arrays of omnidirectional sensors are extended to this compact array (1 cm3) with encouraging results. A frequency-domain minimum-variance beamformer was developed to work with this array. After a calibration of the array, the recovery of sources from any direction is achieved with high fidelity, even in the presence of multiple interferers. SNR gains of 5-12 dB with up to four speech sources were obtained with both indoor and outdoor recordings. This algorithm has been developed for new MEMS-type microphones that further reduce the size of the sensor array.

Lockwood, Michael E.; Jones, Douglas L.; Su, Quang; Miles, Ronald N.

2003-10-01

138

Image interpolation by multivariate B-splines

in terms of A?A'+, , B1, B'+, which are defined as ei Ai = et+1 ot ? 1 a+a ? &+1 AI+1 = a, +a ? a, 6, ? 6, bi 1 ? 61 1+2 1+1 6 '+' 6+, ? 6, (2 ) These four variables depend on the placement of the grid points. The support of a typical bivariate... to interpolation as discussed in chapter II. B. Comparisions Of The Reconstructed Images When the results of bi-linear method is compared with those using bivariate quadratic B-spline method, one observes from the results using the bi-linear method...

Chan, Ki Bun

2012-06-07

139

Maternal MCG Interference Cancellation Using Splined Independent Component Subtraction

Signal distortion is commonly observed when using independent component analysis (ICA) to remove maternal cardiac interference from the fetal magnetocardiogram. This can be seen even in the most conservative case where only the independent components dominated by maternal interference are subtracted from the raw signal, a procedure we refer to as independent component subtraction (ICS). Distortion occurs when the subspaces of the fetal and maternal signals have appreciable overlap. To overcome this problem, we employed splining to remove the fetal signal from the maternal source component. The maternal source components were downsampled and then interpolated to their original sampling rate using a cubic spline. A key aspect of the splining procedure is that the maternal QRS complexes are downsampled much less than the rest of the maternal signal so that they are not distorted, despite their higher bandwidth. The splined maternal source components were projected back onto the magnetic field measurement space and then subtracted from the raw signal. The method was evaluated using data from 24 subjects. We compared the results of conventional, i.e., unsplined, ICS with our method, splined ICS, using matched filtering as a reference. Correlation and subjective assessment of the P-wave and QRS complex were used to assess the performance. Using ICS, we found that the P-wave was adversely affected in 7 of 24 (29%) subjects, all having correlations less than 0.8. Splined ICS showed negligible distortion and improved the signal fidelity to some extent in all subjects. We also demonstrated that maternal T-wave interference could be problematic when the fetal and maternal heartbeats were synchronous. In these instances, splined ICS was more effective than matched filtering. PMID:21712157

Yu, Suhong

2011-01-01

140

A Two-Timescale Discretization Scheme for Collocation

NASA Technical Reports Server (NTRS)

The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.

Desai, Prasun; Conway, Bruce A.

2004-01-01

141

Assignment 5: Curve Fitting by Cubic Spline, Bezier, and B-Spline Curves

Assignment 5: Curve Fitting by Cubic Spline, Bezier, and B-Spline Curves This exercise studies the problem of curve fitting. You are asked to design software to draw cubic Bezier and B-spline curves to fit as follows. As discussed in the class, find a cubic Bezier curve and a cubic B-spline curve to fit the given

Chen, Chaur-Chin

142

Signal Processing 59 (1997) 43-59 ECG data compression by spline approximation

SIGN& PROCESSING Signal Processing 59 (1997) 43-59 ECG data compression by spline approximation transform method for ECG data compression based on B-spline basis functions is proposed. The algorithm allows these basis functions to adapt their shape to the nonstationary behavior of ECG signals

Gabbouj, Moncef

143

Implementation of B-splines in a Conventional Finite Element Framework

The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B...

Owens, Brian C.

2010-01-16

144

ERIC Educational Resources Information Center

This study investigated the influence of frequency effects on the processing of congruent (i.e., having an equivalent first language [L1] construction) collocations and incongruent (i.e., not having an equivalent L1 construction) collocations in a second language (L2). An acceptability judgment task was administered to native and advanced

Wolter, Brent; Gyllstad, Henrik

2013-01-01

145

GEOMETRIC MODELLING WITH MULTIVARIATE B-SPLINES

GEOMETRIC MODELLING WITH MULTIVARIATE B-SPLINES by Timothy Irwin Mueller A dissertation submitted Mueller 1986 All Rights Reserved #12;ABSTRACT The tensor product B-spline surface, while regarded in CAGD. In recent years, the theory of univariate B-splines has been extended to multidimen- sional

Utah, University of

146

Mars Mission Optimization Based on Collocation of Resources

NASA Technical Reports Server (NTRS)

This paper presents a powerful approach for analyzing Martian data and for optimizing mission site selection based on resource collocation. This approach is implemented in a program called PROMT (Planetary Resource Optimization and Mapping Tool), which provides a wide range of analysis and display functions that can be applied to raw data or imagery. Thresholds, contours, custom algorithms, and graphical editing are some of the various methods that can be used to process data. Output maps can be created to identify surface regions on Mars that meet any specific criteria. The use of this tool for analyzing data, generating maps, and collocating features is demonstrated using data from the Mars Global Surveyor and the Odyssey spacecraft. The overall mission design objective is to maximize a combination of scientific return and self-sufficiency based on utilization of local materials. Landing site optimization involves maximizing accessibility to collocated science and resource features within a given mission radius. Mission types are categorized according to duration, energy resources, and in-situ resource utilization. Optimization results are shown for a number of mission scenarios.

Chamitoff, G. E.; James, G. H.; Barker, D. C.; Dershowitz, A. L.

2003-01-01

147

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

148

Reduction of InSAR Noise using Spherical Smoothing Splines

NASA Astrophysics Data System (ADS)

The phase of interferometric SAR is generally affected by decorrelation due to different type of noises such as thermal noise, temporal change and geometric differences. Phase measurements on interferograms must be unwrapped to extract applicable Information. Denoising the interferometric phase is very important to improve the accuracy of measurements and facilitate the phase unwrapping stage. Spherical splines can efficiently lower the noise, if the bandwith and smoothing parameters are chosen correctly. The spherical smoothing spline parameters, namely bandwidth and smoothing parameters, are chosen based on Generalized Cross Validation (GCV) function and signal to noise ratio (SNR). In this paper a new method is presented to reduce the phase noise, over interferograms generated from Envisat images, based on Spherical Splines. Statistical tests and numerical validation of results are used to prove the efficiency of this approach.

Esmaeili, M.; Yousefzadeh, T.

2010-05-01

149

The ground state energies and expectation values of atoms are given by Hartree-Fock-Roothaan calculations with one B-spline set. For the neutral atoms He to Uuo, the total energies, kinetic energies, potential energies, and virial ratios are tabulated. Our total energies are in excellent agreement with the highly accurate 10-digit numerical Hartree-Fock energies given by Koga and Thakkar [T. Koga, A.J. Thakkar, J. Phys. B 29 (1996) 2973]. The virial ratios are in complete agreement to within 12-digits of the exact value -2. Orbital energies, electron densities at the nucleus, electron-nucleus cusp ratios, and radial expectation values

Saito, Shiro L. [School of International Liberal Studies, Chukyo University, Toyota 470-0393 (Japan)], E-mail: luna@trinity.lets.chukyo-u.ac.jp

2009-11-15

150

NASA Astrophysics Data System (ADS)

The ground state energies and expectation values of atoms are given by Hartree-Fock-Roothaan calculations with one B-spline set. For the neutral atoms He to Uuo, the total energies, kinetic energies, potential energies, and virial ratios are tabulated. Our total energies are in excellent agreement with the highly accurate 10-digit numerical Hartree-Fock energies given by Koga and Thakkar [T. Koga, A.J. Thakkar, J. Phys. B 29 (1996) 2973]. The virial ratios are in complete agreement to within 12-digits of the exact value -2. Orbital energies, electron densities at the nucleus, electron-nucleus cusp ratios, and radial expectation values < rn> ( n = 2, 1, -1, -2, -3) are also given.

Saito, Shiro L.

2009-11-01

151

Curve Fitting with Conic Splines

Conic splines are formed by arcs of conics, each defined by its endpoints and the tangents at them plus an intermediate point. Instead of the common general equation that depends on five parameters, an equation with a single parameter is used, thus simplifying significantly the curve fitting problem. The resulting guided conics resemble Bezier polynomials and for parabolas are identical

Theodosios Pavlidis

1983-01-01

152

Spline regression hashing for fast image search.

Techniques for fast image retrieval over large databases have attracted considerable attention due to the rapid growth of web images. One promising way to accelerate image search is to use hashing technologies, which represent images by compact binary codewords. In this way, the similarity between images can be efficiently measured in terms of the Hamming distance between their corresponding binary codes. Although plenty of methods on generating hash codes have been proposed in recent years, there are still two key points that needed to be improved: 1) how to precisely preserve the similarity structure of the original data and 2) how to obtain the hash codes of the previously unseen data. In this paper, we propose our spline regression hashing method, in which both the local and global data similarity structures are exploited. To better capture the local manifold structure, we introduce splines developed in Sobolev space to find the local data mapping function. Furthermore, our framework simultaneously learns the hash codes of the training data and the hash function for the unseen data, which solves the out-of-sample problem. Extensive experiments conducted on real image datasets consisting of over one million images show that our proposed method outperforms the state-of-the-art techniques. PMID:22801510

Liu, Yang; Wu, Fei; Yang, Yi; Zhuang, Yueting; Hauptmann, Alexander G

2012-10-01

153

Linear Envelopes for Uniform B{spline Curves

Linear Envelopes for Uniform B{spline Curves David Lutterkort and Jorg Peters Abstract. We derive an e?ciently computable, tight bound on the distance between a uniform spline and its B{Spline control is the fact that a spline is closely outlined by its B-spline control polygon. The e?ciency of many

Peters, Jörg

154

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

NASA Technical Reports Server (NTRS)

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

155

Spectral collocation solutions to multiparameter Mathieu's system

Spectral collocation solutions to multiparameter Mathieu's system C. I. Gheorghiu "T. Popoviciu of a large number of speci- fied eigenvalues and eigenvectors of Mathieu's system as a multiparameter eigenvalue problem (MEP). The reduced wave equation, for small deflec- tions, is solved directly without

Hochstenbach, Michiel

156

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.

K. Parand; A. R. Rezaei; A. Taghavi

2010-08-13

157

Spline screw multiple rotations mechanism

NASA Technical Reports Server (NTRS)

A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.

Vranish, John M. (inventor)

1993-01-01

158

NASA Astrophysics Data System (ADS)

We have developed the Savart-Plate Lateral-shearing Interferometric Nuller for Exoplanets (SPLINE), which is a kind of a nulling interferometer, for directly imaging exoplanets. The SPLINE consists of two polarizers and a Savart plate between them. The SPLINE can theoretically obtain fully achromatic and stable nulled output. However, a drawback of the SPLINE is its low system throughput due to the polarizers. For improving the system throughput, we propose a dualchannel SPLINE using polarization beam splitters instead of the polarizers. We have carried out laboratory demonstration of the dual-channel SPLINE. The achievable contrast of the SPLINE is limited by residual speckles caused by surface roughness of optical elements. For improving the achievable contrast, we propose a method of wavefront correction using a liquid-crystal spatial light modulator (LCSLM). We have carried out preliminary laboratory demonstration using a liquid-crystal variable retarder (LCVR), instead of the LCSLM, for simulating the proposed wavefront correction method. We report the laboratory demonstration in this paper.

Kitou, Hirofumi; Murakami, Naoshi; Kida, Manabu; Baba, Naoshi; Matsuo, Taro; Kotani, Takayuki; Kawahara, Hajime; Tamura, Motohide

2014-07-01

159

Accuracy and speed in computing the Chebyshev collocation derivative

NASA Technical Reports Server (NTRS)

We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

Don, Wai-Sun; Solomonoff, Alex

1991-01-01

160

An algorithm for computing shape-preserving cubic spline interpolation to data

We present an algorithm for the construction of shape-preserving cubic splines interpolating a set of data point. The method\\u000a is based upon some existence properties recently developed. Graphical examples are given.

P. Costantini; R. Morandi

1984-01-01

161

Curve fitting and modeling with splines using statistical variable selection techniques

NASA Technical Reports Server (NTRS)

The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs, using the B-spline basis, were developed. The program for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.

Smith, P. L.

1982-01-01

162

Smoothness selection for penalized quantile regression splines.

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods. PMID:22628358

Reiss, Philip T; Huang, Lei

2012-01-01

163

Moving Surface Spline Interpolation Based on Greens Function

Some commonly used interpolation algorithms are analyzed briefly in this paper. Among all of the methods, biharmonic spline\\u000a interpolation, which is based on Greens function and proposed by Sandwell, has become the mainstream method for its high\\u000a precision, simplicity and flexibility. However, the minimum curvature method has two flaws. First, it suffers from undesirable\\u000a oscillations between data points, which is

Xingsheng Deng; Zhong-an Tang

2011-01-01

164

Application of B-splines to determining eigen-spectrum of Feshbach molecules

The B-spline basis set method is applied to determining the rovibrational\\u000aeigen-spectrum of diatomic molecules. A particular attention is paid to a\\u000achallenging numerical task of an accurate and efficient description of the\\u000avibrational levels near the dissociation limit (halo-state and Feshbach\\u000amolecules). Advantages of using B-splines are highlighted by comparing the\\u000aperformance of the method with that of the

A. Derevianko; E. Luc-Koenig; F. Masnou-Seeuws

2008-01-01

165

Application of B-splines to determining eigen-spectrum of

The B-spline basis set method is applied to determining the rovibrational eigen-spectrum of diatomic molecules. A particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the

A. Derevianko; E. Luc-Koenig; F. Masnou-Seeuws

166

Regularization of B-Spline Objects Guoliang Xu 1)

By a d-dimensional B-spline object (denoted as Od ), we mean a B-spline curve (d = 1), a B-spline surface a B-spline curve (O1), a B-spline surface (O2) or a B-spline volume (O3). Since B-spline basis is a special case of a B-spline curve, on the interval [0, 1]. Let t = t(s) = s(1-s)+s2, s [0, 1], [0, 2

Texas at Austin, University of

167

Triangular bubble spline surfaces

We present a new method for generating a Gn-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple Gn-condition between two neighboring bubble patches, which are used to construct surface patches, connected with Gn-continuity. For n?2, we describe the obtained Gn-condition in detail. It can be generalized to anyn?3. The construction of a single surface patch is based on GordonCoons interpolation for triangles. Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of G0, G1 and G2-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness. PMID:22267872

Kapl, Mario; Byrtus, Marek; Juttler, Bert

2011-01-01

168

Flexible coiled spline securely joins mating cylinders

NASA Technical Reports Server (NTRS)

Mating cylindrical members are joined by spline to form an integral structure. The spline is made of tightly coiled, high tensile-strength steel spiral wire that fits a groove between the mating members. It provides a continuous bearing surface for axial thrust between the members.

Coppernol, R. W.

1966-01-01

169

Discovery of Collocation Episodes in Spatiotemporal Data

Given a collection of trajectories of moving objects with different types (e.g., pumas, deers, vultures, etc.), we intro- ducetheproblem of discoveringcollocationepisodes in them (e.g., if a puma is moving near a deer, then a vulture is also going to move close to the same deer with high probabil- ity within the next 3 minutes). Collocation episodes catch the inter-movement regularities

Huiping Cao; Nikos Mamoulis; David W. Cheung

2006-01-01

170

Registration of sliding objects using direction dependent B-splines decomposition

NASA Astrophysics Data System (ADS)

Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. This work was presented in part at the 4th International Workshop on Pulmonary Image Analysis during the Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto, Canada (2011).

Delmon, V.; Rit, S.; Pinho, R.; Sarrut, D.

2013-03-01

171

Spline-based tests in survival analysis.

This paper examines a method for testing hypotheses on covariate effects in a proportional hazards model, and also on how effects change over time in regression analysis of survival data. The technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models. The basic idea is to formulate a flexible parametric alternative using fixed knot splines, together with a penalty function that penalizes noisy alternatives more than smooth ones, to focus the power of the tests toward smooth alternatives. The test statistics are the analogs of ordinary likelihood-based statistics, only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log-likelihood. Large-sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases. Numerical results suggest these approximations may be adequate with moderate sized samples. PMID:7981391

Gray, R J

1994-09-01

172

Radial spline assembly for antifriction bearings

NASA Technical Reports Server (NTRS)

An outer race carrier is constructed for receiving an outer race of an antifriction bearing assembly. The carrier in turn is slidably fitted in an opening of a support wall to accommodate slight axial movements of a shaft. A plurality of longitudinal splines on the carrier are disposed to be fitted into matching slots in the opening. A deadband gap is provided between sides of the splines and slots, with a radial gap at ends of the splines and slots and a gap between the splines and slots sized larger than the deadband gap. With this construction, operational distortions (slope) of the support wall are accommodated by the larger radial gaps while the deadband gaps maintain a relatively high springrate of the housing. Additionally, side loads applied to the shaft are distributed between sides of the splines and slots, distributing such loads over a larger surface area than a race carrier of the prior art.

Moore, Jerry H. (inventor)

1993-01-01

173

A collocation model for water-hammer dynamics with application to leak detection

This paper presents a new model for so-called water hammer equations based on a collocation method. This model is shown to fairly represent possible leak effects in a pipeline and thus to be useful in the purpose of leak detection. This is illustrated in simulation by an example of observer-based leak detector relying on this model.

Flor Lizeth Torres Ortiz; Gildas Besancon; Didier Georges

2008-01-01

174

Multi-leak estimator for pipelines based on an orthogonal collocation model

The orthogonal collocation method (OCM) is used to obtain an approximate solution of the water hammer equations which represent one-phase water flow transients in pipeline systems. The OCM provides solutions over the entire spatial domain, therefore it can be used to obtain an accurate model with possible leaks spatially distributed. An estimator can be designed based on the spatially-discretized model

Flor Lizeth Torres Ortiz; Gildas Besanon; Didier Georges

2009-01-01

175

Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation

Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation Brian R by tracking a second UAV flying a predefined pattern. Finally, a method of commanding the observation vector ^s UAV sensor line of sight unit vector p Attraction point u UAV Control vector xt Target state

176

On Using Collocation in Three Dimensions and Solving a Model Semiconductor Problem

A research code has been written to solve an elliptic system of coupled nonlinear par- tial differential equations of conservation form on a rectangularly shaped three-di- mensional domain. The code uses the method of collocation of Gauss points with tricubic Hermite piecewise continuous poly- nomial basis functions. The system of equa- tions is solved by iteration. The system of nonlinear

J. F. Marchiando

1995-01-01

177

In this paper, we consider the problem of matching 2D planar object curves from a database, and tracking moving object curves through an image sequence. The first part of the paper describes a curve data compression method using B-spline curve approximation. We present a new constrained active B-spline curve model based on the minimum mean square error (MMSE) criterion, and

Yu-hua Gu; Tardi Tjahjadi

1999-01-01

178

ECS 178 Course Notes KNOTS IN B-SPLINE CURVES

ECS 178 Course Notes KNOTS IN B-SPLINE CURVES Kenneth I. Joy Institute for Data Analysis concept in B-spline curves. First, they are tied to the order of the spline k, and the number of control The first result is that a B-spline curve is invariant under translation of the knot sequence. The set

California at Davis, University of

179

The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the point particle appear in the equation in the form of the Dirac $\\delta$-function and its derivative. For the approximation of singular source terms, we use the direct derivative projection method without any regularization. The gravitational waveforms are evaluated as a function of time. We compare the results of the spectral collocation method with those of the explicit second-order central-difference method. The numerical results show that the spectral collocation approximation with the direct projection method is accurate and converges rapidly when compared with the finite-difference method.

Jae-Hun Jung; Gaurav Khanna; Ian Nagle

2007-11-16

180

Rational-spline approximation with automatic tension adjustment

NASA Technical Reports Server (NTRS)

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Schiess, J. R.; Kerr, P. A.

1984-01-01

181

Direct optimization method for reentry trajectory design

NASA Astrophysics Data System (ADS)

The software package called `Reentry and Atmospheric Transfer Trajectory' (RATT) was developed under ESA contract for the design of atmospheric trajectories. It includes four software TOP (Trajectory OPtimization) programs, which optimize reentry and aeroassisted transfer trajectories. 6FD and 3FD (6 and 3 degrees of freedom Flight Dynamic) are devoted to the simulation of the trajectory. SCA (Sensitivity and Covariance Analysis) performs covariance analysis on a given trajectory with respect to different uncertainties and error sources. TOP provides the optimum guidance law of a three degree of freedom reentry of aeroassisted transfer (AAOT) trajectories. Deorbit and reorbit impulses (if necessary) can be taken into account in the optimization. A wide choice of cost function is available to the user such as the integrated heat flux, or the sum of the velocity impulses, or a linear combination of both of them for trajectory and vehicle design. The crossrange and the downrange can be maximized during reentry trajectory. Path constraints are available on the load factor, the heat flux and the dynamic pressure. Results on these proposed options are presented. TOPPHY is the part of the TOP software corresponding to the definition and the computation of the optimization problemphysics. TOPPHY can interface with several optimizes with dynamic solvers: TOPOP and TROPIC using direct collocation methods and PROMIS using direct multiple shooting method. TOPOP was developed in the frame of this contract, it uses Hermite polynomials for the collocation method and the NPSOL optimizer from the NAG library. Both TROPIC and PROMIS were developed by the DLR (Deutsche Forschungsanstalt fuer Luft und Raumfahrt) and use the SLSQP optimizer. For the dynamic equation resolution, TROPIC uses a collocation method with Splines and PROMIS uses a multiple shooting method with finite differences. The three different optimizers including dynamics were tested on the reentry trajectory of the ACRV (Assured crew return vehicle), the emergency capsule of the Space Station Freedom. Conclusions are drawn from the different optimization method comparisons. The collocation method (TOPOP and TROPIC) is robust and preferable for obtaining an initial guess of the optimum trajectory but not accurate enough. A refinement of the optimum trajectory is performed with PROMIS which is more accurate for the dynamic equation resolution.

Jallade, S.; Huber, P.; Potti, J.; Dutruel-Lecohier, G.

182

Optimal spline smoothing of fMRI time series by generalized cross-validation.

Linear parametric regression models of fMRI time series have correlated residuals. One approach to address this problem is to condition the autocorrelation structure by temporal smoothing. Smoothing splines with the degree of smoothing selected by generalized cross-validation (GCV-spline) provide a method to find an optimal smoother for an fMRI time series. The purpose of this study was to determine if GCV-spline of fMRI time series yields unbiased variance estimates of linear regression model parameters. GCV-spline was evaluated with a real fMRI data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fMRI data. This study only considered fMRI experimental designs of boxcar type. The results from the real data suggest that GCV-spline determines appropriate amounts of smoothing. The simulations show that the variance estimates are, on average, unbiased. The unbiased variance estimates come at some cost to signal detection efficiency. This study demonstrates that GCV-spline is an appropriate method for smoothing fMRI time series. PMID:12725770

Carew, John D; Wahba, Grace; Xie, Xianhong; Nordheim, Erik V; Meyerand, M Elizabeth

2003-04-01

183

Efficient modeling of the earth's magnetic field with harmonic splines

The geophysical method of harmonic splines produces magnetic field models at th5 core surface which are maximally smooth to the extent that they minimize certain special norms, and do not exhibit the highly oscillatory fields generated by models derived from a least-square analysis with a truncated sphe5ical harmonic series. Such modeling, however, calls for the solution of a square system

R. L. Parker; Loren Shure

1982-01-01

184

ECS 178 Course Notes THE B-SPLINE PATCH

is the surface extension of the B-spline curve. Whereas a curve is a function of one variable and takes for the Bezier patches and B-spline curves. Definition of the B-spline Patch The extension of B-spline curves) looks much like the analytic equation for the B-spline curve the sums run over all the control points

California at Davis, University of

185

A B-spline approach for empirical mode decompositions

We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated\\u000a by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline\\u000a intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments.\\u000a We present numerical implementations of the B-spline

Qiuhui Chen; Norden Huang; Sherman D. Riemenschneider; Yuesheng Xu

2006-01-01

186

Optimization of Low-Thrust Spiral Trajectories by Collocation

NASA Technical Reports Server (NTRS)

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.

Falck, Robert D.; Dankanich, John W.

2012-01-01

187

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only requires information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed the method is suitable for the integration into large scale neuromusculoskeletal models. PMID:22176708

Sartori, Massimo; Reggiani, Monica; van den Bogert, Antonie J.; Lloyd, David G.

2011-01-01

188

Collocation and its impacts on central office backup power systems

The 1996 Telecommunications Act led to a huge expansion in the number and size of collocators (CLECs or Collocated Local Exchange Carriers). Due to maintenance, weight, and environmental issues associated with DC plants; CLECs usually want the incumbent (ILEC) to provide power to their equipment. The incumbents can recoup their costs if they take the proper steps; however there are

Curtis Ashton

1998-01-01

189

Convex Interpolating Splines of Arbitrary Degree

NASA Technical Reports Server (NTRS)

Shape preserving approximations are constructed by interpolating the data with polynomial splines of arbitrary degree. A regularity condition is formulated on the data which insures the existence of such a shape preserving spline, an algorithm is presented for its construction, and the uniform norm of the error is bound which results when the algorithm is used to produce an approximation to a given f epsilon Ca,b.

Neuman, E.

1985-01-01

190

Relative orbit control of collocated geostationary spacecraft

NASA Astrophysics Data System (ADS)

A relative orbit control concept for collocated geostationary spacecraft is presented. One chief spacecraft, controlled from the ground, is responsible for the orbit determination and control of the remaining vehicles. Any orbit relative to the chief is described in terms of equinoctial orbit element differences and a linear mapping is employed for quick transformation from relative orbit measurements to orbit element differences. It is demonstrated that the concept is well-suited for spacecraft that are collocated using eccentricity-inclination vector separation and this formulation still allows for the continued use of well established and currently employed stationkeeping schemes, such as the Sun-pointing-perigee strategy. The relative approach allows to take determinisitc thruster cross-coupling effects in the computation of stationkeeping corrections into account. The control cost for the proposed concept is comparable to ground-based stationkeeping. A relative line-of-sight constraint between spacecraft separated in longitude is also considered and an algorithm is developed to provide enforcement options. The proposed on-board control approach maintains the deputy spacecraft relative orbit, is competitive in terms of propellant consumption, allows enforcement of a relative line-of-sight constraint and offers increased autonomy and flexibility for future missions.

Rausch, Raoul R.

191

NASA Technical Reports Server (NTRS)

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Gottlieb, David; Shu, Chi-Wang

1994-01-01

192

Construction of fractional spline wavelet bases

NASA Astrophysics Data System (ADS)

We extend Schoenberg's B-splines to all fractional degrees (alpha) > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions x(alpha ) (one-sided) or x(alpha )* (symmetric); in each case, they are (alpha) -Hoelder continuous for (alpha) > 0. They satisfy most of the properties of the traditional B-splines; in particular, the Biesz basis condition and the two-scale relation, which makes them suitable for the construction of new families of wavelet bases. What is especially interesting from a wavelet perspective is that the fractional B-splines have a fractional order of approximately ((alpha) + 1), while they reproduce the polynomials of degree [(alpha) ]. We show how they yield continuous-order generalization of the orthogonal Battle- Lemarie wavelets and of the semi-orthogonal B-spline wavelets. As (alpha) increases, these latter wavelets tend to be optimally localized in time and frequency in the sense specified by the uncertainty principle. The corresponding analysis wavelets also behave like fractional differentiators; they may therefore be used to whiten fractional Brownian motion processes.

Unser, Michael A.; Blu, Thierry

1999-10-01

193

Generalized Thin-Plate Spline Warps Adrien Bartoli1

Generalized Thin-Plate Spline Warps Adrien Bartoli1 Mathieu Perriollat2 Sylvie Chambon3 1 Universit Corresponding author: Adrien Bartoli Adrien.Bartoli@gmail.com Abstract The Thin-Plate Spline warp has been shown

Bartoli, Adrien

194

Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

1988-01-01

195

Using Rational B-Spline Neural Networks for Curve Approximation

Rational B-spline neural network (RBNN) is a neural network can be used for curves and surfaces approximation using rational B-spline model. The approximation is solved by learning process of rational B-spline neural networks from observation data points. A hybrid genetic based algorithm for optimizing knots, control points and weights of RBNN

TANG VAN TO

196

B-SPLINE NONPARAMETRIC REGRESSION MODELS AND INFORMATION CRITERIA

: (a) Discontinuity. (b) Heteroscedasticity. The dashed curves are estimated by B-spline nonlinearB-SPLINE NONPARAMETRIC REGRESSION MODELS AND INFORMATION CRITERIA Seiya Imoto and Sadanori Konishi Abstract. We consider the use of B-spline nonparametric regression models to analyze data with complex

Imoto, Seiya

197

B(asic)-Spline Basics Carl de Boor

curves: Allow the coefficients, be they B-spline coefficients or coefficients in some polynomial form (univariate) B-splines that are of interest in CAGD. The intent is to give a self-contained and complete development of the material in as simple and direct a way as possible. For this reason, the B-splines

Liblit, Ben

198

Efficient one-sided linearization of spline geometry Jorg Peters

curved object. Consequently, despite their geometrically indicative control structure, objects in b-spline. This paper surveys a new, computationally efficient technique for lin- earizing curved spline geometry, bounding such geometry from one side and constructing curved spline geometry that stays to one side

Peters, Jörg

199

B(asic)Spline Basics Carl de Boor #

curves: Allow the coe#cients, be they Bspline coe#cients or coe#cients in some polynomial form (univariate) Bsplines that are of interest in CAGD. The intent is to give a selfcontained and complete development of the material in as simple and direct a way as possible. For this reason, the Bsplines

Liblit, Ben

200

Bezier-and B-spline techniques Hartmut Prautzsch

B´ezier- and B-spline techniques Hartmut Prautzsch Wolfgang Boehm Marco Paluszny March 26, 2002 #12- spline representations evolved as the major tool to handle curves and surfaces. These representations. It is the purpose of this book to provide a solid and unified derivation of the various properties of B´ezier and B-spline

Prautzsch, Hartmut

201

B-Splines for Physically-Based Michael M. Stark

January 9, 2002 Abstract Although B-spline curves and surfaces have enjoyed a long established place Richard F. Riesenfeld School of Computing University of Utah Abstract Although B-spline curvesB-Splines for Physically-Based Rendering Michael M. Stark William Martin Elaine Cohen Tom Lyche

Utah, University of

202

Significance of operating experience with poison splines at KE Reactor

The demonstrated operating efficiency performance which has resulted from poison spline usage forces an economic decision concerning the self-supported and bumper fuel element programs. As originally conceived the projection fuel elements would preclude the insertion of a spline under the fuel charge; thus it is very important that means be devised either to make poison spline usage compatible with future

1960-01-01

203

B-Splines Approximation Industrial and Systems Engineering

1 B-Splines Approximation Yuan Yuan Industrial and Systems Engineering University of Wisconsin Madison Apr.27, 2010 #12;Outline · B-splines and their properties Subspace $k,t · B-splines approximation Distance from continuous functions to $k,t · Knots placement · Questions? 2 #12;B

Recht, Ben

204

Moment Computation for Objects with Spline Curve Boundary

A new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary. The explicit formulae are obtained for area and low order moment calculation. The complexity of calculation depends on the moment order, spline degree, and the number of control points used in spline representation. The formulae proposed use the advantage

Stanislav Sheynin; Alexander Tuzikov

2003-01-01

205

In this paper we are going to discuss and analyze the different methods which are developed to detect the Lung nodules which cause the lung cancer. At the end of analyzing different methods, the new methodology of detecting the lung nodules using Spline Wavelet technique has been proposed in this paper. Continuous modeling of data often required in medical imaging, Polynomial Splines are especially useful to consider image data as continuum rather than discrete array of pixels. The multi resolution property of Splines makes them prime candidates for constructing wavelet bases. Wavelet tool also let us to compress the original CT image to greater factor without any sacrifice in accuracy of nodule detection. Different Algorithms for segmentation/ detection of lung nodules from CT image is discussed in this paper. PMID:23675284

Senthil Kumar, T. K.; Ganesh, E. N.

2013-01-01

206

NASA Technical Reports Server (NTRS)

A partial spline model is a model for a response as a function of several variables, which is the sum of a smooth function of several variables and a parametric function of the same plus possibly some other variables. Partial spline models in one and several variables, with direct and indirect data, with Gaussian errors and as an extension of GLIM to partially penalized GLIM models are described. Application to the modeling of change of regime in several variables is described. Interaction splines are introduced and described and their potential use for modeling non-linear interactions between variables by semiparametric methods is noted. Reference is made to recent work in efficient computational methods.

Wahba, Grace

1987-01-01

207

Translating Collocations for Bilingual Lexicons: A Statistical Approach

Collocations are notoriously difficult for non-native speakers to translate, primarily because they are opaque and cannot be translated on a word-by-word basis. We describe a program named Champollion which, given a pair of parallel corpora in two different languages and a list of collocations in one of them, automatically produces their translations. Our goal is to provide a tool for

Frank A. Smadja; Kathleen R. Mckeown; Vasileios Hatzivassiloglou

1996-01-01

208

Subcell resolution in simplex stochastic collocation for spatial discontinuities

NASA Astrophysics Data System (ADS)

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC-SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers' equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC-SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

Witteveen, Jeroen A. S.; Iaccarino, Gianluca

2013-10-01

209

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

210

A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion.

This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.]. PMID:25324060

Steininger, Gavin; Dosso, Stan E; Holland, Charles W; Dettmer, Jan

2014-10-01

211

Smoothing two-dimensional Malaysian mortality data using P-splines indexed by age and year

NASA Astrophysics Data System (ADS)

Nonparametric regression implements data to derive the best coefficient of a model from a large class of flexible functions. Eilers and Marx (1996) introduced P-splines as a method of smoothing in generalized linear models, GLMs, in which the ordinary B-splines with a difference roughness penalty on coefficients is being used in a single dimensional mortality data. Modeling and forecasting mortality rate is a problem of fundamental importance in insurance company calculation in which accuracy of models and forecasts are the main concern of the industry. The original idea of P-splines is extended to two dimensional mortality data. The data indexed by age of death and year of death, in which the large set of data will be supplied by Department of Statistics Malaysia. The extension of this idea constructs the best fitted surface and provides sensible prediction of the underlying mortality rate in Malaysia mortality case.

Kamaruddin, Halim Shukri; Ismail, Noriszura

2014-06-01

212

Modeling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines

NASA Astrophysics Data System (ADS)

Our intention is the modeling of seismic wave propagation from displacement measurements by seismographs at the Earth's surface. The elastic behaviour of the Earth is usually described by the Cauchy-Navier equation. A system of fundamental solutions for the Fourier transformed Cauchy-Navier equation are the Hansen vectors L, M and N. We apply an inverse Fourier transform to obtain an orthonormal function system depending on time and space. By means of this system we construct certain splines, which are then used for interpolating the given data. Compared to polynomial interpolation, splines have the advantage that they minimize some curvature measure and are, therefore, smoother. First, we test this method on a synthetic wave function. Afterwards, we apply it to realistic earthquake data. (P. Kammann, Modelling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines, Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2005)

Kammann, P.

2005-12-01

213

Tensegrity spline beam and grid shell structures

This paper considers a class of tensegrity structures with continuous tubular compression booms forming curved splines, which may be deployed from straight by prestressing a cable bracing system. A free-form arch structure for the support of prestressed membranes is reviewed and the concepts are extended to a two-way spanning system for double layer grid shell structures. A numerical analysis based

S. M. L Adriaenssens; M. R Barnes

2001-01-01

214

Monotone and convex cubic spline interpolation

Given a set of monotone and convex data, we present a necessary and sufficient condition for the existence of cubic differentiable\\u000a interpolating splines which are monotone and convex. Further, we discuss their approximation properties when applied to the\\u000a interpolation of functions having preassigned degree of smoothness.

Paolo Costantini; Rossana Morandi

1984-01-01

215

Local Filters of B-spline Wavelets

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the local- ity of their decomposition and reconstruction filters. How- ever, Haar wavelets are not satisfactory for some applica- tions due to their non-continuous behaviour. Having a par- ticular level of smoothness is important for many applica- tions. B-spline wavelets are capable of

Faramarz F. Samavati; Richard H. Bartels

2004-01-01

216

Quantitative Coronary Angiography with Deformable Spline Models

Although current edge-following schemes can be very efficient in determining coronary boundaries, they may fail when the feature to be followed is disconnected (and the scheme is unable to bridge the discontinuity) or branch points exist where the best path to follow is indeterminate. Here, the authors present new deformable spline algorithms for determining vessel boundaries, and enhancing their centerline

Andreas K. Klein; F. Lee; Amir A. Amini

1997-01-01

217

A Spline Regression Model for Latent Variables

ERIC Educational Resources Information Center

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the

Harring, Jeffrey R.

2014-01-01

218

Continuous Groundwater Monitoring Collocated at USGS Streamgages

NASA Astrophysics Data System (ADS)

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 USGS Fact Sheet 2012-3054 was released online, summarizing the results of the pilot project.

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

2012-12-01

219

Collocation and Pattern Recognition Effects on System Failure Remediation

NASA Technical Reports Server (NTRS)

Previous research found that operators prefer to have status, alerts, and controls located on the same screen. Unfortunately, that research was done with displays that were not designed specifically for collocation. In this experiment, twelve subjects evaluated two displays specifically designed for collocating system information against a baseline that consisted of dial status displays, a separate alert area, and a controls panel. These displays differed in the amount of collocation, pattern matching, and parameter movement compared to display size. During the data runs, subjects kept a randomly moving target centered on a display using a left-handed joystick and they scanned system displays to find a problem in order to correct it using the provided checklist. Results indicate that large parameter movement aided detection and then pattern recognition is needed for diagnosis but the collocated displays centralized all the information subjects needed, which reduced workload. Therefore, the collocated display with large parameter movement may be an acceptable display after familiarization because of the possible pattern recognition developed with training and its use.

Trujillo, Anna C.; Press, Hayes N.

2007-01-01

220

Modeling and rendering heterogeneous fog in real-time using B-Spline wavelets

Modeling and rendering heterogeneous fog in real-time using B-Spline wavelets Anthony Giroud-la-Vallée biri@univ-umlv.fr ABSTRACT Heterogeneous fogs are often modeled with several layers of different method to render heterogeneous fog in real-time. The extinction function of our fog, related to its

Paris-Sud XI, Université de

221

Reconfigurable arrays of collocated sensors and actuators for modal isolation

NASA Astrophysics Data System (ADS)

Arrays of sensors and actuators designed to provide robust broadband feedback control with high performance and limited modeling are the subject of this paper. The reconfigurable array technique proposed here enables the design of reduced- order controllers for complex structures and offers the potential to improve closed-loop robustness and to broaden the region of good performance even as the plant changes. The weighted summation of sensor signals senses the modes that are relevant to performance while rejecting the remaining modes; therefore reducing the required complexity of the controller. These weights are obtained from the minimization of a cost function and under certain assumptions; it can be shown that a single optimum solution exists. The use of reconfigurable arrays is motivated by the need to control the vibration of complex structures. A thirty element collocated actuator and sensor array was bonded to a cylinder section. Array weights were computed and successfully applied to isolate target modes. Different methods of computing the weights are implemented and compared. The deleterious effects of spatial aliasing and the performance as a function of the array size are experimentally explored.

Fripp, Michael L. R.; Atalla, Mauro J.; Hagood, Nesbitt W.

2000-06-01

222

NASA Astrophysics Data System (ADS)

We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.

Ruberti, M.; Averbukh, V.; Decleva, P.

2014-10-01

223

CAGD Handbook Spline Basics (as of 25sep01) 1. Piecewise polynomials (p. 1)

CAGD Handbook Spline Basics (as of 25sep01) 1. Piecewise polynomials (p. 1) 2. B-splines defined. 13) 11. Differentiation and integration (p. 14) 12. Evaluation (p. 15) 13. Spline curves (p. 16) 14 that (univariate) splines, i.e., smooth piecewise polynomial functions, are weighted sums of B-splines. 1

Liblit, Ben

224

CAGD Handbook # Spline Basics (as of 25sep01) 1. Piecewise polynomials (p. 1)

CAGD Handbook # Spline Basics (as of 25sep01) 1. Piecewise polynomials (p. 1) 2. Bsplines defined. 13) 11. Di#erentiation and integration (p. 14) 12. Evaluation (p. 15) 13. Spline curves (p. 16) 14 that (univariate) splines, i.e., smooth piecewise polynomial functions, are weighted sums of Bsplines. 1

Liblit, Ben

225

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation a particular choice of algorithm involving multilevel collocation and smoothing. Our test case linearization was not continuously invertible. The smoothing `iteration' was thus intended to deal

Fasshauer, Greg

226

Curve Matching by using B-spline Curves

This paper presents an algorithm for estimating the control points of the B-spline and curve matching which is achieved by using the dissimilarity measure based on the knot associated with the B-spline curves. The B-splines stand as one of the most efficient curve representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and

Tet Toe; Tang Van To

227

Multiple-knot and rational cubic beta-splines

Goodman (Properties of Beta-splines. J. Approx. Theory 44, 2 (June 1985), 132-153) gave an explicit formula for cubic Beta-splines on a uniform knot sequence with varying ?1 and ?2 values at the knots. We establish an alternative explicit formula for cubic Beta-splines on a nonuniform knot sequence with constant ?1 = 1 and varying ?2 values at the knots. This

Barry Joe

1989-01-01

228

Development and flight tests of vortex-attenuating splines

NASA Technical Reports Server (NTRS)

The ground tests and full-scale flight tests conducted during development of the vortex-attenuating spline are described. The flight tests were conducted using a vortex generating aircraft with and without splines; a second aircraft was used to probe the vortices generated in both cases. The results showed that splines significantly reduced the vortex effects, but resulted in some noise and climb performance penalties on the generating aircraft.

Hastings, E. C., Jr.; Patterson, J. C., Jr.; Shanks, R. E.; Champine, R. A.; Copeland, W. L.; Young, D. C.

1975-01-01

229

Scattered Data Interpolation with Multilevel B-Splines

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines areintroduced to compute a C2-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofinehierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desiredinterpolation function. Large performance gains are realized by using B-spline refinement

Seungyong Lee; George Wolberg; Sung Yong Shin

1997-01-01

230

Isotropic polyharmonic B-splines: scaling functions and wavelets

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of ra- dial basis functions. We show that Rabut's elementary polyhar- monic B-splines do not converge to a Gaussian as the order param- eter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more

Dimitri Van De Ville; Thierry Blu; Michael Unser

2005-01-01

231

Discovery of Collocation Episodes in Spatiotemporal Data Huiping Cao, Nikos Mamoulis, and David W, vultures, etc.), we intro- duce the problem of discovering collocation episodes in them (e.g., if a puma within the next 3 minutes). Collocation episodes catch the inter-movement regularities among different

Cheung, David Wai-lok

232

Collocational Strategies of Arab Learners of English: A Study in Lexical Semantics.

ERIC Educational Resources Information Center

Arab learners of English encounter a serious problem with collocational sequences. The present study purports to determine the extent to which university English language majors can use English collocations properly. A two-form translation test of 16 Arabic collocations was administered to both graduate and undergraduate students of English. The

Muhammad, Raji Zughoul; Abdul-Fattah, Hussein S.

233

Collocation, Semantic Prosody, and Near Synonymy: A Cross-Linguistic Perspective

This paper explores the collocational behaviour and semantic prosody of near synonyms from a cross-linguistic perspective. The importance of these concepts to language learning is well recognized. Yet while collocation and semantic prosody have recently attracted much interest from researchers studying the English language, there has been little work done on collocation and semantic prosody on languages other than English.

RICHARD XIAO; TONY MCENERY

2006-01-01

234

The objectives of this paper are to contrast the relative variability of replicate laboratory measurements of selected chemical components of fine particulate matter (PM) with total variability from collocated measurements and to compare the magnitudes of the uncertainties determined from collocated sampler data with those currently being provided to U.S. Environmental Protection Agency (EPA)'s Air Quality System (AQS) database by RTI International (RTI). Pointwise uncertainty values are needed for modeling and data analysis and should include all the random errors affecting each data point. Total uncertainty can be decomposed into two primary components: analytical measurement uncertainty and sampling uncertainty. Analytical measurement uncertainties are relatively easy to calculate from routine quality control (QC) data. Sampling uncertainties, on the other hand, are comparatively difficult to measure. In this paper, the authors describe data from collocated samplers to provide a snapshot of whole-system uncertainty for several important chemical species. The components of uncertainty were evaluated for key species from each of the analytical methods employed by the PM2.5 Speciation Trends Network (STN) program: gravimetry, ion chromatography (IC), X-ray fluorescence (XRF), and thermal-optical analysis for organic carbon and elemental carbon. The results show that the laboratory measurement uncertainties are typically very small compared with uncertainties calculated from the differences between samples collected from collocated samplers. These differences are attributable to the "field" components uncertainty, which may include contamination and/or losses during shipping, handling, and sampling, as well as other distortions of the concentration level due to flow and sample volume variations. Uncertainties calculated from the collocation results were found to be generally similar to the uncertainties currently being loaded into EPA's AQS system, with some exceptions described below. PMID:16681213

Flanagan, James B; Jayanty, R K M; Rickman, Edward E; Peterson, Max R

2006-04-01

235

Efficient evaluation of nonlocal pseudopotentials via Euler exponential spline interpolation.

An Euler exponential spline (EES) based formalism is employed to derive new expressions for the electron-atom nonlocal pseudopotential interaction (NL) in electronic structure calculations performed using a plane wave basis set that can be computed more rapidly than standard techniques. Two methods, one that is evaluated by switching between real and reciprocal space via fast Fourier transforms, and another that is evaluated completely in real space, are described. The reciprocal-space or g-space-based technique, NLEES-G, scales as NMlogM approximately N2logN, where N is the number of electronic orbitals and M is the number of plane waves. The real-space based technique, NLEES-R, scales as N2. The latter can potentially be used within a maximally spatially localized orbital method to yield linear scaling, while the former could be employed within a maximally delocalized orbital method to yield NlogN scaling. This behavior is to be contrasted with standard techniques, which scale as N3. The two new approaches are validated using several examples, including solid silicon and liquid water, and demonstrated to be improvements on other, reduced-order nonlocal techniques. Indeed, the new methods have a low overhead and become more efficient than the standard technique for systems with roughly 20 or more atoms. Both NLEES methods are shown to work stably and efficiently within the Car-Parrinello ab initio molecular dynamics framework, owing to the existence of p-2 continuous derivatives of a pth-order spline. PMID:16144012

Lee, Hee-Seung; Tuckerman, Mark E; Martyna, Glenn J

2005-09-01

236

An Algebraic Spline Model of Molecular Surfaces for Energetic Computations

In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation. PMID:21519111

Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang

2009-01-01

237

The B-spline basis set method is applied to determining the rovibrational eigen-spectrum of diatomic molecules. A particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the

A. Derevianko; E. Luc-Koenig; F. Masnou-Seeuws

2009-01-01

238

Quantitative analysis of dynamic contrast-enhanced MR images based on Bayesian P-splines.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided. PMID:19272996

Schmid, Volker J; Whitcher, Brandon; Padhani, Anwar R; Yang, Guang-Zhong

2009-06-01

239

Cardiac motion tracking with multilevel B-splines and SinMod from tagged MRI

NASA Astrophysics Data System (ADS)

Cardiac motion analysis can play an important role in cardiac disease diagnosis. Tagged magnetic resonance imaging (MRI) has the ability to directly and non-invasively alter tissue magnetization and produce tags on the deforming tissue. This paper proposes an approach to analysis of tagged MR images using a multilevel B-splines fitting model incorporating phase information. The novelty of the proposed technique is that phase information is extracted from SinMod.1 By using real tag intersections extracted directly from tagged MR image data and virtual tag intersections extracted from phase information, both considered to be scattered data, multilevel B-spline fitting can result in accurate displacement motion fields. The B-spline approximation which also serves to remove noise in the displacement measurements is performed without specifying control point locations explicitly and is very fast. Dense virtual tag intersections based on SinMod were created and incorporated into the multilevel B-spline fitting process. Experimental results on simulated data from the 13- parameter kinematic model of Arts et al.2 and in vivo canine data demonstrate further improvement in accuracy and effectiveness of the proposed method.

Wang, Hui; Amini, Amir A.

2011-03-01

240

Mobiphos: a collocated-synchronous mobile photo sharing application

People use photographs for numerous reasons with one of the most common uses of both analog and digital photographs is as an artifact to share and discuss with others. While the practic e of photo sharing has been thoroughly examined in the HCI community, there is currently very little research on easily capturing and sharing content within groups of collocated

James Clawson; Amy Voida; Nirmal J. Patel; Kent Lyons

2008-01-01

241

A Self-Sensing Piezoelectric Actuator for Collocated Control

A technique has been developed which allows a single piece of piezoelec tric material to concurrently sense and actuate in a closed loop system. The motivation behind the technique is that such a self-sensing actuator will be truly collocated and has applications in active and intelligent structures, such as vibration suppression. A theoreti cal basis for the self-sensing actuator is

Jeffrey J. Dosch; Daniel J. Inman; Ephrahim Garcia

1992-01-01

242

Validation of ocean wind and wave data using triple collocation

Significant wave height and wind speed fields from ERA-40 are validated against buoy, ERS-1, and Topex altimeter measurements. To do so, we propose and apply a triple collocation statistical model. The model takes into account the random errors in observations and model results and allows the estimation of the variances of the errors. We first examine the case where the

S. Caires; A. Sterl

2003-01-01

243

NASA/CR2003212153 A Stochastic Collocation Algorithm

NASA/CR2003212153 A Stochastic Collocation Algorithm for Uncertainty Analysis Lionel Mathelin and M. Yousuff Hussaini Florida State University, Tallahassee, Florida February 2003 #12;The NASA STI Program Office . . . in Profile Since its founding, NASA has been dedicated to the advancement

Mathelin, Lionel

244

Flatness and collocation based methodology for satellite trajectory planning

In the aim of providing Low Earth Orbit (LEO) satellite with a highly reliable path planner, we develop in this paper a methodology based on flatness and collocation. We prove here that we can cut down time of orbital maneuvers to increase duration of data acquisition. Simulation results demonstrate the potential and advantages of the proposed approach with respect to

Christophe Louembet; Franck Cazaurang; Ali Zolghadri

245

Redefining Creativity--Analyzing Definitions, Collocations, and Consequences

ERIC Educational Resources Information Center

How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,

Kampylis, Panagiotis G.; Valtanen, Juri

2010-01-01

246

NASA Technical Reports Server (NTRS)

A method based on the use of constrained spline fits is used to overcome the difficulties arising when body-wave data in the form of T-delta are reduced to the tau-p form in the presence of cusps. In comparison with unconstrained spline fits, the method proposed here tends to produce much smoother models which lie approximately in the middle of the bounds produced by the extremal method. The method is noniterative and, therefore, computationally efficient. The method is applied to the lunar seismic data, where at least one triplication is presumed to occur in the P-wave travel-time curve. It is shown, however, that because of an insufficient number of data points for events close to the antipode of the center of the lunar network, the present analysis is not accurate enough to resolve the problem of a possible lunar core.

Jarosch, H. S.

1982-01-01

247

High order approximation of conic sections by quadratic splines

High order approximation of conic sections by quadratic splines Michael Floater SINTEF P.O. Box 124, Blindern 0314 Oslo Norway December 1993. Revised, October 1994 Abstract. Given a segment of a conic section and cylinder. Keywords. approximation, conic sections, quadratic splines §1. Introduction The approximate

Floater, Michael S.

248

Instant Trend-Seasonal Decomposition of Time Series with Splines

Instant Trend-Seasonal Decomposition of Time Series with Splines Luis Francisco Rosales1 Tatyana to decompose a times series into trend, seasonal and remainder components. This fully data-driven technique is based on penalized splines and makes an explicit characterization of the varying seasonality

Krivobokova, Tatyana

249

Flexible smoothing with B-splines and penalties

B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections

Paul H. C. Eilers; Brian D. Marx

1996-01-01

250

A multiresolution spline with application to image mosaics

We define a multiresolution spline technique for combining two or more images into a larger image mosaic. In this procedure, the images to be splined are first decomposed into a set of band-pass filtered component images. Next, the component images in each spatial frequency hand are assembled into a corresponding bandpass mosaic. In this step, component images are joined using

Peter J. Burt; Edward H. Adelson

1983-01-01

251

This article presents a variant of the spectral turning bands method that allows fast and accurate simulation of intrinsic\\u000a random fields with power, spline, or logarithmic generalized covariances. The method is applicable in any workspace dimension\\u000a and is not restricted in the number and configuration of the locations where the random field is simulated; in particular,\\u000a it does not require

Xavier Emery; Christian Lantujoul

2008-01-01

252

ANZIAM J. 42 (E) ppC712--C734, 2000 C712 Finite element thin plate splines in density

ANZIAM J. 42 (E) ppC712--C734, 2000 C712 Finite element thin plate splines in density estimation approximated by a finite element method and that doing so will make the method scalable. Contents 1---the Roberts Estimate . . . . . . . . . . . . . . C720 3 Approximating a Solution C722 3.1 A Finite Element

Keinan, Alon

253

NASA Astrophysics Data System (ADS)

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.

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

2014-01-01

254

CSC6870 Computer Graphics II B-Spline Curves and NURBS

CSC6870 Computer Graphics II B-Spline Curves and NURBS CSC6870 Computer Graphics II Motivation continuity CSC6870 Computer Graphics II B-spline Curve CSC6870 Computer Graphics II B-Splines · Curve Computer Graphics II B-Spline Properties · Double endpoint: Curve will be tangent to line between first

Hua, Jing

255

Non-uniform Subdivision for B-splines of Arbitrary Degree S. Schaefer, R. Goldman

degree. To subdivide a B-spline curve of degree d, the algorithm proceeds in two phases. The first step a sequence of piecewise linear curves that in the limit converges to the uniform B-spline defined-Riesenfeld subdivision, can be constructed for non-uniform B-splines. In particular, given a B-spline curve of degree d

Schaefer, Scott

256

Surface Reconstruction with Triangular B-splines Ying He and Hong Qin

will produce a discontinu- ity curve across the whole patch. Triangular B-splines, or DMS splines, introducedSurface Reconstruction with Triangular B-splines Ying He and Hong Qin Department of Computer|qin}@cs.sunysb.edu Abstract This paper presents a novel modeling technique for re- constructing a triangular B-spline surface

Qin, Hong

257

A New Approach to Tchebyche an B-Splines Daniel Bister and Hartmut Prautzsch

A New Approach to Tchebyche an B-Splines Daniel Bister and Hartmut Prautzsch Abstract. Originally, Tchebyche an B-splines have been de ned by generalized divided di erences. In this paper, we de ne Tchebyche an B-splines by integration. Based upon this de nition, all basic algorithms for Tchebyche an splines

Prautzsch, Hartmut

258

Translational Covering of Closed Planar Cubic B-Spline Curves Cristina Neacsu, Karen Daniels

Translational Covering of Closed Planar Cubic B-Spline Curves Cristina Neacsu, Karen Daniels recent results on B-spline curve envelopes, we bound the distance from the spline curve to its are planar, uniform cubic B-spline curves. We consider G to consist of translations. This problem

Daniels, Karen M.

259

Approximate merging of B-spline curves via knot adjustment and constrained optimization

Approximate merging of B-spline curves via knot adjustment and constrained optimization Chiew of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points

Tai, Chiew-Lan

260

On-Line Geometric Modeling Notes DEFINITION OF A B-SPLINE CURVE

On-Line Geometric Modeling Notes DEFINITION OF A B-SPLINE CURVE Kenneth I. Joy Visualization present the direct definition of the B-Spline curve. This definition is given in two ways: first definition. The B-Spline Curve Analytical Definition A B-spline curve P(t), is defined by P(t) = n i=0 Pi

California at Davis, University of

261

Radiation energy budget studies using collocated AVHRR and ERBE observations

NASA Technical Reports Server (NTRS)

Changes in the energy balance at the top of the atmosphere are specified as a function of atmospheric and surface properties using observations from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner. By collocating the observations from the two instruments, flown on NOAA-9, the authors take advantage of the remote-sensing capabilities of each instrument. The AVHRR spectral channels were selected based on regions that are strongly transparent to clear sky conditions and are therefore useful for characterizing both surface and cloud-top conditions. The ERBE instruments make broadband observations that are important for climate studies. The approach of collocating these observations in time and space is used to study the radiative energy budget of three geographic regions: oceanic, savanna, and desert.

Ackerman, Steven A.; Inoue, Toshiro

1994-01-01

262

Context Awareness and Uncertainty in Collocated Collaborative Systems

Context awareness is a necessary feature for mobile collocated collaborative learning. In this paper we describe how requirements\\u000a for context-aware cooperative learning activities are derived from the jigsaw technique augmented with the use of mobile devices,\\u000a applications to support the activities of groups, and tools to provide context-awareness to detect group formation. The emergence\\u000a of groups is detected based on

Roc Messeguer; Pedro Damin-reyes; Jess Favela; Leandro Navarro

2008-01-01

263

A Collocation-Based WSD Model: RFR-SUM

In this paper, the concept of Relative Frequency Ratio (RFR) is presented to evaluate the strength of collocation. Based on\\u000a RFR, a WSD Model RFR-SUM is put forward to disambiguate polysemous Chinese word sense. It selects 9 frequently used polysemous\\u000a words as examples, and achieves the average precision up to 92:50% in open test. It has compared the model with

Weiguang Qu; Zhifang Sui; Genlin Ji; Shiwen Yu; Junsheng Zhou

2007-01-01

264

ML reconstruction from dynamic list-mode PET data using temporal splines

We implemented and evaluated a maximum likelihood-optimality condition iteration algorithm (ML-OCI) to reconstruct dynamic PET data. The time activity curves (TACs) were reconstructed on a spatially segmented image. The segmented image paradigm effectively cancels out spatial reconstruction issues allowing a time domain evaluation of our method. The TACs were represented on a B-spline basis. We investigated different parameters of this

J. Verhaeghe; Y. D'Asseler; S. Vandenberghe; S. Staelens; R. Van de Walle; I. Lemahieu

2004-01-01

265

Trajectory Design and Control of a Wheel-type Mobile Robot Using B-spline Curve

In flexible trajectory control of a mobile robot it is preferable to design a smooth trajectory which passes specified points with specified tangents in a two dimensional plane. A trajectory design method which satisfies the above condition is presented using a Bspline curve. In order to use the designed B-spline curve for a two-wheel-driven-type mobile mechanism the possibility of using

Kiyoshi Komoriya; Kazuo Tanie

1989-01-01

266

A new approach for lofted B-spline surface interpolation to serial contours

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface

H. B. Jung; K. Kim

2004-01-01

267

[Eco-environmental evaluation and spatial-temporal collocation of regional land consolidation].

Eco-environmental evaluation and spatial-temporal collocation of land consolidation is the basis of regional land consolidation. Taking Qingzhou County of Shandong Province as an example, this paper established the eco-environmental evaluation index system and evaluation model of land consolidation, based on the systematic analysis of land consolidation characteristics and natural and social conditions of Qingzhou County. The comprehensive score of each evaluation unit was obtained by integrated index evaluation method and GIS techniques, and the spatial-temporal collocation of regional land consolidation was proposed accordingly. The results indicated that in Qingzhou County, the total area of cultivated and un-utilized land was 1446 km2, among which, the land consolidation area in near future mainly distributed in the northwest part of plain region, occupying 15.35% of the total, mid-phase land consolidation area mainly distributed in the northwest and central parts of plain region, occupying 13.58%, land consolidation area in specified future mainly distributed in the north part of plain region, occupying 40.71%, and non-land consolidation area mainly distributed in hilly region, occupying 30.36%. These results could provide scientific instruction for the land consolidation planning and implement in Qingzhou County. PMID:17066707

Wang, Ailing; Zhao, Genxiang; Wang, Ruiyan; Yuan, Xiangming

2006-08-01

268

We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.

Jakeman, John D., E-mail: jdjakem@sandia.gov [Sandia National Laboratories, Albuquerque, NM 87185 (United States); Narayan, Akil, E-mail: akil.narayan@umassd.edu [Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747 (United States)] [Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747 (United States); Xiu, Dongbin, E-mail: dxiu@purdue.edu [Department of Mathematics, Purdue University, West Lafayette, IN 47907 (United States)] [Department of Mathematics, Purdue University, West Lafayette, IN 47907 (United States)

2013-06-01

269

Spline-locking screw fastening strategy

NASA Technical Reports Server (NTRS)

A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotics or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced space manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.

Vranish, John M.

1992-01-01

270

Spline-Locking Screw Fastening Strategy (SLSFS)

NASA Technical Reports Server (NTRS)

A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotic or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.

Vranish, John M.

1991-01-01

271

Computational dealings in nonlinear spline regression

& k-1 in each k [k-p-I] interval [t. t ] . S is a subset of class C (~ ~) i' i+1 ' k where p is the largest number of knots which coincide. If no knots coincide, then p is assumed to be the value l. The concept of the B-spline function M (t...= t. ? t i+1 P2 i+2 N2=t-t. i-1 M3 = t - t i C2 = A Cl = (N2*C2 + Pl*A )/(M2 + Pl) CZ = (M3*A + P2*C2) /(N3 + P2) i Cl = (M3*C2 + Pl*C1)/(M3+ Pl) S=C1 ? y e Sl = Sl + S*S The subroutine EQUATE as described in [2] was also greatly modified...

Hrncir, Stanley Godfrey

2012-06-07

272

The spline probability hypothesis density filter

NASA Astrophysics Data System (ADS)

The Probability Hypothesis Density Filter (PHD) is a multitarget tracker for recursively estimating the number of targets and their state vectors from a set of observations. The PHD filter is capable of working well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. The SMC-PHD filter uses particles to provide target state estimates, which can lead to a high computational load, whereas the GM-PHD filter does not use particles, but restricts to linear Gaussian mixture models. The SMC-PHD filter technique provides only weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state and thus suffers from the well-known degeneracy problem. This paper proposes a B-Spline based Probability Hypothesis Density (S-PHD) filter, which has the capability to model any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models and the S-PHD filter can also provide continuous estimates of the probability density function of the system state. In addition, by moving the knots dynamically, the S-PHD filter ensures that the splines cover only the region where the probability of the system state is significant, hence the high efficiency of the S-PHD filter is maintained at all times. Also, unlike the SMC-PHD filter, the S-PHD filter is immune to the degeneracy problem due to its continuous nature. The S-PHD filter derivations and simulations are provided in this paper.

Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam

2012-06-01

273

Rational spectral collocation method for a coupled system of ...

Jun 27, 2011 ... http://www.global-sci.org/jcm ... from asymptotic analysis about the singularity solution are employed to determine the ... Introduction. In this paper, we consider a coupled system of m ? 2 singularly perturbed linear equations...

2011-06-21

274

Wind generation scheduling with pump storage unit by Collocation method

Wind generation is currently undergoing the fastest rate of growth of any form of electricity generation in the world. Integration of wind power into systems could be problematic, however, due to availability and variability of wind supply. As a proven storage technology, pump storage may provide\\/absorb additional capacity so as to hedge against adverse situations. A scheduling software is needed

Feng Gao; Arne Hallam; Chien-Ning Yu

2009-01-01

275

A collocation method for certain elliptic boundary-value problems

225-234. 44 VITA Susan Kathleen Bord, born December 30, 1947, in McGregor, Texas, the daughter of Alexander and Lillian Zacharias, attended the McGregor Schools until 1966. In 1968 she enrolled in Texas State Technical Institute and was graduated... 225-234. 44 VITA Susan Kathleen Bord, born December 30, 1947, in McGregor, Texas, the daughter of Alexander and Lillian Zacharias, attended the McGregor Schools until 1966. In 1968 she enrolled in Texas State Technical Institute and was graduated...

Hord, Susan Kathleen

2012-06-07

276

On developing B-spline registration algorithms for multi-core processors

NASA Astrophysics Data System (ADS)

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields.

Shackleford, J. A.; Kandasamy, N.; Sharp, G. C.

2010-11-01

277

Smoothing in occupational cohort studies: an illustration based on penalised splines

Aims: To illustrate the contribution of smoothing methods to modelling exposure-response data, Cox models with penalised splines were used to reanalyse lung cancer risk in a cohort of workers exposed to silica in California's diatomaceous earth industry. To encourage application of this approach, computer code is provided. Methods: Relying on graphic plots of hazard ratios as smooth functions of exposure, the sensitivity of the curve to amount of smoothing, length of the exposure lag, and the influence of the highest exposures was evaluated. Trimming and data transformations were used to down-weight influential observations. Results: The estimated hazard ratio increased steeply with cumulative silica exposure before flattening and then declining over the sparser regions of exposure. The curve was sensitive to changes in degrees of freedom, but insensitive to the number or location of knots. As the length of lag increased, so did the maximum hazard ratio, but the shape was similar. Deleting the two highest exposed subjects eliminated the top half of the range and allowed the hazard ratio to continue to rise. The shape of the splines suggested a parametric model with log hazard as a linear function of log transformed exposure would fit well. Conclusions: This flexible statistical approach reduces the dependence on a priori assumptions, while pointing to a suitable parametric model if one exists. In the absence of an appropriate parametric form, however, splines can provide exposure-response information useful for aetiological research and public health intervention. PMID:15377772

Eisen, E; Agalliu, I; Thurston, S; Coull, B; Checkoway, H

2004-01-01

278

Noise correction on LANDSAT images using a spline-like algorithm

NASA Technical Reports Server (NTRS)

Many applications using LANDSAT images face a dilemma: the user needs a certain scene (for example, a flooded region), but that particular image may present interference or noise in form of horizontal stripes. During automatic analysis, this interference or noise may cause false readings of the region of interest. In order to minimize this interference or noise, many solutions are used, for instane, that of using the average (simple or weighted) values of the neighboring vertical points. In the case of high interference (more than one adjacent line lost) the method of averages may not suit the desired purpose. The solution proposed is to use a spline-like algorithm (weighted splines). This type of interpolation is simple to be computer implemented, fast, uses only four points in each interval, and eliminates the necessity of solving a linear equation system. In the normal mode of operation, the first and second derivatives of the solution function are continuous and determined by data points, as in cubic splines. It is possible, however, to impose the values of the first derivatives, in order to account for shapr boundaries, without increasing the computational effort. Some examples using the proposed method are also shown.

Vijaykumar, N. L. (principal investigator); Dias, L. A. V.

1985-01-01

279

Uniform Powell-Sabin Splines for the Polygonal Hole Problem.

National Technical Information Service (NTIS)

An algorithm is described for smoothly filling in a polygonal hole in a surface, with a parametric uniform Powell-Sabin spline surface patch. It uses interpolation and subdivision techniques for iteratively determining an approximating solution. No assump...

J. Windmolders, P. Dierckx

2001-01-01

280

Correct resolution rendering of trimmed spline surfaces , Jorg Petersa

A standard approach to designing geometry in computer aided design, is to "overfit", i.e. create spline. The underlying challenge is the same as when determining the fill region of a planar decal [5] � except

Peters, Jörg

281

B-Spline Curve Fitting Using Dominant Points

\\u000a Motivated by an insight that properly selected points, called dominant points, can play an important role in producing better curve approximation, we propose a new approach for B-spline curve\\u000a fitting to a sequence of points. The approach is substantially different from the conventional ones in knot placement and\\u000a dominant point selection. It can generate a B-spline curve in good quality

Joo-haeng Lee

2006-01-01

282

Numerical solution of nonlinear hyperbolic conservation laws using exponential splines

Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain tension parameters associated with the exponential spline allows the sharp resolution of shocks and the suppression of any attendant oscillations. Specifically, spatial derivatives are replaced by nodal

B. J. McCartin; A. Jameson

1990-01-01

283

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

Alwan, Aravind; Aluru, N.R.

2013-12-15

284

B-spline interpolation for bend intra-oral radiographs.

Digital subtraction radiography (DSR) has been demonstrated to improve the detection of minute bone changes during the diagnosis of Periodontal diseases. However, during a dental X-ray session, it is not possible to control the bending of the X-ray film when installed in a patient's mouth. This leads to errors in the subsequent analysis. Error compensation can be done by a warping transformation, in conjunction with a reference wire grid attached to the X-ray film. However, the wire grid has to be attached to the film manually. The grid itself is a source of error in that it obscures the image and causes information loss. In this paper we propose a compensation method without the use of a reference grid. It is a simple algorithm based on B-spline interpolation and image scaling. No prior information about the bending is required. When compared with warping transformation, the method induces less disturbance to the pixel values during the compensation process. As a result, the proposed method produces more accurate image data for subsequent analysis. PMID:17416358

Leung, Chung-Chu; Kwok, Paul Chi-Kong; Zee, Kwan-Yat; Chan, Francis Huo-Yuen

2007-11-01

285

Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation

A numerical solution to a generalized Kortewegde Vries (KdV) equation is obtained using the Galerkin method with quadratic B-spline finite element method (FEM) over which the nonlinear term is locally linearized and using the Adomians Decomposition Method (ADM). Test problems concerning the motion and interaction of soliton solutions are used to compare the FEM with the ADM. The present methods

Turabi Geyikli

2005-01-01

286

User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010

The Wilson-Fowler spline is widely used in computer aided manufacturing, but is not available in all commercial CAD/CAM systems. These three programs provide a capability for generating, comparing, and approximating Wilson-Fowler splines. SPLPKG generates a spline passing through given nodes, and computes a piecewise linear approximation to the spline. WFCMPR computes the difference between two splines with common nodes. WFAPPX computes the difference between a spline and a piecewise linear curve. The programs are in Fortran 77 and are machine independent.

Fletcher, S.K.

1985-02-01

287

Smoothing spline ANOVA frailty model for recurrent event data.

Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data. PMID:21457192

Du, Pang; Jiang, Yihua; Wang, Yuedong

2011-12-01

288

B-spline calculations of oscillator strengths in noble gases

NASA Astrophysics Data System (ADS)

B-spline box-based multi-channel calculations of transition probabilities in noble gases are reported for energy levels up to n= 12. Energy levels and oscillator strengths for transitions from the p6 ground-state configuration, as well as for transitions between excited states, have been computed in the Breit-Pauli approximation. Individually optimized, term-dependent sets of non-orthogonal valence orbitals are used to account for the strong term dependence in the one-electron orbitals. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with experimental and other theoretical data. It is shown that the present method can be used for accurate calculations of oscillator strengths for states with intermediate to high n-values, for which it is difficult to apply standard multi-configuration Hartree-Fock (MCHF) methods. Recent developments based on the extension of our computer codes from the semi-relativistic Breit-Pauli Hamiltonian to the full relativistic Dirac-Breit Hamiltonian are also reported.

Zatsarinny, Oleg; Bartschat, Klaus

2009-05-01

289

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing multilevel collocation and smoothing. Our test case is that of a linear differential equation, although invertible. The smoothing `iteration' was thus intended to deal with the case when [DyF(x0, y0

Jerome, Joseph W.

290

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and

Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing involving multilevel collocation and smoothing. Our test case is that of a linear differential equation was not continuously invertible. The smoothing `iteration' was thus intended to deal with the case when [DyF(x0 ; y0

Heller, Barbara

291

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

ERIC Educational Resources Information Center

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

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

2012-01-01

292

Acquiring Collocations for Lexical Choice between NearSynonyms Diana Zaiu Inkpen and Graeme Hirst

word choices for the sentence. ISaurus does not include such knowledge. The focus of the work weAcquiring Collocations for Lexical Choice between NearSynonyms Diana Zaiu Inkpen and Graeme Hirst of knowledge is useful in the process of lexical choice between nearsynonyms. We acquire collocations

Inkpen, Diana

293

ORIGINAL ARTICLE Using job-shop scheduling tasks for evaluating collocated

-shop scheduling task Á Evaluation Á Collocated environments Á Computer-supported collaborative work Á User study 1ORIGINAL ARTICLE Using job-shop scheduling tasks for evaluating collocated collaboration Desney S on shared displays. Unfortunately, there is a lack of experi- mental tasks to evaluate the effectiveness

Rajamani, Sriram K.

294

A Comparative Empirical Study of Communication in Distributed and Collocated Development Teams

Communication models adopted in large-scale software engineering projects have significant impact on the efficacy of communication. We strove to understand these models by empirically examining synchronous communication within distributed and collocated teams at a large Fortune 500 organization. Our data imply that the overhead for tool support of synchronous communication for distributed teams are generally unacceptably high and that collocated

Ban Al-Ani

2008-01-01

295

A modal filter approach to non-collocated vibration control of structures

NASA Astrophysics Data System (ADS)

This paper employs modal filters for simultaneous and independent control of multiple vibration modes of a flexible structure embedded with a non-collocated pair of sensor and actuator. Each modal filter of second order is designed to be sensitive to the target mode for control while insensitive to the others. Based on the fact that there are only in- and out-of-phase modes in lightly and proportionally damped finite structures, those in-phase modes are controlled in the same way as that for collocated control using negative feedback, while those out-of-phase modes are controlled exactly in the opposite way using positive feedback. These two are equivalent as far as single mode control is concerned and are electrical realizations of a mechanical dynamic vibration absorber. Feedback control experiments were conducted on a cantilever beam embedded with a piezoelectric actuator at the root and an accelerometer at the end tip. The results reveal a number of peculiar advantages of using non-collocated control over collocated control. Non-collocated plants generally exhibit better high-frequency roll-off characteristics because there are weaker mechanical and electrical feedthrough couplings between non-collocated transducers. Furthermore, the high frequency control spillover can be greatly eliminated by appropriately adjusting the gains of modal filters. It is thus often possible to make the performance and robustness of non-collocated control as well as or even better than those using collocated control.

Kim, Sang-Myeong; Oh, Jae-Eung

2013-04-01

296

Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations

ERIC Educational Resources Information Center

Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,

Liu, Dilin

2010-01-01

297

AnL1 smoothing spline algorithm with cross validation

NASA Astrophysics Data System (ADS)

We propose an algorithm for the computation ofL1 (LAD) smoothing splines in the spacesWM(D), with . We assume one is given data of the formyiD(f(ti) +?i, iD1,...,N with {itti}iD1N ?D, the?i are errors withE(?i)D0, andf is assumed to be inWM. The LAD smoothing spline, for fixed smoothing parameter??;0, is defined as the solution,s?, of the optimization problem (1/N)?iD1N yi-g(ti +?JM(g), whereJM(g) is the seminorm consisting of the sum of the squaredL2 norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s?, would be expected to give robust smoothed estimates off in situations where the?i are from a distribution with heavy tails. The solution to such a problem is a "thin plate spline" of known form. An algorithm for computings? is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The "data driven" selection of the smoothing parameter is achieved by minimizing aCV(?) score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in ??0 taken on the above SQPs parametrized in?, with the optimal smoothing parameter taken to be that value of? at which theCV(?) score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.

Bosworth, Ken W.; Lall, Upmanu

1993-08-01

298

Registration of segmented histological images using thin plate splines and belief propagation

NASA Astrophysics Data System (ADS)

We register images based on their multiclass segmentations, for cases when correspondence of local features cannot be established. A discrete mutual information is used as a similarity criterion. It is evaluated at a sparse set of location on the interfaces between classes. A thin-plate spline regularization is approximated by pairwise interactions. The problem is cast into a discrete setting and solved efficiently by belief propagation. Further speedup and robustness is provided by a multiresolution framework. Preliminary experiments suggest that our method can provide similar registration quality to standard methods at a fraction of the computational cost.

Kybic, Jan

2014-03-01

299

ECS 178 Course Notes ANALYTIC DEFINITION OF A B-SPLINE CURVE

ECS 178 Course Notes ANALYTIC DEFINITION OF A B-SPLINE CURVE Kenneth I. Joy Institute for Data will the analytic definition of the B-spline curve look like? The real question is what will the blending functions curve. The B-Spline Curve Analytical Definition A B-spline curve P(t), is defined by P(t) = n i=0 Pi

California at Davis, University of

300

We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical results and demonstrate the distinctions between the various stochastic identification objectives.

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

2013-01-01

301

BSPLND, A B-Spline N-Dimensional Package for Scattered Data Interpolation

the contribution of each control point to f(x, y) based on its distance to (x, y). Note that as B-spline curvesBSPLND, A B-Spline N-Dimensional Package for Scattered Data Interpolation Michael P. Weis Tracker for any set of scattered data using a hierarchical set of cubic B-splines. BSPLND extends the technique

Lewis, Robert R.

302

On-Line Geometric Modeling Notes CUBIC UNIFORM B-SPLINE CURVE REFINEMENT

On-Line Geometric Modeling Notes CUBIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy Overview The binary subdivision of the uniform B-spline curves and surfaces motivate much of the work that is used to subdivide a curve or surface into multiple components. In the uniform B-spline case

California at Davis, University of

303

A Geometric B-Spline Over the Triangular Domain Christopher K. Ingram

to the public. ii #12;Abstract For modelling curves, B-splines [3] are among the most versatile control schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 B´ezier Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 B-SplinesA Geometric B-Spline Over the Triangular Domain by Christopher K. Ingram A thesis presented

Waterloo, University of

304

ECS 178 Course Notes CUBIC UNIFORM B-SPLINE CURVE REFINEMENT

ECS 178 Course Notes CUBIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy Institute for Data The binary subdivision of the uniform B-spline curves and surfaces motivate much of the work on subdivision to subdivide a curve or surface into multiple components. In the uniform B-spline case a subdivided component

California at Davis, University of

305

BSPLINE: Stata modules to compute B-splines parameterized by their values at reference points

bspline and frencurv, each of which generates a basis of splines in an X-variable, for use in the varlist of a regression command (such as regress or glm) for fitting a spline in the X-variable. bspline generates a basis of Schoenberg B-splines, whereas frencurv (\\

Roger Newson

2000-01-01

306

intersections of two parametric B-Spline curves. We use an intersection of the control polygons the most important of these properties is that the coefficients of a curve represented in terms of B-splines to as the control polygon) will converge to the curve. B-splines are nonnegative and sum to one which means

Sahay, Sundeep

307

Volumetric Parameterization and Trivariate B-spline Fitting using Harmonic Tobias Martin

Volumetric Parameterization and Trivariate B-spline Fitting using Harmonic Functions Tobias Martin trivariate B-spline to data so that simulation attributes can also be modeled. The resulting model represent material attributes or other interior features. The trivariate B-spline geometric and attribute

Utah, University of

308

T-splines and T-NURCCs Thomas W. Sederberg and Jianmin Zheng

of Beirut Abstract This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The pa Graphics]: Computa- tional Geometry and Object Modeling--curve, surface, solid and object representations

Nasri, Ahmad H.

309

Single-knot Wavelets for Non-uniform B-splines Martin Bertram

We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces,k and Nj,k, respectively. A coarse-scale 1 #12;B-spline curve given by de Boor points di can be represented to a fitting operation, where the details removed from a B-spline curve are represented in the space W

Hering-Bertram, Martin

310

Teaching B-splines Is Not Difficult! John Lowther and Ching-Kuang Shene

and Information Science EducationComputer Science Education General Terms Design Keywords Curves, B-splines, knot mathematical discussion. DesignMentor supports B´ezier, rational B´ezier, B-spline and NURBS curvesTeaching B-splines Is Not Difficult! John Lowther and Ching-Kuang Shene Department of Computer

Shene, Ching-Kuang

311

Fairing Triangular B-splines of Arbitrary Topology Ying He, Xianfeng Gu, and Hong Qin

Fairing Triangular B-splines of Arbitrary Topology Ying He, Xianfeng Gu, and Hong Qin Stony Brook University E-mail: {yhe|gu|qin}@cs.sunysb.edu (a) (b) (c) (d) (e) (f) (g) Abstract Triangular B-splines tools with triangular B-splines are less-developed. This is mainly because users have to handle a large

Qin, Hong

312

23rd European Workshop on Computational Geometry, 2007 Complexity of Approximation by Conic Splines

in a simple bi- section algorithm for computing an optimal parabolic or conic spline. 1 Introduction23rd European Workshop on Computational Geometry, 2007 Complexity of Approximation by Conic Splines that the complexity, i.e., the number of elements, of a parabolic or conic spline approximating a sufficiently smooth

Vegter, Gert

313

How to fly an aircraft with control theory and splines

NASA Technical Reports Server (NTRS)

When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.

Karlsson, Anders

1994-01-01

314

The high-level error bound for shifted surface spline interpolation

Radial function interpolation of scattered data is a frequently used method for multivariate data fitting. One of the most frequently used radial functions is called shifted surface spline, introduced by Dyn, Levin and Rippa in \\\\cite{Dy1} for $R^{2}$. Then it's extended to $R^{n}$ for $n\\\\geq 1$. Many articles have studied its properties, as can be seen in \\\\cite{Bu,Du,Dy2,Po,Ri,Yo1,Yo2,Yo3,Yo4}. When dealing

Lin-Tian Luh

2006-01-01

315

If You Know B-Splines Well, You Also Know NURBS! John Fisher, John Lowther and Ching-Kuang Shene

, NURBS, curves and surfaces 1. INTRODUCTION B-splines and NURBS (i.e., Non-Uniform Rational B- Splines.e., a NURBS curve is the projec- tion of a higher dimensional B-spline curve), Section 4 uses NURBSvis students to draw a circle using a B-spline curve. This is im- possible and serves as a very good motivation

Shene, Ching-Kuang

316

Longitudinal data are routinely collected in biomedical research studies. A natural model describing longitudinal data decomposes an individual's outcome as the sum of a population mean function and random subject-specific deviations. When parametric assumptions are too restrictive, methods modeling the population mean function and the random subject-specific functions nonparametrically are in demand. In some applications, it is desirable to estimate a covariance function of random subject-specific deviations. In this work, flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models, where the functional forms of the population mean and the subject-specific curves are unspecified. We estimate nonparametric components of the model by penalized spline (P-spline, Biometrics 2001; 57:253-259), and reparameterize the random curve covariance function by a modified Cholesky decomposition (Biometrics 2002; 58:121-128) which allows for unconstrained estimation of a positive-semidefinite matrix. To provide smooth estimates, we penalize roughness of fitted curves and derive closed-form solutions in the maximization step of an EM algorithm. In addition, we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject-level source and observation-level source. We apply these methods to the multi-level Framingham Heart Study data to estimate age-specific heritability of systolic blood pressure nonparametrically. PMID:21491474

Wang, Yuanjia

2011-07-10

317

Feature Oriented Composition Of B-Spline Cristin Barghiel

are added to composite spline surfaces in a multi-layered fashion by means of an e cient displacement scheme, and has encouraged me to explore the area of geometric design. I would also wish to thank my readers, Dr of computer graphics. ii #12;Trademarks Silicon Graphics is a registered trademark of Silicon Graphics

Waterloo, University of

318

Interpolating Mean Rainfall Using Thin Plate Smoothing Splines

Thin plate smoothing splines provide accurate, operationally straightforward and computationally efficient solutions to the problem of the spatial interpolation of annual mean rainfall for a standard period from point data which contains many short period rainfall means. The analyses depend on developing a statistical model of the spatial variation of the observed rainfall means, considered as noisy estimates of standard

M. F. Hutchinson

1995-01-01

319

Airfoil Design via Cubic Splines Ferguson's Curves Revisited

Airfoil Design via Cubic Splines Ferguson's Curves Revisited Andr´as S´obester , Andy J. Keane since the 1960s, and we propose it as a means of airfoil parameterization, it being ideally suited show that in the interest of parameterization parsimony, adequate airfoil shape control can be achieved

Sóbester, András

320

Minimizing the symmetric difference distance in conic spline approximation

Minimizing the symmetric difference distance in conic spline approximation Sunayana Ghosh and Gert Vegter Abstract. We show that the complexity (the number of elements) of an op- timal parabolic or conic of general conic arcs of varying type. The constants c1 and c2 are ex- pressed in the affine curvature

Vegter, Gert

321

NASA Technical Reports Server (NTRS)

The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.

Eren, K.

1980-01-01

322

This paper examines the possibility of collocating a cellulosic ethanol processing plant with certain Louisiana sugar mills, chosen based on their strategic locations and cane grinding capacity. The prospective plants are compared based on transportation costs and overall economic performance.

Paul M. Darby; Tyler B. Mark

2012-01-01

323

An H2 Upper Bound Approach for Control of Collocated Structural Systems

This paper presents an explicit expression for an upper bound on the H2 norm for structural systems with collocated sensors and actuators. First, we consider an open-loop collocated structural system and obtain an upper bound for the H2 norm using a particular solution for the linear matrix inequality formulation of the H2 norm analysis conditions. Next, we address the problem

Mona Meisami-Azad; Javad Mohammadpour; Karolos M. Grigoriadis

2007-01-01

324

In this paper, for the actual in-service pipeline detection, an edge detection method based on fourth-order B-spline wavelet multi-scale local modulus maxima is proposed. We extract defect edge using wavelet maximum algorithm, select fine length, invariant moment, gray scale energy and so on, several key characteristic parameters that are good for defect identification, and use BP neural network of single-output

Peixin Yuan; Jun Tan; Jiahui Cong

2009-01-01

325

Volume xxx, (1999n) number yyy pp. 000--000 HBsplines: a Blend of Hermite splines and Bsplines

on Bspline curves which de gree depends on the order of continuity we look for. More precisely or less heuristically 3 ). For instance, if we search for a C 2 in terpolating curve (i.e. cubic BsplineVolume xxx, (1999n) number yyy pp. 000--000 HBsplines: a Blend of Hermite splines and Bsplines

Grisoni, Laurent

326

Fast simulation of x-ray projections of spline-based surfaces using an append buffer

NASA Astrophysics Data System (ADS)

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, the simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640 480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically.

Maier, Andreas; Hofmann, Hannes G.; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca

2012-10-01

327

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

328

BSR: B-spline atomic R-matrix codes

NASA Astrophysics Data System (ADS)

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].

Zatsarinny, Oleg

2006-02-01

329

Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, time-varying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.

Brown, C; Adcock, A; Azevedo, S; Liebman, J; Bond, E

2010-12-28

330

Parallel iterative solution of the Hermite Collocation equations on GPUs II

NASA Astrophysics Data System (ADS)

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

Vilanakis, N.; Mathioudakis, E.

2014-03-01

331

Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification

NASA Astrophysics Data System (ADS)

Multi-element uncertainty quantification approaches can robustly resolve the high sensitivities caused by discontinuities in parametric space by reducing the polynomial degree locally to a piecewise linear approximation. It is important to extend the higher degree interpolation in the smooth regions up to a thin layer of linear elements that contain the discontinuity to maintain a highly accurate solution. This is achieved here by introducing Essentially Non-Oscillatory (ENO) type stencil selection into the Simplex Stochastic Collocation (SSC) method. For each simplex in the discretization of the parametric space, the stencil with the highest polynomial degree is selected from the set of candidate stencils to construct the local response surface approximation. The application of the resulting SSC-ENO method to a discontinuous test function shows a sharper resolution of the jumps and a higher order approximation of the percentiles near the singularity. SSC-ENO is also applied to a chemical model problem and a shock tube problem to study the impact of uncertainty both on the formation of discontinuities in time and on the location of discontinuities in space.

Witteveen, Jeroen A. S.; Iaccarino, Gianluca

2013-04-01

332

Interference effects and nonlinearities that are inherent in an adsorption equilibrium add challenges to the task of modeling fixed-bed adsorption processes. In particular, the interference effect tends to produce steep transient concentration fronts, which are enhanced by the high convection to dispersion ratio that is found in normal bed operation conditions. This causes spatial stiffness and renders numerical computations difficult

Wangyun Won; Kwang Soon Lee

2011-01-01

333

Railroad inspection based on ACFM employing a non-uniform B-spline approach

NASA Astrophysics Data System (ADS)

The stresses sustained by rails have increased in recent years due to the use of higher train speeds and heavier axle loads. For this reason surface and near-surface defects generate by Rolling Contact Fatigue (RCF) have become particularly significant as they can cause unexpected structural failure of the rail, resulting in severe derailments. The accident that took place in Hatfield, UK (2000), is an example of a derailment caused by the structural failure of a rail section due to RCF. Early detection of RCF rail defects is therefore of paramount importance to the rail industry. The performance of existing ultrasonic and magnetic flux leakage techniques in detecting rail surface-breaking defects, such as head checks and gauge corner cracking, is inadequate during high-speed inspection, while eddy current sensors suffer from lift-off effects. The results obtained through rail inspection experiments under simulated conditions using Alternating Current Field Measurement (ACFM) probes, suggest that this technique can be applied for the accurate and reliable detection of surface-breaking defects at high inspection speeds. This paper presents the B-Spline approach used for the accurate filtering the noise of the raw ACFM signal obtained during high speed tests to improve the reliability of the measurements. A non-uniform B-spline approximation is employed to calculate the exact positions and the dimensions of the defects. This method generates a smooth approximation similar to the ACFM dataset points related to the rail surface-breaking defect.

Chacn Muoz, J. M.; Garca Mrquez, F. P.; Papaelias, M.

2013-11-01

334

Control theory and splines, applied to signature storage

NASA Technical Reports Server (NTRS)

In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.

Enqvist, Per

1994-01-01

335

Fast and stable evaluation of box-splines via the BB-form

NASA Astrophysics Data System (ADS)

To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, the box-spline is converted to and tabulated as piecewise polynomial in BB-form (Bernstein-Bzier-form). We show that the BB-coefficients can be derived and stored as integers plus a rational scale factor and derive a hash table for efficiently accessing the polynomial pieces. This pre-processing, the resulting evaluation algorithm and use in a widely-used ray-tracing package are illustrated for splines based on two trivariate box-splines: the seven-directional box-spline on the Cartesian lattice and the six-directional box-spline on the face-centered cubic lattice.

Kim, Minho; Peters, Jrg

2009-04-01

336

Purpose To investigate the effect of B-spline-based elastic image registration on adaptive optics scanning laser ophthalmoscopy (AO-SLO)-assisted capillary visualization. Methods AO-SLO videos were acquired from parafoveal areas in the eyes of healthy subjects and patients with various diseases. After nonlinear image registration, the image quality of capillary images constructed from AO-SLO videos using motion contrast enhancement was compared before and after B-spline-based elastic (nonlinear) image registration performed using ImageJ. For objective comparison of image quality, contrast-to-noise ratios (CNRS) for vessel images were calculated. For subjective comparison, experienced ophthalmologists ranked images on a 5-point scale. Results All AO-SLO videos were successfully stabilized by elastic image registration. CNR was significantly higher in capillary images stabilized by elastic image registration than in those stabilized without registration. The average ratio of CNR in images with elastic image registration to CNR in images without elastic image registration was 2.10 1.73, with no significant difference in the ratio between patients and healthy subjects. Improvement of image quality was also supported by expert comparison. Conclusions Use of B-spline-based elastic image registration in AO-SLO-assisted capillary visualization was effective for enhancing image quality both objectively and subjectively. PMID:24265796

Uji, Akihito; Ooto, Sotaro; Hangai, Masanori; Arichika, Shigeta; Yoshimura, Nagahisa

2013-01-01

337

Explicit B-spline regularization in diffeomorphic image registration

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline flavored diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools. PMID:24409140

Tustison, Nicholas J.; Avants, Brian B.

2013-01-01

338

Prediction of gastro-intestinal absorption using multivariate adaptive regression splines.

Multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) were used for modelling the gastro-intestinal absorption of 140 drug-like molecules. The published absorption values for these molecules were used as response variable and calculated molecular descriptors as potential explanatory variables. Both methods were compared and their potential use in quantitative structure-activity relationship (QSAR) context evaluated. The predictive abilities of the models were studied using different sequences of Monte Carlo cross validation (MCCV). It was shown that both types of models had good predictive abilities and that for the data used, MARS gave better results than TMARS. It could be concluded that both methods could be valuable for QSAR modelling. PMID:16040225

Deconinck, E; Xu, Q S; Put, R; Coomans, D; Massart, D L; Vander Heyden, Y

2005-10-01

339

de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves

The de Boor-Fix dual functionals are a potent tool for deriving results about piecewise polynomial B-spline curves. In this\\u000a paper we extend these functionals to Tchebycheffian B-spline curves and then use them to derive fundamental algorithms that\\u000a are natural generalizations of algorithms for piecewise polynomial B-spline algorithms. Then, as a further example of the\\u000a utility of this approach, we introduce

P. J. Barry

1996-01-01

340

ECS 178 Course Notes B EZIER CURVES ARE B-SPLINE CURVES

ECS 178 Course Notes B ´EZIER CURVES ARE B-SPLINE CURVES Kenneth I. Joy Institute for Data Analysis, this is obvious. Since B-Spline curves are piecewise B´ezier curves, it follows directly that a single B´ezier curve must be a B-Spline. You are right! But it is also informative to "find" a B´ezier curve

California at Davis, University of

341

Transformation of a Dynamic B-Spline Curve into Piecewise Power Basis Representation

In the fields of computer aided geometric design and computer graphics, B-spline curves and surfaces are often adopted as\\u000a a geometric modelling tool and their evaluation is frequently required for a various geometric processing. In this paper,\\u000a we present a new algorithm to convert B-spline curves into piecewise polynomials in power form. The proposed algorithm considers\\u000a recursive B-spline basis function

Joonghyun Ryul; Youngsong Chol; Deok-soo Kim

2002-01-01

342

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

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

2008-01-01

343

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

NASA Astrophysics Data System (ADS)

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

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

344

A new hybrid interpolation method for information exchange in computational aeroelasticity

Interpolation methods are very important in computational aeroelasticity in both the closely and loosely coupled analysis method. In this paper, the characteristics of thin plate splines (TPS), multiquadrics surface spline methods(MQ) and kriging method were first analyzed for interface data interpolation in computational aeroelasticity. Through the analysis of different methods, a hybrid interpolation method is proposed which combines the thin

Xiao-liang Wang; Wenbin Song

2010-01-01

345

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

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

346

Integral control of collocated smart structures Sumeet S. Aphale, Andrew J. Fleming, and S. O. Reza structures with collocated sensors and actuators. The technique is called Integral Resonant Control (IRC). We. This structure permits the direct application of integral feedback and results in good stability and damping

Fleming, Andrew J.

347

Miniaturized Multi-Band Antenna via Element Collocation

The resonant frequency of a microstrip patch antenna may be reduced through the addition of slots in the radiating element. Expanding upon this concept in favor of a significant reduction in the tuned width of the radiator, nearly 60% of the antenna metallization is removed, as seen in the top view of the antennas radiating element (shown in red, below, left). To facilitate an increase in the gain of the antenna, the radiator is suspended over the ground plane (green) by an air substrate at a height of 0.250? while being mechanically supported by 0.030? thick Rogers RO4003 laminate in the same profile as the element. Although the entire surface of the antenna (red) provides 2.45 GHz operation with insignificant negative effects on performance after material removal, the smaller square microstrip in the middle must be isolated from the additional aperture in order to afford higher frequency operation. A low insertion loss path centered at 2.45 GHz may simultaneously provide considerable attenuation at additional frequencies through the implementation of a series-parallel, resonant reactive path. However, an inductive reactance alone will not permit lower frequency energy to propagate across the intended discontinuity. To mitigate this, a capacitance is introduced in series with the inductor, generating a resonance at 2.45 GHz with minimum forward transmission loss. Four of these reactive pairs are placed between the coplanar elements as shown. Therefore, the aperture of the lower-frequency outer segment includes the smaller radiator while the higher frequency section is isolated from the additional material. In order to avoid cross-polarization losses due to the orientation of a transmitter or receiver in reference to the antenna, circular polarization is realized by a quadrature coupler for each collocated antenna as seen in the bottom view of the antenna (right). To generate electromagnetic radiation concentrically rotating about the direction of propagation, ideally one-half of the power must be delivered to the output of each branch with a phase shift of 90 degrees and identical amplitude. Due to this, each arm of the coupler is spaced ?/4 wavelength apart.

Martin, R. P.

2012-06-01

348

Convergence of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods.

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

349

Spline-Based Smoothing of Airfoil Curvatures

NASA Technical Reports Server (NTRS)

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.; Krist, S.

2008-01-01

350

A Bayesian-optimized spline representation of the electrocardiogram.

We introduce an implementation of a novel spline framework for parametrically representing electrocardiogram (ECG) waveforms. This implementation enables a flexible means to study ECG structure in large databases. Our algorithm allows researchers to identify key points in the waveform and optimally locate them in long-term recordings with minimal manual effort, thereby permitting analysis of trends in the points themselves or in metrics derived from their locations. In the work described here we estimate the location of a number of commonly-used characteristic points of the ECG signal, defined as the onsets, peaks, and offsets of the P, QRS, T, and R' waves. The algorithm applies Bayesian optimization to a linear spline representation of the ECG waveform. The location of the knots-which are the endpoints of the piecewise linear segments used in the spline representation of the signal-serve as the estimate of the waveform's characteristic points. We obtained prior information of knot times, amplitudes, and curvature from a large manually-annotated training dataset and used the priors to optimize a Bayesian figure of merit based on estimated knot locations. In cases where morphologies vary or are subject to noise, the algorithm relies more heavily on the estimated priors for its estimate of knot locations. We compared optimized knot locations from our algorithm to two sets of manual annotations on a prospective test data set comprising 200 beats from 20 subjects not in the training set. Mean errors of characteristic point locations were less than four milliseconds, and standard deviations of errors compared favorably against reference values. This framework can easily be adapted to include additional points of interest in the ECG signal or for other biomedical detection problems on quasi-periodic signals. PMID:24149574

Guilak, F G; McNames, J

2013-11-01

351

B-spline neural networks based PID controller for Hammerstein systems

B-spline neural networks based PID controller for Hammerstein systems X. Hong1 , S. Iplikci2 S: B-spline neural network, Hammerstein model, PID con- troller, adaptive control, system desirable in nonlinear system identification and control. In this work a new PID controller is introduced

Chen, Sheng

352

Schoenberg's polynomial B-splines of odd degrees: A brief review of application

NASA Astrophysics Data System (ADS)

A brief overview of applications of Schoenberg's polynomial B-splines of odd degrees in mathematical statistics, computational mathematics, and statistical radio engineering is provided. Exact formulas for the found Schoenberg B-spline of 15th degree are presented. High-quality approximations of smooth functions with an infinite Fourier transform by functions with a finite Fourier transform are found.

Alekseev, V. G.; Sukhodoev, V. A.

2012-10-01

353

Fairing Triangular B-splines of Arbitrary Topology Ying He, Xianfeng Gu, and Hong Qin

Fairing Triangular B-splines of Arbitrary Topology Ying He, Xianfeng Gu, and Hong Qin Center triangular B-spline. (a) shows the spherical domain with 682 triangles. (b), (c) and (d) shows a degree 5 (C4 (e) does not change too much, but the curvature distribution improves significantly. The red curves

Qin, Hong

354

On the degree elevation of B-spline curves and corner cutting

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new

Guozhao Wang; Chongyang Deng

2007-01-01

355

Splines with parameters that can be explained in words to non-mathematicians

This contribution is based on my programs bspline and frencurv, which are used to generate bases for Schoenberg B-splines and splines parameterized by their values at reference points on the X-axis (presented in STB-57 as insert sg151). The program frencurv (\\

Roger Newson

2001-01-01

356

to transform static images into dynamic structures to perform virtual tasks such as facial surgery.2 HoweverDepartment of Surgery, University of Toronto ABSTRACT We introduce a mathematical primitive called the B-spline solid when fitting discrete sampled data to a continuous B-spline solid model. Visible Human image data

Toronto, University of

357

Approximation by Conic Splines Sunayana Ghosh, Sylvain Petitjean and Gert Vegter

Approximation by Conic Splines Sunayana Ghosh, Sylvain Petitjean and Gert Vegter Abstract. We show that the complexity of a parabolic or conic spline approx- imating a sufficiently smooth curve with non-1/5 + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed

Vegter, Gert

358

APPROXIMATION BY CONIC SPLINES SUNAYANA GHOSH, SYLVAIN PETITJEAN, AND GERT VEGTER

APPROXIMATION BY CONIC SPLINES SUNAYANA GHOSH, SYLVAIN PETITJEAN, AND GERT VEGTER Abstract. We show that the complexity of a parabolic or conic spline approx- imating a sufficiently smooth curve with non-1/5 + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed

Petitjean, Sylvain

359

Use of tensor product splines in magnet optimization

Variational Metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated.

Davey, K.R. (American Maglev, Inc., New Smyrna Beach, FL (United States))

1999-05-01

360

Full-turn symplectic map from a generator in a Fourier-spline basis

Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been applied to a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10{sup 7} turns on an IBM RS6000 model 320 workstation, in a run of about one day.

Berg, J.S.; Warnock, R.L.; Ruth, R.D. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Forest, E. [Lawrence Berkeley Lab., CA (United States)

1993-04-01

361

With many predictors, choosing an appropriate subset of the covariates is a crucial, and difficult, step in nonparametric regression. We propose a Bayesian nonparametric regression model for curve-fitting and variable selection. We use the smoothing spline ANOVA framework to decompose the regression function into interpretable main effect and interaction functions. Stochastic search variable selection via MCMC sampling is used to search for models that fit the data well. Also, we show that variable selection is highly-sensitive to hyperparameter choice and develop a technique to select hyperparameters that control the long-run false positive rate. The method is used to build an emulator for a complex computer model for two-phase fluid flow. PMID:19789732

Reich, Brian J.; Storlie, Curtis B.; Bondell, Howard D.

2009-01-01

362

Determination of loose spline coupling coefficients of rotor bearing systems in turbomachinery

NASA Astrophysics Data System (ADS)

Analytical and experimental studies have been carried out to determine the stiffness and damping coefficients of loose spline couplings used in high speed rotating machinery from which a realistic assessment of rotor stability can be made at the turbomachinery design stage. This is believed to be the first attempt ever to determine these coefficients experimentally. Experimental modal parameters of the rotor bearing system with a spline coupling are found using modal testing for given spline geometry, misalignment, lubrication condition, torque, and rotational speeds. A dual rotor computer algorithm which contains a spline coupling model is developed in order to calculate the analytical modal parameters. Support bearing coefficients are obtained using a pressure dam bearing computer code which employs lubrication theory. Spline coupling coefficients are determined by adjusting the model until the analytical modal parameters match the experimental modal parameters. Both computer simulations and impact testing show that shaft speed and torque are the most important parameters which affect the system natural frequency and logarithmic decrement. However, the modal parameters are not very sensitive to the spine coupling coefficients. Only the second natural frequency shows any sensitivity to the spline angular stiffness. The lateral stiffness coefficient of the spline coupling decreases as rotational speed increases. Lateral and angular damping do not influence the modal parameter until unreasonably large values are considered. This is due to the large value of damping in the pressure dam bearings. Since the modal parameters are insensitive to the spline coefficients, a set of error bounds for the experimental values are chosen to determine the ranges of the loose spline coupling coefficients. The results show that the value of the spline lateral stiffness is between 2.0 x10(exp 7) and 8.0 x 10(exp 8) N/m and the spline angular stiffness is between 2.0 x 10(exp 5) and 8.0 x 10(exp 8) N/m, and the spline angular stiffness is between 2.0 x 10(exp 6) Nm/rad. However, it is impossible to identify the spline damping coefficients because the effect of the support bearing damping coefficients suppress the nonsynchronous whirling motion due to the spline friction even at speeds above the first critical speed.

Park, Sang Kyu

363

Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multidimensional displacements/strain components from multidimensional data sets. We describe the mathematical formulation for two- and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 10?4 samples in range and 2.2 10?3 samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 10?3 samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE is broadly applicable across imaging applications. PMID:18807190

Viola, Francesco; Coe, Ryan L.; Owen, Kevin; Guenther, Drake A.; Walker, William F.

2008-01-01

364

Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production or energy expenditure (EE). Multivariate adaptive regression splines (MARS) is a nonparametric method that estimates complex nonlinear relationships by a series of spline functions of the independent predictors. The specific aim of this study is to construct MARS models based on heart rate (HR) and accelerometer counts (AC) to accurately predict EE, and hence 24-h total EE (TEE), in children and adolescents. Secondarily, MARS models will be developed to predict awake EE, sleep EE, and activity EE also from HR and AC. MARS models were developed in 109 and validated in 61 normal-weight and overweight children (ages 5-18 yr) against the criterion method of 24-h room respiration calorimetry. Actiheart monitor was used to measure HR and AC. MARS models were based on linear combinations of 23-28 basis functions that use subject characteristics (age, sex, weight, height, minimal HR, and sitting HR), HR and AC, 1- and 2-min lag and lead values of HR and AC, and appropriate interaction terms. For the 24-h, awake, sleep, and activity EE models, mean percent errors were -2.5 +/- 7.5, -2.6 +/- 7.8, -0.3 +/- 8.9, and -11.9 +/- 17.9%, and root mean square error values were 168, 138, 40, and 122 kcal, respectively, in the validation cohort. Bland-Altman plots indicated that the predicted values were in good agreement with the observed TEE, and that there was no bias with increasing TEE. Prediction errors for 24-h TEE were not statistically associated with age, sex, weight, height, or body mass index. MARS models developed for the prediction of EE from HR monitoring and accelerometry were demonstrated to be valid in an independent cohort of children and adolescents, but require further validation in independent, free-living populations. PMID:19892930

Zakeri, Issa F; Adolph, Anne L; Puyau, Maurice R; Vohra, Firoz A; Butte, Nancy F

2010-01-01

365

Security Awareness in Virtual Communities: The Case of Non-collocated Academic Research the security risk factor linked with virtual collaboration. This study examines the security awareness settings. The paper suggests that a security awareness program aimed at academics should be initiated

Paris-Sud XI, Université de

366

Strategies in Translating Collocations in Religious Texts from Arabic into English

ERIC Educational Resources Information Center

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

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

2010-01-01

367

EVIDENCE OF THE WEST SAKHALIN CURRENT IN ERS-2 AND ENVISAT COLLOCATED SAR IMAGES

Collocated ERS-2 SAR and Envisat ASAR images acquired on 4 October 2003 with time difference of about 28 min have trapped the West Sakhalin Current (WSC) during its maximum intensity. The current was observed as a narrow strip the width of about 15 km adjacent to the northwestern Sakhalin coast. Backscatter contrasts in the convergence region between the Tsushima Current

V. A. Dubina; L. M. Mitnik

368

This paper presents an active noise cancellation technique for recovering wearable biosensor signals corrupted by bodily motion. A finger mounted photoplethysmograph (PPG) ring sensor with a collocated MEMS accelerometer is considered. The system by which finger acceleration disturbs PPG output is identified and a means of modeling this relationship is prescribed using either FIR or Laguerre models. This means of

Peter T. Gibbs; Levi B. Wood; H. Harry Asada

369

This paper presents an active noise cancellation technique for recovering wearable biosensor signals corrupted by bodily motion. A finger mounted photoplethysmograph (PPG) ring sensor with a collocated MEMS accelerometer is considered. The system by which finger acceleration disturbs PPG output is identified and a means of modeling this relationship is prescribed using either FIR or Laguerre models. This means of

Peter T. Gibbs; Levi B. Wood; H. Harry Asada

2005-01-01

370

How may learners be helped to write acceptable academic articles? What type of assistance do they require in becoming more competent and effective writers? These are questions that language teachers have long been struggling to address. In this connection, the present study focuses on how to make Japanese learners more aware of word collocations in English, since such awareness has

Hiroshi OHTAKE; Brian MORREN

371

Unsteady laminar flow in a circular tube: A test of the HERCOL (Hermitian collocation) computer code

HERCOL, a computer code for the integration of second-order differential equations in one space dimension by Hermitian collocation was used to calculate the unsteady velocity profiles for laminar flow in a circular tube. The code was tested for stability and accuracy for the problem for which an analytical solution exists prior to application to a like problem in which the

James F. Welch; James A. Hurley; Michael P. Glover; Ryan D. Nassimbene; Marilyn R. Yetzbacher

1991-01-01

372

Acquiring Collocations for Lexical Choice between Near-Synonyms Diana Zaiu Inkpen and Graeme Hirst

word choices for the sentence. I-Saurus does not include such knowledge. The focus of the work weAcquiring Collocations for Lexical Choice between Near-Synonyms Diana Zaiu Inkpen and Graeme Hirst behaviour. This type of knowledge is useful in the process of lexical choice between near-synonyms. We

Inkpen, Diana

373

1 Running Head: COMMUNICATION TECHNOLOGY FOR TEAMS The effects of multimedia communication;2 The effects of multimedia communication technology on non-collocated teams: a case study 1. Introduction editorial details and in formatting from the official version. Keywords: teams, workplace meetings, virtual

Carletta, Jean

374

Utilizing Lexical Data from a Web-Derived Corpus to Expand Productive Collocation Knowledge

ERIC Educational Resources Information Center

Collocations are of great importance for second language learners, and a learner's knowledge of them plays a key role in producing language fluently (Nation, 2001: 323). In this article we describe and evaluate an innovative system that uses a Web-derived corpus and digital library software to produce a vast concordance and present it in a way

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

2010-01-01

375

ERIC Educational Resources Information Center

To date, there has been little empirical research exploring the relationship between implicit and explicit lexical knowledge (of collocations). As a first step in addressing this gap, two laboratory experiments were conducted that evaluate different conditions (enriched, enhanced, and decontextualized) under which both adult native speakers

Sonbul, Suhad; Schmitt, Norbert

2013-01-01

376

Lexical Collocation and Topic Occurrence in Well-Written Editorials: A Study in Form.

ERIC Educational Resources Information Center

To explore the concept of lexical collocation, or relationships between words, a study was conducted based on three assumptions: (1) that a text structure for a unit of discourse was analogous to that existing at the level of the sentence, (2) that such a text form could be discovered if a large enough sample of generically similar texts was

Addison, James C., Jr.

377

Optimal symmetric ℋ2 controllers for systems with collocated sensors and actuators

This paper addresses the problem of designing the optimal symmetric ℋ2 controller for a plant with collocated sensors and actuators but with possibly asymmetric disturbance injection and performance specification. For such a control problem, the generalized plant has a symmetric block representing the transfer matrix from the control input to the measured output. A complete solution to the optimal ℋ2

Guang-Hong Yang; Li Qiu

2001-01-01

378

TRIPLE COLLOCATION OF SUMMER1 PRECIPITATION RETRIEVALS FROM SEVIRI OVER2

radars provide48 information on precipitation occurrence and intensity and the networks of these radars1 TRIPLE COLLOCATION OF SUMMER1 PRECIPITATION RETRIEVALS FROM SEVIRI OVER2 EUROPE WITH GRIDDED RAIN GAUGE AND3 WEATHER RADAR DATA4 5 6 R. A. Roebeling1,2 , E.L.A. Wolters1 , J.F. Meirink1 and H. Leijnse1

Stoffelen, Ad

379

Frequent Collocates and Major Senses of Two Prepositions in ESL and ENL Corpora

ERIC Educational Resources Information Center

This contribution assesses in quantitative terms frequent collocates and major senses of "between" and "through" in the corpus of Cameroonian English (CCE), the corpus of East-African (Kenya and Tanzania) English which is part of the International Corpus of English (ICE) project (ICE-EA), and the London Oslo/Bergen (LOB) corpus of British English.

Nkemleke, Daniel

2009-01-01

380

Collocational Competence of Arabic Speaking Learners of English: A Study in Lexical Semantics.

ERIC Educational Resources Information Center

This study examined learners' productive competence in collocations and idioms by means of their performance on two interdependent tasks. Participants were two groups of English as a Foreign Language undergraduate and graduate students from the English department at Jordan's Yarmouk University. The two tasks included the following: a multiple

Zughoul, Muhammad Raji; Abdul-Fattah, Hussein S.

381

Tangential derivative of singular boundary integrals with respect to the position of collocation potential and elastic problems are considered. A proper definition of the derivative of a strongly singular residual function is found to be equal to the derivative of the strongly singular BIE residual when

Paris-Sud XI, Université de

382

Collocational Differences between L1 and L2: Implications for EFL Learners and Teachers

ERIC Educational Resources Information Center

Collocations are one of the areas that produce problems for learners of English as a foreign language. Iranian learners of English are by no means an exception. Teaching experience at schools, private language centers, and universities in Iran suggests that a significant part of EFL learners' problems with producing the language, especially at

Sadeghi, Karim

2009-01-01

383

Coexistence Wi-Fi MAC Design for Mitigating Interference Caused by Collocated Bluetooth

to analyze the throughput and transmission delay of the Wi-Fi device. The analytical model is validated1 Coexistence Wi-Fi MAC Design for Mitigating Interference Caused by Collocated Bluetooth Alex Chia--A non-collaborative coexistence mechanism for wireless- fidelity (Wi-Fi) and bluetooth (BT) systems

Kuo, C.-C. "Jay"

384

Your Participation Is "Greatly/Highly" Appreciated: Amplifier Collocations in L2 English

ERIC Educational Resources Information Center

The current study sets out to investigate collocational knowledge for a set of 13 English amplifiers among native and nonnative speakers of English, by providing a partial replication of one of the projects reported on in Granger (1998). The project combines both phraseological and distributional approaches to research into formulaic language to

Edmonds, Amanda; Gudmestad, Aarnes

2014-01-01

385

NASA Astrophysics Data System (ADS)

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.

2009-12-01

386

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

387

NASA Astrophysics Data System (ADS)

Tooth stiffness is a very important parameter in studying both static and dynamic behaviour of spline couplings and gears. Many works concerning tooth stiffness calculation are available in the literature, but experimental results are very rare, above all considering spline couplings. In this work experimental values of spline coupling tooth stiffness have been obtained by means of a special hexapod measuring device. Experimental results have been compared with the corresponding theoretical and numerical ones. Also the effect of angular misalignments between hub and shaft has been investigated in the experimental planning.

Cur, Francesca; Mura, Andrea

2013-11-01

388

Determination of airplane model structure from flight data using splines and stepwise regression

NASA Technical Reports Server (NTRS)

A procedure for the determination of airplane model structure from flight data is presented. The model is based on a polynomial spline representation of the aerodynamic coefficients, and the procedure is implemented by use of a stepwise regression. First, a form of the aerodynamic force and moment coefficients amenable to the utilization of splines is developed. Next, expressions for the splines in one and two variables are introduced. Then the steps in the determination of an aerodynamic model structure and the estimation of parameters are discussed briefly. The focus is on the application to flight data of the techniques developed.

Klein, V.; Batterson, J. G.

1983-01-01

389

NASA Technical Reports Server (NTRS)

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

390

Objectives To explore the effects of computed tomography (CT) image characteristics and B-spline knot spacing (BKS) on the spatial accuracy of a B-spline deformable image registration (DIR) in the head-and-neck geometry. Methods The effect of image feature content, image contrast, noise, and BKS on the spatial accuracy of a B-spline DIR was studied. Phantom images were created with varying feature content and varying contrast-to-noise ratio (CNR), and deformed using a known smooth B-spline deformation. Subsequently, the deformed images were repeatedly registered with the original images using different BKSs. The quality of the DIR was expressed as the mean residual displacement (MRD) between the known imposed deformation and the result of the B-spline DIR. Finally, for three patients, head-and-neck planning CT scans were deformed with a realistic deformation field derived from a rescan CT of the same patient, resulting in a simulated deformed image and an a-priori known deformation field. Hence, a B-spline DIR was performed between the simulated image and the planning CT at different BKSs. Similar to the phantom cases, the DIR accuracy was evaluated by means of MRD. Results In total, 162 phantom registrations were performed with varying CNR and BKSs. MRD-values < 1.0 mm were observed with a BKS between 1020 mm for image contrast ? 250 HU and noise < 200 HU. Decreasing the image feature content resulted in increased MRD-values at all BKSs. Using BKS = 15 mm for the three clinical cases resulted in an average MRD < 1.0 mm. Conclusions For synthetically generated phantoms and three real CT cases the highest DIR accuracy was obtained for a BKS between 1020 mm. The accuracy decreased with decreasing image feature content, decreasing image contrast, and higher noise levels. Our results indicate that DIR accuracy in clinical CT images (typical noise levels < 100 HU) will not be effected by the amount of image noise. PMID:25074293

2014-01-01

391

In this paper, the design of an acceleration sensor based active vibration control for a cantilever beam with bonded piezoelectric patches is studied. The problem of phase hysteresis and time delay caused by the non-collocated sensor\\/actuator pairs is considered. The system's dynamic model considering the non-collocated placement of the acceleration sensor and the piezoelectric patch actuator is derived. The phenomenon

Zhi-Cheng Qiu; Jian-Da Han; Xian-Min Zhang; Yue-Chao Wang; Zhen-Wei Wu

2009-01-01

392

Is the sky pure today? AwkChecker: an assistive tool for detecting and correcting collocation errors

Collocation preferences represent the commonly used expressions, idioms, and word pairings of a language. Because collocation preferences arise from consensus usage, rather than a set of well-defined rules, they must be learned on a case-by-case basis, making them particularly challenging for non-native speakers of a language. To assist non-native speakers with these parts of a language, we developed AwkChecker, the

Taehyun Park; Edward Lank; Pascal Poupart; Michael Terry

2008-01-01

393

Power series expansion method for determining collective quantities

NASA Astrophysics Data System (ADS)

A method of extracting the collective profiles from the microscopic many-body quantum dynamics is presented. In this paper a power series expansion method is introduced with the aim of utilizing the spline interpolation method.

Iwata, Yoritaka

2013-04-01

394

NASA Astrophysics Data System (ADS)

A spectral Chebyshev-collocation method is devised for the 1-1/2 layer non-linear reduced-gravity equations. Following a general description of spectral methods with their application to meteorological and oceanographic problems the implementation of the numerical technique is described. A bicharacteristic scheme is applied to solve the equations at the boundaries incorporating the boundary conditions. This treatment enables stable time integrations (spectral methods in general are very sensitive to boundary errors). A simple transfinite grid generation method is used to construct grids over irregular (non-rectangular) simply-connected domains. The model is used in a study of the dynamics of Yanai (or mixed Rossby-gravity) wave packets. These are of interest because of the observations of equatorial instability waves (which have the characteristics of Yanai waves) and their role in the momentum and heat budgets in the tropics. A series of experiments is performed to investigate the generation of the waves by simple cross-equatorial wind stress forcings in various configurations and the influence of a western boundary on them. They may be generated in the interior ocean as well as from a western boundary. The observations from all the oceans indicate that the waves have a preferential period and wavelength of around 26 days and 1000 km respectively. This is seen in the model results too and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.

Kelly, Brian Gerard Joseph

395

Recovering coseismic point ground tilts from collocated high-rate GPS and accelerometers

NASA Astrophysics Data System (ADS)

Rotational along with translational and strain measurements are essential for a complete description of the motion of a deformable body in a seismic event. We propose a new seismogeodetic approach where collocated high-rate GPS and accelerometer measurements are combined to estimate permanent and dynamic coseismic ground tilts at a point, whereas at present, only dynamic tilts are measured with either a dense seismic array or an expensive ring laser gyroscope. We estimate point tilts for a five-story structure on a shake table subjected to 13 earthquake strong motion records of increasing intensity. For the most intense record from the 2002 M7.9 Denali earthquake, we observe a peak-to-peak dynamic tilt of 0.12 and a permanent tilt of 0.16 for the structure's roof. Point tilts derived from networks of collocated GPS and accelerometers can be used to estimate the rotational component of the seismic wavefield for improved earthquake source characterization.

Geng, Jianghui; Melgar, Diego; Bock, Yehuda; Pantoli, Elide; Restrepo, Jos

2013-10-01

396

The convergence problem of collocation solutions in the framework of the stochastic interpretation

NASA Astrophysics Data System (ADS)

The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. "Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic" Dante Alighieri, La Divina Commedia, Inferno, IV - 136

Sans, F.; Venuti, G.

2011-01-01

397

NASA Technical Reports Server (NTRS)

Raman lidar is a leading candidate for providing the detailed space- and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water vapor data during three nights in November 1992 while the systems were collocated at the Goddard Space Flight Center. Although these lidar systems differ substantially in their design, measured water vapor profiles agreeed within 0.15 g/kg between altitudes of 1 and 5 km. Comparisons with coincident radiosondes showed all instruments agreed within 0.2 g/kg in this same altitude range. Both lidars also clearly showed the advection of water vapor in the middle troposphere and the pronounced increase in water vapor in the nocturnal boundary layer that occurred during one night.

Goldsmith, J. E. M.; Bisson, Scott E.; Ferrare, Richard A.; Evans, Keith D.; Whiteman, David N.; Melfi, S. H.

1994-01-01

398

A Comparison of Collocation-Based Similarity Measures in Query Expansion

Abstract In this paper, we present a comparison of collocation-based similarity measures: Jaccard, Dice and Cosine similarity measures,for the proper,selection of additional search terms in query expansion. In addition, we consider two more similarity measures: average conditional probability (ACP) and normalized,mutual,information,(NMI). ACP is the mean,value of two conditional probabilities between a query,term,and,an additional,search term. NMI is a normalized,value of the

Myoung-Cheol Kim; Key-Sun Choi

1999-01-01

399

Design and Application of a Collocated Capacitance Sensor for Magnetic Bearing Spindle

NASA Technical Reports Server (NTRS)

This paper presents a collocated capacitance sensor for magnetic bearings. The main feature of the sensor is that it is made of a specific compact printed circuit board (PCB). The signal processing unit has been also developed. The results of the experimental performance evaluation on the sensitivity, resolution and frequency response of the sensor are presented. Finally, an application example of the sensor to the active control of a magnetic bearing is described.

Shin, Dongwon; Liu, Seon-Jung; Kim, Jongwon

1996-01-01

400

It is an accident of history that the current model of the fuel cycle is a separate set of facilities connected by transportation. The question is whether collocation and integration of reprocessing and fuel fabrication with the repository significantly reduce the costs of a closed fuel cycle while improving system performance in terms of safety and long-term repository performance. This paper examines the question in terms of higher-level functional requirements of reprocessing systems and geological repositories.

Forsberg, C. [Massachusetts Institute of Technology, 77 Massachusetts Ave., Room 24-207A Cambridge, Massachusetts 02139 (United States); Lewis, L. [Idaho National Laboratory, Idaho Falls, Idaho 83415 (United States)

2013-07-01

401

Hedonic aspects are increasingly considered as an important factor in user acceptance of information systems, especially for activities with high self-fulfilling value for the users. In this paper we report on the results of an ex- periment investigating the hedonic qualities of an interactive large-display workspace for collocated collaboration in sales-oriented travel advisory. The re- sults show a higher hedonic

Jasminko Novak; Susanne Schmidt

2009-01-01

402

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

Bayan Babakhani; Vries de Theo J. A; Amerongen van Job

2012-01-01

403

On Improving Performance of VoD Systems Based on Collocated Access Points

This paper addresses the problem of scalable delivery of video-on-demand (VoD) to mobile devices. In a previous work, we introduced a novel design for VoD systems op- erating over 802.11 networks, in which collocated Access Points (APs) work in non-overlapping channels orches- trated by the Wireless Channel Manager (WCM), a cen- tral unit that performs association control of clients to

Leonardo Bidese de Pinho; Claudio Luis de Amorim

404

Quiet Clean Short-haul Experimental Engine (QCSEE). Ball spline pitch change mechanism design report

NASA Technical Reports Server (NTRS)

Detailed design parameters are presented for a variable-pitch change mechanism. The mechanism is a mechanical system containing a ball screw/spline driving two counteracting master bevel gears meshing pinion gears attached to each of 18 fan blades.

1978-01-01

405

NASA Astrophysics Data System (ADS)

and validation of geophysical measurement systems typically require knowledge of the "true" value of the target variable. However, the data considered to represent the "true" values often include their own measurement errors, biasing calibration, and validation results. Triple collocation (TC) can be used to estimate the root-mean-square-error (RMSE), using observations from three mutually independent, error-prone measurement systems. Here, we introduce Extended Triple Collocation (ETC): using exactly the same assumptions as TC, we derive an additional performance metric, the correlation coefficient of the measurement system with respect to the unknown target, ?t,Xi. We demonstrate that ?t,Xi2 is the scaled, unbiased signal-to-noise ratio and provides a complementary perspective compared to the RMSE. We apply it to three collocated wind data sets. Since ETC is as easy to implement as TC, requires no additional assumptions, and provides an extra performance metric, it may be of interest in a wide range of geophysical disciplines.

McColl, Kaighin A.; Vogelzang, Jur; Konings, Alexandra G.; Entekhabi, Dara; Piles, Mara.; Stoffelen, Ad

2014-09-01

406

NASA Technical Reports Server (NTRS)

An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.

Robbins, J. W.

1985-01-01

407

A methodology to predict fretting wear in complex couplings is described and validated against results obtained from a reduced scale aeroengine-type spline coupling subjected to complex cyclic load cases. The methodology uses three-dimensional finite element analysis, together with coefficient of friction data obtained from stroke controlled round-against-flat fretting tests, to determine spline tooth contact pressure and slip distributions; the latter

C. H. H. Ratsimba; I. R. McColl; E. J. Williams; S. B. Leen; H. P. Soh

2004-01-01

408

Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines

Ridges are extremal curves of principal curvatures on a surface that indicate salient intrinsic features of its shape. This paper presents a novel approach for extracting ridges of improved quality from isosurfaces of volumetric scalar-valued grids by converting them to implicit trivariate B-spline representations. A robust tracing approach demonstrated to extract ridges accurately from parametric B-spline surfaces is extended to

Suraj Musuvathy; Tobias Martin; Elaine Cohen

2010-01-01

409

Constrained shape modification of cubic B-spline curves by means of knots

Abstract The effect of the modification of knot values on the shape of B-spline curves is examined,in this paper. The modification of a knot of a Bspline curve of order k generates a one-parameter family of curves.This family has an envelope which is also a B-spline curve with the same control polygon and of order k 2 1: Applying this

Imre Juhsz; Mikls Hoffmann

2004-01-01

410

A-splines: local interpolation and approximation using Gk-continuous piecewise real algebraic curves

We provide sufficient conditions for the BernsteinBzier (BB) form of an implicitly defined bivariate polynomial over a triangle, such that the zero contour of the polynomial defines a smooth and single sheeted real algebraic curve segment. We call a piecewise Gk-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that

Chandrajit L. Bajaj; Guoliang Xu

1999-01-01

411

Comparison Between Polynomial, Euler Beta-Function and Expo-Rational B-Spline Bases

NASA Astrophysics Data System (ADS)

Euler Beta-function B-splines (BFBS) are the practically most important instance of generalized expo-rational B-splines (GERBS) which are not true expo-rational B-splines (ERBS). BFBS do not enjoy the full range of the superproperties of ERBS but, while ERBS are special functions computable by a very rapidly converging yet approximate numerical quadrature algorithms, BFBS are explicitly computable piecewise polynomial (for integer multiplicities), similar to classical Schoenberg B-splines. In the present communication we define, compute and visualize for the first time all possible BFBS of degree up to 3 which provide Hermite interpolation in three consecutive knots of multiplicity up to 3, i.e., the function is being interpolated together with its derivatives of order up to 2. We compare the BFBS obtained for different degrees and multiplicities among themselves and versus the classical Schoenberg polynomial B-splines and the true ERBS for the considered knots. The results of the graphical comparison are discussed from analytical point of view. For the numerical computation and visualization of the new B-splines we have used Maple 12.

Kristoffersen, Arnt R.; Dechevsky, Lubomir T.; Laksa?, Arne; Bang, Brre

2011-12-01

412

NASA Astrophysics Data System (ADS)

We introduce a mathematical primitive called the B-spline solid that can be used to create deformable models of muscle shape. B-spline solids can be used to model skeletal muscle for the purpose of building a data library of reusable, deformable muscles that are reconstructed from actual muscle data. Algorithms are provided for minimizing shape distortions that may be caused when fitting discrete sampled data to a continuous B-spline solid model. Visible Human image data provides a good indication of the perimeter of a muscle, but is not suitable for providing internal muscle fiber bundle arrangements which are important for physical simulation of muscle function. To obtain these fiber bundle orientations, we obtain 3-D muscle fiber bundle coordinates by triangulating optical images taken from three different camera views of serially dissected human soleus specimens. B-spline solids are represented as mathematical three-dimensional vector functions which can parameterize an enclosed volume as well as its boundary surface. They are based on B-spline basis functions, allowing local deformations via adjustable control points and smooth continuity of shape. After the B-spline solid muscle model is fitted with its external surface and internal volume arrangements, we can subsequently deform its shape to allow simulation of animated muscle tissue.

Ng-Thow-Hing, Victor; Agur, Anne; Ball, Kevin A.; Fiume, Eugene; McKee, Nancy

1998-05-01

413

A meshless point collocation treatment of transient bioheat problems.

A meshless numerical method is proposed for the solution of the transient bioheat equation in two and three dimensions. The Pennes bioheat equation is extended in order to incorporate water evaporation, tissue damage, and temperature-dependent tissue properties during tumor ablation. The conductivity of the tissue is not assumed constant but is treated as a local function to simulate local variability due to the existence of usually unclear interfacing of healthy and pathological segments. In this way, one avoids the need for accurate identification of the boundaries between pathological and healthy regions, which is a typical problem in medical practice, and sidesteps, evidently, the corresponding mathematical treatment of such boundaries, which is usually a tedious procedure with some inevitable degree of approximation. The numerical results of the new method for test applications of the bioheat transfer equation are validated against analytical predictions and predictions of other numerical methods. 3D simulations are presented that involve the modeling of tumor ablation and account for metabolic heat generation, blood perfusion, and heat ablation using realistic values for the various parameters. An evaluation of the effective medium approximation to homogenize conductivity fields for use with the bioheat equation is also provided. PMID:24574248

Bourantas, G C; Loukopoulos, V C; Burganos, V N; Nikiforidis, G C

2014-05-01

414

Smart point landmark distribution for thin-plate splines

NASA Astrophysics Data System (ADS)

Landmark placement is crucial in manual demarcation and registration of anatomical structures, registration of different image modalities (i.e. MRI/CT), labeling training data for lip and face principal component models, training for neural networks, and signal interpolation to name some applications. Although landmark placement at curvature and coordinate extrema (e.g. corners of the mouth, lowest point on the lower lip) is fairly unambiguous, the placement of point landmarks along a linear contour is subjective. Unfortunately the user's choice of landmark placement determines the quality of the resulting registration. In this paper, we present an algorithm to remove these undesired degrees of freedom by re-placing landmarks along the contour. Ambiguous landmarks are moved so as to minimize a thin plate spline energy while constraining the landmarks to the originally specified contour. The resulting landmark placement results in a smoother registration while still interpolating the contours and fixed landmarks. The results show that the ambiguity of manual landmark placement along contours does affect the smoothness of the interpolated registration, and that significantly smoother interpolations can be achieved using our approach. This procedure may also benefit other applications employing landmarks by eliminating unintended curvature (variation) from the landmark data.

Lewis, John P.; Hwang, Hea-Juen; Neumann, Ulrich; Enciso, Reyes

2004-05-01

415

NASA Astrophysics Data System (ADS)

Generalized linear models are widely-used statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms by a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on penalized maximum likelihood and on the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines which is attractive for nonparametric components. Then, we approach solving the P-IRLS problem using continuous optimization techniques. They become an important complementary technology and alternative to the penalty methods with the flexibility of choosing the penalty parameter adaptively. In particular, we model and treat the constrained P-IRLS problem by the elegant framework of conic quadratic programming. This paper is of a more theoretical nature and a preparation of real-world applications in future.

Taylan, Pakize; Weber, Gerhard-Wilhelm; Liu, Lian

2010-06-01

416

Determination of risk of post seismic fires in collocated facilities

Fire is a well-recognized secondary effect following earthquakes. The damage resulting from a fire can be more extensive than that caused by the direct physical damage due to shaking and other geotechnical effects. Previous post-seismic fire frequency estimates have commonly been derived for exceeding a given severe peak ground acceleration (pga). The estimate combined the return frequency of the given pga, the probability of the damage state occurring at the defined pga, and the conditional probability of fire for the single damage state. This approach assumed that the fire risk for lower intensity events could be neglected. This paper describes an alternate method where the low-intensity seismic events are not neglected.

Joshi, J.R.

2000-02-18

417

Including the relativistic kinetic energy in a spline-augmented plane-wave band calculation

The first-order relativistic correction to the kinetic energy of an electron, the mass-velocity term, is not bounded from below. It can, therefore, not be used within a variational framework. To overcome this deficiency we developed a method to include the entire relativistic kinetic energy {radical}(p{sup 2}c{sup 2}+m{sub 0}{sup 2}c{sup 4}){minus}m{sub 0}c{sup 2} in a spline-augmented plane-wave band calculation. The first results for silver are quite promising, especially for d and p states: The analysis of the energies of the core states as well as of the valence band structure suggests that the energies of d bands are reproduced within 1 mRy. However, the combination of the relativistic kinetic energy with the Darwin term leads to energies which are too low for s-like valence states by 10 mRy. Therefore, the s and d valence band complex is spread out and the Fermi level is lowered by the same amount as the s states. We expect to overcome these deficiencies in future investigations by using a alternative form of the relativistic potential correction along the lines proposed by Douglas and Kroll. {copyright} {ital 1997} {ital The American Physical Society}

Fehrenbach, G.M.; Schmidt, G. [Sektion Physik der Ludwig Maximilians Universitaet Muenchen, Theresienstrae 37, 80333 Munich (Federal Republic of Germany)] [Sektion Physik der Ludwig Maximilians Universitaet Muenchen, Theresienstrae 37, 80333 Munich (Federal Republic of Germany)

1997-03-01

418

Both the multivariate adaptive regression splines (MARS) and the two-step MARS (TMARS) methodologies were applied in a quantitative structure-retention relationship (QSRR) context. For seven RPLC systems, QSRR models were built that describe the retention times of a set of peptides using a large set of molecular descriptors as potential predictor variables. The use of QSRR models for chromatographic retention prediction of peptides may be valuable in proteomic research to improve the number of correct peptide identifications. Always, 70% of the samples was used to derive the QSRR models (calibration set), whereas the remaining 30% of the peptides were treated as an independent external test set. For four systems, the models obtained by TMARS have better predictive abilities than the MARS models. The MARS and TMARS model performance was compared with those of other multivariate modelling techniques. For five out of seven systems it was observed that the uninformative variable elimination by the partial least squares (PLS) approach outperforms all other methods studied. For three systems predictive errors smaller than 30 s were obtained. PLS regression and a multiple linear regression model based on three descriptors led to the best predictivities for the remaining two systems. PMID:17443841

Put, Raf; Vander Heyden, Yvan

2007-05-01

419

Energy stable, collocated high order schemes for incompressible flows on distorted grids

NASA Astrophysics Data System (ADS)

An energy preserving finite difference scheme for incompressible, constant density flows is presented. It is building on the idea of the skew-symmetric rewriting of the non-linear transport term. In contrast to former schemes collocated grids can be used, while exactly preserving the energy conservation and still avoiding the odd-even decoupling of the Laplacian. High order derivatives can be utilized. A formulation for curvilinear grids is discussed and strict skew-symmetry and perfect conservation is found for arbitrary transformations in two dimensions and quite general, but not fully general transformations in three dimensions.

Reiss, Julius

2012-09-01

420

Application of Collocated GPS and Seismic Sensors to Earthquake Monitoring and Early Warning

We explore the use of collocated GPS and seismic sensors for earthquake monitoring and early warning. The GPS and seismic data collected during the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquakes are analyzed by using a tightly-coupled integration. The performance of the integrated results is validated by both time and frequency domain analysis. We detect the P-wave arrival and observe small-scale features of the movement from the integrated results and locate the epicenter. Meanwhile, permanent offsets are extracted from the integrated displacements highly accurately and used for reliable fault slip inversion and magnitude estimation. PMID:24284765

Li, Xingxing; Zhang, Xiaohong; Guo, Bofeng

2013-01-01

421

Gearbox Reliability Collaborative Analytic Formulation for the Evaluation of Spline Couplings

Gearboxes in wind turbines have not been achieving their expected design life; however, they commonly meet and exceed the design criteria specified in current standards in the gear, bearing, and wind turbine industry as well as third-party certification criteria. The cost of gearbox replacements and rebuilds, as well as the down time associated with these failures, has elevated the cost of wind energy. The National Renewable Energy Laboratory (NREL) Gearbox Reliability Collaborative (GRC) was established by the U.S. Department of Energy in 2006; its key goal is to understand the root causes of premature gearbox failures and improve their reliability using a combined approach of dynamometer testing, field testing, and modeling. As part of the GRC program, this paper investigates the design of the spline coupling often used in modern wind turbine gearboxes to connect the planetary and helical gear stages. Aside from transmitting the driving torque, another common function of the spline coupling is to allow the sun to float between the planets. The amount the sun can float is determined by the spline design and the sun shaft flexibility subject to the operational loads. Current standards address spline coupling design requirements in varying detail. This report provides additional insight beyond these current standards to quickly evaluate spline coupling designs.

Guo, Y.; Keller, J.; Errichello, R.; Halse, C.

2013-12-01

422

. Intergenerational gaming, console games, video games, Wii, Playstation Introduction Since the 1920s, there have been1 Voida, A. & Greenberg, S. (2009). Collocated intergenerational console gaming. Research Report. Collocated Intergenerational Console Gaming Amy Voida & Saul Greenberg Department of Computer Science

Greenberg, Saul

423

-collocated measurements is studied. The measurement of P+jQ in a line or at a bus is usually accomplished by measuring is introduced. The paper reports a way to correct for non-collocation of measurements. Index Terms market it is increasingly important to find cost effective ways to improve system visibility and account

424

Penalized splines for smooth representation of high-dimensional Monte Carlo datasets

NASA Astrophysics Data System (ADS)

Detector response to a high-energy physics process is often estimated by Monte Carlo simulation. For purposes of data analysis, the results of this simulation are typically stored in large multi-dimensional histograms, which can quickly become both too large to easily store and manipulate and numerically problematic due to unfilled bins or interpolation artifacts. We describe here an application of the penalized spline technique (Marx and Eilers, 1996) [1] to efficiently compute B-spline representations of such tables and discuss aspects of the resulting B-spline fits that simplify many common tasks in handling tabulated Monte Carlo data in high-energy physics analysis, in particular their use in maximum-likelihood fitting.

Whitehorn, Nathan; van Santen, Jakob; Lafebre, Sven

2013-09-01

425

NASA Astrophysics Data System (ADS)

The B-spline R-matrix (BSR) with pseudostates method is employed to treat electron collisions with carbon atoms. Predictions for elastic scattering, excitation, and ionization are presented for incident energies between threshold and 60 eV. The structure description is further improved compared to a previous BSR calculation by Zatsarinny [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.71.042702 71, 042702 (2005)]. This change in the structure model, together with the inclusion of a large number of pseudostates in the close-coupling expansion, has a major influence on the theoretical predictions, especially at intermediate energies, where many of the excitation cross sections are reduced significantly. Estimates for ionization cross sections are also provided.

Wang, Yang; Zatsarinny, Oleg; Bartschat, Klaus

2013-01-01

426

NASA Astrophysics Data System (ADS)

The B-spline R-matrix-with-pseudostates (BSR) method is employed to treat electron collisions with nitrogen atoms. Predictions for elastic scattering, excitation, and ionization are presented for all transitions between the lowest 21 states of nitrogen in the energy range from threshold to 120 eV. The structure description has been further improved compared to a previous BSR calculation by Tayal and Zatsarinny [J. Phys. B 38, 3631 (2005), 10.1088/0953-4075/38/20/001]. This change in the structure model, together with the inclusion of a large number of pseudostates in the close-coupling expansion, has a major influence on the theoretical predictions, especially at intermediate energies, where many of the excitation cross sections are reduced significantly. Ionization cross sections for the ground and metastable initial states are also provided. Finally, we carry out an accurate ab initio treatment of the prominent shape resonance just above the elastic threshold.

Wang, Yang; Zatsarinny, Oleg; Bartschat, Klaus

2014-06-01

427

, Rice University, Houston, Texas, USA Abstract A rational B-spline curve or surface is a collection control over the morph between two rational B-spline curves or sur- faces. Here we propose a technique for designing customized morphs by attaching appropriate mass distributions to target B-spline curves

Ju, Tao

428

Automated B-Spline Curve Representation Incorporating MDL and Error-Minimizing Control Point Insertion, but despite the long existence of B-spline curve-fitting techniques, it is difficult to find a fully automated 2.1 Parameterization When handling image curves, the B-spline parameterization along the fitted

Cham, Tat Jen

429

Resource demand analyses indicate that algal biodiesel production would require unsustainable amounts of freshwater and fertilizer supplies. Alternatively, municipal wastewater effluent can be used, but this restricts production of algae to areas near wastewater treatment plants (WWTPs), and to date, there has been no geospatial analysis of the feasibility of collocating large algal ponds with WWTPs. The goals of this analysis were to determine the available areas by land cover type within radial extents (REs) up to 1.5 miles from WWTPs; to determine the limiting factor for algal production using wastewater; and to investigate the potential algal biomass production at urban, near-urban, and rural WWTPs in Kansas. Over 50% and 87% of the land around urban and rural WWTPs, respectively, was found to be potentially available for algal production. The analysis highlights a trade-off between urban WWTPs, which are generally land-limited but have excess wastewater effluent, and rural WWTPs, which are generally water-limited but have 96% of the total available land. Overall, commercial-scale algae production collocated with WWTPs is feasible; 29% of the Kansas liquid fuel demand could be met with implementation of ponds within 1 mile of all WWTPs and supplementation of water and nutrients when these are limited. PMID:22970803

Fortier, Marie-Odile P; Sturm, Belinda S M

2012-10-16

430

Spatial scales of altocumulus clouds observed with collocated CALIPSO and CloudSat measurements

NASA Astrophysics Data System (ADS)

Altocumulus (Ac) clouds are important, yet climate models have difficulties in simulating and predicting these clouds, due to their small horizontal scales and thin vertical extensions. In this research, 4 years of collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) lidar and CloudSat radar measurements is analyzed to study the along-track horizontal scales and vertical depths of Ac clouds. Methodology to calculate Ac along-track horizontal scale and vertical depth using collocated CALIPSO and CloudSat measurements is introduced firstly. The global mean Ac along-track horizontal scale is 40.2 km, with a standard deviation of 52.3 km. Approximately 93.6% of Ac cannot be resolved by climate models with a grid resolution of 1. The global mean mixed-phase Ac vertical depth is 1.96 km, with a standard deviation of 1.10 km. Global distributions of the Ac along-track horizontal scales and vertical depths are presented and possible factors contributing to their geographical differences are analyzed. The result from this study can be used to improve Ac parameterizations in climate models and validate the model simulations.

Zhang, Damao; Luo, Tao; Liu, Dong; Wang, Zhien

2014-11-01

431

Spatial scales of altocumulus clouds observed with collocated CALIPSO and CloudSat measurements

NASA Astrophysics Data System (ADS)

Altocumulus (Ac) clouds are important, yet climate models have difficulties in simulating and predicting these clouds, due to their small horizontal scales and thin vertical extensions. In this research, 4 years of collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) lidar and CloudSat radar measurements is analyzed to study the along-track horizontal scales and vertical depths of Ac clouds. Methodology to calculate Ac along-track horizontal scale and vertical depth using collocated CALIPSO and CloudSat measurements is introduced firstly. The global mean Ac along-track horizontal scale is 40.2 km, with a standard deviation of 52.3 km. Approximately 93.6% of Ac cannot be resolved by climate models with a grid resolution of 1. The global mean mixed-phase Ac vertical depth is 1.96 km, with a standard deviation of 1.10 km. Global distributions of the Ac along-track horizontal scales and vertical depths are presented and possible factors contributing to their geographical differences are analyzed. The result from this study can be used to improve Ac parameterizations in climate models and validate the model simulations.

Zhang, Damao; Luo, Tao; Liu, Dong; Wang, Zhien

2014-10-01

432

NASA Astrophysics Data System (ADS)

Hedonic aspects are increasingly considered as an important factor in user acceptance of information systems, especially for activities with high self-fulfilling value for the users. In this paper we report on the results of an experiment investigating the hedonic qualities of an interactive large-display workspace for collocated collaboration in sales-oriented travel advisory. The results show a higher hedonic stimulation quality of a touch-based large-display travel advisory workspace than that of a traditional workspace with catalogues. Together with the feedback of both customers and travel agents this suggests the adequacy of using touch-based large-displays with visual workspaces for supporting the hedonic stimulation of user experience in collocated collaboration settings. The relation of high perception of hedonic quality to positive emotional attitudes towards the use of a large-display workspace indicates that even in utilitarian activities (e.g. reaching sales goals for travel agents) hedonic aspects can play an important role. This calls for reconsidering the traditional divide of hedonic vs. utilitarian systems in current literature, to a more balanced view towards systems which provide both utilitarian and hedonic sources of value to the user.

Novak, Jasminko; Schmidt, Susanne

433

coefficients k, v, b. o by minimizing the difference between the measured snd predicted eigenvalues and eigenvectors. 6. Plot k 6z b versus ZXspline and v JL p versus A@spline with speed as a. parameter for a given torque, misalignment, and spline oil flow..., and the sleeve housing are positioned appropriately along the test shaft. Straight fits rather than tapered fits are used to connect the torque shaft coupling to the outboard gear unit low speed shaft and the torque actuator flanges to the torque shaft...

Rombado, Gabriel

2012-06-07

434

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head

NASA Astrophysics Data System (ADS)

This paper deals with calculation of the quadratic triangular B-spline surface of the human head for the purpose of its modeling in the standard videocodec MPEG-4 SNHC. In connection with this we propose an algorithm of generation of the knot net and present the results of its application for triangulation of the 3D polygonal model Candide. Then for the model and generated knot net as well as an established distribution of control points we show the results of the calculated quadratic triangular B-spline surface of the human head including its textured version for the texture of the selected avatar.

Mihalk, Jn

2011-09-01

435

SummaryA procedure for the simultaneous quantitation of Al(III) and Cr(III) ions by reversed-phase HPLC, after pre-column complexation\\u000a with 8-hydroxyquinoline, is described. The deconvolution of the partially overlapped peaks was by the Kalman filter method\\u000a which yielded accurate and precise results.\\u000a \\u000a Background removal from the chromatograms was by a new approach employing cubic splines as interpolators between the peak\\u000a valleys.\\u000a \\u000a \\u000a \\u000a Finally,

T. Rotunnol; F. Palmisano; G. Tiravanti; P. G. Zambonin

1990-01-01

436

B in simulation and -20 dB in measurement. MIMO channel capacity measurements have been performed and demonstrate-collocated antennas, radiation pattern diversity, MIMO system, channel capacity measurements I. INTRODUCTION ULTIPLE Input Multiple Output (MIMO) systems can drastically improve wireless communication capacity

Paris-Sud XI, Université de

437

Collocation experiments are incomparable to check geodetic instrument quality and stability. At the Grasse observatory, France, we had the opportunity to have 3 independent laser ranging stations very close one to each other (about 20m): a Satellite Laser Ranging (SLR) station, a Lunar Laser Ranging (LLR) station, and the French Transportable Laser Ranging Station (FTLRS). Thus, we used this unique

J. Nicolas; P. Exertier; O. Laurain; P. Bonnefond; J. F. Mangin; F. Barlier

2004-01-01

438

This study examines the different mechanisms of online social ties underlying individual knowledge sharing through comparative perspectives of collocated vs geographically dispersed teams. By integrating social capital theory and social cognitive theory, this study develops a theoretical model that predicts individual knowledge sharing. Next, the study uses social network analysis to empirically test the proposed model using 186 participants: 84

Ayoung Suh; Kyung-shik Shin

2010-01-01

439

Modeling of hollow fiber asymmetric membranes can provide useful guidelines to achieve desirable separations of multicomponent gas mixtures. Especially in cases of high commercial interest, such as hydrogen recovery from refinery streams, the accurate prediction of membrane separation performance is important. In this work, the appropriate model equations are solved by orthogonal collocation to approximate differential equations, and to solve

S. P Kaldis; G. C Kapantaidakis; G. P Sakellaropoulos

2000-01-01

440

Underground collocation of nuclear power reactors and the nuclear waste management facilities supporting those reactors, termed an underground nuclear park (UNP), appears to have several advantages compared to the conventional approach to siting reactors and waste management facilities. These advantages include the potential to lower reactor capital and operating cost, lower nuclear waste management cost, and increase margins of physical

Carl W Myers; Ned Z Elkins

2008-01-01

441

Collocational complex prepositions (CCPs, e.g., in the hands of) are prefabricated strings of words that play a prepositional role in natural language. Typically, CCPs are formed by a first preposition (P1) followed by a content word (N1) and a second, final preposition (P2) (in the - P1 - hands - N1 - of - P2). Despite their default structure stored

Nicola Molinaro; Paolo Canal; Francesco Vespignani; Francesca Pesciarelli; Cristina Cacciari

2012-01-01

442

A method of generating smooth surface using C-curves

A method of constructing piecewise G1 continuous spline surface using boundary C-curves is presented. C-curves are developed by the basis (sin t, cos t, t, 1), and it overcomes some shortcomings of the nonuniform rational B-splines (NURBS) model. How to develop C-curve into surface becomes a very important problem. Using the convex combination method proposed by Nielson, a piecewise G1

Wei Li; Zhuoqi Wu; Ichiro Hagiwara

2005-01-01

443

NASA Astrophysics Data System (ADS)

The collocated-mesh scheme is often favored over the staggered-mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates. The collocated mesh scheme does not conserve kinetic energy however, and few careful checks of the impact of these errors have been made. In this work, analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme: (1) errors arising from the interpolations used to estimate the velocity on the cell faces, and (2) errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes. It is shown that the interpolation error can be eliminated through the use of first-order accurate centered interpolation operators with mesh-independent weights. The pressure error appears to be intrinsic to the scheme and it is shown to scale as O(? t2? x2). The effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow. Neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the Cartesian mesh is stretched in only one direction. The inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error. The standard second-order centered interpolation is shown to lead to severe numerical oscillations, while the kinetic energy-conserving first-order centered interpolation produces solutions that are almost as smooth as those obtained with a third-order upwind interpolation. When compared in channel flow simulations, however, the first-order centered interpolation is shown to be far superior to the third-order upwind interpolation, the latter being adversely affected by numerical dissipation. Only slight differences were noted when comparing channel flow simulations using first-order and second-order centered interpolations. These results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly-constructed non-dissipative centered interpolations.

Felten, Frdric N.; Lund, Thomas S.

2006-07-01

444

Tomography with few data: Use of collocation methods in acoustic pyrometry

Kaiserslautern 1996 pages 251{263 1Institut fur Numerische und instrumentelle Mathematik, Einsteinstr. 62, D-48149 Munster. E-mail: helmut.sielschott@uni-muenster.de 2Kraftwerk Niederau em, Abt. KF-F, Postfach by Prof. Dr. F. Natterer. Kraftwerk Niederau em, Abt. KF-F, Postfach 1461, D-50104 Bergheim #12;252 Fig. 1

Münster, Westfälische Wilhelms-Universität

445

Statistical models help marketers explore the nature of marketing phenomena for effective targeting of customers within local areas. However, conventional multiple regression (MR) models can only reveal patterns in a simple way by forcing data into linear relationships, whereas it may be advantageous to tease out more complex relationships within the data. Multivariate adaptive regression splines (MARS) is applied to

Hongwei Lu; Mark D. Uncles; Gary D. Gregory; Lihua Zhao

446

We present in this paper a series of operators coming from various domains of mathematical analysis (approximation theory, differential geometry, optimization and partial differential equations (PDE's)) and able to give adequate responses to low level image processing tasks like contrasting, segmenting and contouring objects of interest in bio-medical images. These operators are essentially based on powerful analytic tools, like splines,

Jacques Demongeot

2007-01-01

447

Fast Conversion of Dynamic B-Spline Curves into a Set of Power Form Polynomial Curves

Computation of the characteristic points such as inflection points or cusp on a curve is often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed in a set of polynomial curves in a power form. Once a curve is represented in a power form, a point

Deok-soo Kim; Joonghyun Ryu; Hyun-chan Lee; Hayong Shin; Taeboom Jang

2000-01-01

448

The Effect of Shape Parameters on Hyperbolic Polynomial Uniform B-Spline Curve Model

In this paper, we have studied in depth hyperbolic polynomial uniform B-spline model with shape parameters. Based on this model, we have given an example of freedom curve modeling, and analyzed the effect that different shape parameters have on the change of the shape of the curves. We also developed a space freedom surface modeling system (SFSMS) on the Microsoft

Liu Xumin; Guan Yong; Xu Weixiang; Shang Yuanyuan

2009-01-01

449

A Thin-Plate Spline Calibration Model for Fingerprint Sensor Interoperability

A Thin-Plate Spline Calibration Model for Fingerprint Sensor Interoperability Arun Ross, Member fingerprint, face, iris, and speech. In the context of fingerprint technology, variations are observed in the acquired images of a fingerprint due to differences in sensor resolution, scanning area, sensing technology

Ross, Arun Abraham

450

Principal Warps: Thin-Plate Splines and the Decomposition of Deformations

One conventional tool for interpolating surfaces over scat- tered data, the thin-plate spline, has an elegant algebra expressing the dependence of the physical bending energy of a thin metal plate on point constraints. For interpolation of a surface over a fixed set of nodes in the plane, the bending energy is a quadratic form in the heights assigned to the

Fred L. Bookstein

1989-01-01

451

From SIAM News, Volume 38, Number 4, May 2005 The Extensive Use of Splines at Boeing

application, common across many industries, is computer-aided manufacturing. Here, in addition to representing few remaining areas in either manufacturing or engineering in which these interesting functions have geometric parts, splines can be used to represent machine tool cutter paths. They can also be used

Moehlis, Jeff

452

Bivariate Splines for Hurricane Path Forecasting Bree Ettinger and Ming-Jun Lai

. A notorious example is Hurricane Katrina in 2005 which hit New Orleans and damaged the city significantly. In particular, after Hurricane Katrina, more buoys were placed in the Gulf of Mexico. Several technologies haveBivariate Splines for Hurricane Path Forecasting Bree Ettinger and Ming-Jun Lai 1 Introduction

Lai, Ming-Jun

453

A spline-based parameter and state estimation technique for static models of elastic surfaces

NASA Technical Reports Server (NTRS)

Parameter and state estimation techniques for an elliptic system arising in a developmental model for the antenna surface in the Maypole Hoop/Column antenna are discussed. A computational algorithm based on spline approximations for the state and elastic parameters is given and numerical results obtained using this algorithm are summarized.

Banks, H. T.; Daniel, P. L.; Armstrong, E. S.

1983-01-01

454

Forecasting the Hourly Ontario Energy Price by Multivariate Adaptive Regression Splines

1 Forecasting the Hourly Ontario Energy Price by Multivariate Adaptive Regression Splines H. In this paper, the MARS technique is applied to forecast the hourly Ontario energy price (HOEP). The MARS models values of the latest pre- dispatch price and demand information, made available by the Ontario

Cañizares, Claudio A.

455

Highly successful learning based on modified Catmull-Rom spline activation function

A sigmoidal-like activation function, a modified Catmull-Rom spline activation function, is proposed. The advantages of the proposed activation are low complexity of the hardware implementation and arithmetic operation. Since it gives a good error signal for updating the weight values, the usual gradient based training algorithm can be used to train the network with the proposed activation function. Our experiments

Khamron Sunat; Chidchanok Lursinsap

2001-01-01

456

Polynomial spline confidence bands for time series trend Q. Shao a,n

author. E-mail addresses: qin.shao@utoledo.edu (Q. Shao), yanglijian@suda.edu.cn, yang@stt.msu.edu (LPolynomial spline confidence bands for time series trend Q. Shao a,n , L. Yang b,c,1 a Department. Yang). 1 His research was supported by NSF awards DMS 0706518 and DMS 1007594, and funding from

457

Submitted to the Annals of Applied Statistics BIVARIATE SPLINES FOR OZONE CONCENTRATION

§ In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed robust than the ones based on thin-plate splines. 1. Introduction. Ground-level ozone is a harmful that air quality warnings associated with ground-level ozone have had an impact on outdoor activi- ties

Lai, Ming-Jun

458

Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery

Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery Qingzhi Guo-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number to separate regression intervals were optimized. Compared to a polynomial model with the same number

459

Modeling of Hormone Secretion-Generating Mechanisms With Splines: A Pseudo-Likelihood

Modeling of Hormone Secretion-Generating Mechanisms With Splines: A Pseudo-Likelihood Approach Anna for the investigation of underlying hormone secretion-generating mechanism. Characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by the slow

Wang, Yuedong

460

A Bayesian approach to generalised partial linear regression models is proposed, where regression functions are modelled nonparametrically using regression splines, with assumptions about shape and smoothness. The knots may be modelled as fixed or free, incorporating a reversible-jump Markov chain Monte Carlo algorithm for the latter. The modelling framework along with vague prior distributions provides more flexibility compared with other

Mary C. Meyer; Amber J. Hackstadt; Jennifer A. Hoeting

2011-01-01

461

GPU-based trimming and tessellation of NURBS and T-Spline surfaces

As there is no hardware support neither for rendering trimmed NURBS -- the standard surface representation in CAD -- nor for T-Spline surfaces the usability of existing rendering APIs like OpenGL, where a run-time tessellation is performed on the CPU, is limited to simple scenes. Due to the irregular mesh data structures required for trimming no algorithms exists that exploit

Michael Guthe; kos Balzs; Reinhard Klein

2005-01-01

462

Interpolation of Magnetic Fields and their Gradients for MEG Data with 3D Spline Functions

this paper, the magnetic fields and their gradients are interpolated with the splinefunctions on a closed surface. In section 2 we introduce the set of 3D spline functions[11]which will be used. In section 3 we describe the mesh generation for the helmet surfaceand in section 4 the interpolation of the magnetic fields and their gradients. Finally, themagnetic fields and their

Shuang-ren Zhao; Heinz Heer; Andreas A. Ioannides; Michael Wagener; Horst Halling; Hans-W. Mller-Grtner

1996-01-01

463

Pi, Archimedes and circular splines P. Sablonni`ere, INSA & IRMAR, Rennes

Pi, Archimedes and circular splines P. Sablonni`ere, INSA & IRMAR, Rennes June 11, 2013 Abstract by two subdivision algorithms. 1 Introduction: Archimedes and the computation of In his famous treatise On the quadrature of the circle [1], Archimedes (287-212 b.c.) gave the following upper and lower bounds for 3 + 10

Boyer, Edmond

464

Test Score Reporting Referenced to Doubly-Moderated Cut Scores Using Splines

ERIC Educational Resources Information Center

This study discusses and presents an example of a use of spline functions to establish and report test scores using a moderated system of any number of cut scores. Our main goals include studying the need for and establishing moderated standards and creating a reporting scale that is referenced to all the standards. Our secondary goals are to make

Schafer, William D.; Hou, Xiaodong

2011-01-01

465

Inversion of the strain-life and strain-stress relationships for use in metal fatigue analysis

NASA Technical Reports Server (NTRS)

The paper presents closed-form solutions (collocation method and spline-function method) for the constants of the cyclic fatigue life equation so that they can be easily incorporated into cumulative damage analysis. The collocation method involves conformity with the experimental curve at specific life values. The spline-function method is such that the basic life relation is expressed as a two-part function, one applicable at strains above the transition strain (strain at intersection of elastic and plastic lines), the other below. An illustrative example is treated by both methods. It is shown that while the collocation representation has the advantage of simplicity of form, the spline-function representation can be made more accurate over a wider life range, and is simpler to use.

Manson, S. S.

1979-01-01

466

NASA Technical Reports Server (NTRS)

As part of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), we have obtained and analyzed measurements made from collocated aircraft of the absorption of solar radiation within the atmospheric column between the two aircraft. The measurements were taken during October 1995 at the ARM site in Oklahoma. Relative to a theoretical radiative transfer model, we find no evidence for excess solar absorption in the clear atmosphere and significant evidence for its existence in the cloudy atmosphere. This excess cloud solar absorption appears to occur in both visible (0.224-0.68 microns) and near-infrared (0.68-3.30 microns) spectral regions, although not at 0.5 microns for the visible contribution, and it is shown to be true absorption rather than an artifact of sampling errors caused by measuring three-dimensional clouds.

Valero, Francisco P. J.; Cess, Robert D.; Zhang, Minghua; Pope, Shelly K.; Bucholtz, Anthony; Bush, Brett; Vitko, John, Jr.

1997-01-01

467

Using multivariate adaptive regression splines to estimate subadult age from diaphyseal dimensions.

Subadult age estimation is considered the most accurate parameter estimated in a subadult biological profile, even though the methods are deficient and the samples from which they are based are inappropriate. The current study addresses the problems that plague subadult age estimation and creates age estimation models from diaphyseal dimensions of modern children. The sample included 1,310 males and females between the ages of birth and 12 years. Eighteen diaphyseal length and breadth measurements were obtained from Lodox Statscan radiographic images generated at two institutions in Cape Town, South Africa, between 2007 and 2012. Univariate and multivariate age estimation models were created using multivariate adaptive regression splines. k-fold cross-validated 95% prediction intervals (PIs) were created for each model, and the precision of each model was assessed. The diaphyseal length models generated the narrowest PIs (2 months to 6 years) for all univariate models. The majority of multivariate models had PIs that ranged from 3 months to 5 and 6 years. Mean bias approximated 0 for each model, but most models lost precision after 10 years of age. Univariate diaphyseal length models are recommended for younger children, whereas multivariate models are recommended for older children where the inclusion of more variables minimized the size of the PIs. If diaphyseal lengths are not available, multivariate breadth models are recommended. The present study provides applicable age estimation formulae and explores the advantages and disadvantages of different subadult age estimation models using diaphyseal dimensions. Am J Phys Anthropol 154:376-386, 2014. 2014 Wiley Periodicals, Inc. PMID:24782395

Stull, Kyra E; L'Abb, Ericka N; Ousley, Stephen D

2014-07-01

468

A new multicomponent analysis method, based on principal component analysis-multivariate adaptive regression splines (PC-MARS) is proposed for the determination of dialkyltin compounds. In Tween-20 micellar media, dimethyl and dibutyltin react with morin to give fluorescent complexes with the maximum emission peaks at 527 and 520nm, respectively. The spectrofluorimetric matrix data, before building the MARS models, were subjected to principal component analysis and decomposed to PC scores as starting points for the MARS algorithm. The algorithm classifies the calibration data into several groups, in each a regression line or hyperplane is fitted. Performances of the proposed methods were tested in term of root mean square errors of prediction (RMSEP), using synthetic solutions. The results show the strong potential of PC-MARS, as a multivariate calibration method, to be applied to spectral data for multicomponent determinations. The effect of different experimental parameters on the performance of the method were studied and discussed. The prediction capability of the proposed method compared with GC-MS method for determination of dimethyltin and/or dibutyltin. PMID:23851178

Ghasemi, Jahan B; Zolfonoun, Ehsan

2013-11-01

469

Black hole evolution by spectral methods

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one

Lawrence E. Kidder; Mark A. Scheel; Saul A. Teukolsky; Eric D. Carlson; Gregory B. Cook

2000-01-01

470

Spectral methods for partial differential equations

NASA Technical Reports Server (NTRS)

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

Hussaini, M. Y.; Streett, C. L.; Zang, T. A.

1983-01-01

471

A spline-based technique for estimating flow velocities using two-camera multi-line MTV

Applications of spline-based data reduction techniques for molecular tagging velocimetry (MTV) are explored for the case in which two cameras are employed. To accommodate two cameras, an affine warp-mapping scheme that correlates the two camera views is introduced, and the associated uncertainties quantified. Spline-based techniques are examined for both multiple line and grid-based images. The high spatial resolution of the

R. Sadr; J. C. Klewicki

2003-01-01

472

The symmetric control systems have some interesting properties. This paper studies a class of symmetric system consists of a collocated second-order plant and a static output feedback controller. For the system, it is known that the internal stability and the robustness of the closed-loop system are guaranteed based only on the non-parametric structure condition. Our objective is to propose an

Tomoyuki Nagashio; Takashi Kida

2009-01-01

473

B-spline finite elements for plane elasticity problems

The finite element method since its development in the 1950â??s has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions...

Aggarwal, Bhavya

2007-04-25

474

An acoustic vector-sensor consists of three identical but orthogonally oriented acoustic particle-velocity sensors, plus a pressure sensor-all spatially collocated in a point-like geometry. At any point in space, this tri-axial acoustic vector-sensor can sample an acoustic wavefield as a 3 1 vector, instead of simply as a scalar of pressure. This vector, after proper self-normalization, would indicate the incident wave-field's propagation direction, and thus the incident emitter's azimuth-elevation direction-of-arrival. This "self-normalization" direction-of-arrival estimator is predicated on the spatial-collocation among the three particle-velocity sensors and the pressure-sensor. This collocation constriction is relaxed here by this presently proposed idea, to realize a spatially distributed acoustic vector-sensor, allowing its four component-sensors to be separately located. This proposed scheme not only retains the algorithmic advantages of the aforementioned "self-normalization" direction-of-arrival estimator, but also will significantly extend the spatial aperture to improve the direction-finding accuracy by orders of magnitude. PMID:23556569

Song, Yang; Wong, Kainam Thomas

2013-04-01

475

SLR data fitting and spline technique for matching continueous progressively intervals

NASA Astrophysics Data System (ADS)

Chebyshev polynomials are used to fit the satellite laser ranging (SLR) data. The spline technique is given to obtain a continuous approximation function of matching these Chebyshev polynomials developed for fitting data over progressively classified separate intervals. An algorithm for the used technique as well as its application on the laser ranging data taken for the satellite AJISAI are given. The results followed by the discussion of the used technique are also presented.

Hanna, Yousry

476

Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions

An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.

Jerome Blair

2008-05-15

477

To create curves in computer graphics, we use, among others, B-splines since they make it possible to effectively produce\\u000a curves in a continuous way using a small number of de Boors control points. The properties of these curves have also been\\u000a used to define and create boundary geometry in boundary problems solving using parametric integral equations system (PIES).\\u000a PIES was

Eugeniusz Zieniuk

2007-01-01

478

Multi-resolution Mesh Fitting by B-spline Surfaces for Reverse Engineering

This paper presents a new multi-resolution mesh fitting algorithm, extending the adaptive patch-based fitting scheme where each underlying quadrilateral is recursively subdivided into four sub-patches. In this paper, the G 1 continuity constraints, which mainly consist of perpendicular constraints and twist compatibility constraints, are deduced for B-spline patches. In order to construct a unique Bspline patch for each quadrilateral, the

Sen Zhang; Zhigang Li; Hui Zhang; Junhai Yong

2011-01-01

479

In this paper we apply the composite eta3 splines to collision-free curvature-derivative continuous shorter path planning of wheeled mobile robots, modelled as unicycle, within known static environments. The path planning problem is formulated as a bi-objective optimization problem of searching a sequence of N ordered intermediate configurations between start and goal configurations over the group of all possible configurations that

Han-Chih Chang; Jing-Sin Liu

2009-01-01

480

A New Adaptive B-spline VFC Snake for Object Contour Extraction

\\u000a We propose a new adaptive B-spline VFC Snake model for object contour extraction. Bing Li et al. proposed vector field convolution\\u000a (VFC) snake which has the advantages of superior noise robustness, reducing computational cost, and large capture range. However,\\u000a it suffers from slow convergence speed due to large number of control points, as well as from difficulties in determining\\u000a the

Hoang-Nam Nguyen; An-Chen Lee

2010-01-01

481

A flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented. Panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow-up periods. The model assumes that the counts for each subject are generated by mixtures of nonhomogeneous Poisson processes with smooth intensity functions modeled with penalized splines. Time-dependent covariate effects are also incorporated into the process intensity using splines. Discrete mixtures of these nonhomogeneous Poisson process spline models extract functional information from underlying clusters representing hidden subpopulations. The motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Mature moths arise from hidden, but distinct, subpopulations and monitoring the subpopulation responses was of interest. Within-cluster random effects are used to account for correlation structures and heterogeneity common to this type of data. An estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation. PMID:18047528

Nielsen, J D; Dean, C B

2008-09-01

482

A nonrational B-spline profiled horn with high displacement amplification for ultrasonic welding.

A new horn with high displacement amplification for ultrasonic welding is developed. The profile of the horn is a nonrational B-spline curve with an open uniform knot vector. The ultrasonic actuation of the horn exploits the first longitudinal displacement mode of the horn. The horn is designed by an optimization scheme and finite element analyses. Performances of the proposed horn have been evaluated by experiments. The displacement amplification of the proposed horn is 41.4% and 8.6% higher than that of the traditional catenoidal horn and a Bzier-profile horn, respectively, with the same length and end surface diameters. The developed horn has a lower displacement amplification than the nonuniform rational B-spline profiled horn but a much smoother stress distribution. The developed horn, the catenoidal horn, and the Bzier horn are fabricated and used for ultrasonic welding of lap-shear specimens. The bonding strength of the joints welded by the open uniform nonrational B-spline (OUNBS) horn is the highest among the three horns for the various welding parameters considered. The locations of the failure mode and the distribution of the voids of the specimens are investigated to explain the reason of the high bonding strength achieved by the OUNBS horn. PMID:25081407

Nguyen, Huu-Tu; Nguyen, Hai-Dang; Uan, Jun-Yen; Wang, Dung-An

2014-12-01

483

NASA Astrophysics Data System (ADS)

The quantification of the variability of bedform geometry is necessary for scientific and practical purposes. For the former purpose, it is necessary for modeling bed roughness cross-strata sets, vertical sorting, sediment transport rates, transition between two-dimensional and three-dimensional dunes, velocity pulsations, flow over bedforms, interaction between flow over bedforms and groundwater, and transport of contaminants. For practical purposes the study of the variability of bedforms is important to predict floods and flow resistance, to predict uplifting of manmade structures underneath a river beds, to track future changes of bedform and biota following dam removal, to estimate the relationship between bedform characteristics and biota, in river restoration, among others. Currently there is not a standard nomenclature and procedure to separate bedform features such as sand waves, dunes and ripples which are commonly present in large rivers. Likewise, there is not a standard definition of the scope for the different scales of such bedform features. The present study proposes a standardization of the nomenclature and symbolic representation of bedform features and elaborates on the combined application of robust spline filter and continuous wavelet transforms to separate the morphodynamic features. A fully automated robust spline procedure for uniformly sampled datasets is used. The algorithm, based on a penalized least squares method, allows fast smoothing of uniformly sampled data elements by means of the discrete cosine transform. The wavelet transforms, which overcome some limitations of the Fourier transforms, are applied to identify the spectrum of bedform wavelengths. The proposed separation method is applied to a 370-m width and 1.028-km length swath bed morphology data of the Parana River, one of the world's largest rivers, located in Argentina. After the separation is carried out, the descriptors (e.g. wavelength, slope, and amplitude for both stoss and lee sides) of the dunes and ripples are statistically analyzed. Thus, a complete hierarchization and quantitative description of the spatial configuration of the bed is obtained. To the best of our knowledge, no previous study has retrieved such information.

Gutierrez, R. R.; Abad, J. D.; Parsons, D. R.

2011-12-01

484

Unsteady laminar flow in a circular tube: A test of the HERCOL (Hermitian collocation) computer code

NASA Astrophysics Data System (ADS)

HERCOL, a computer code for the integration of second-order differential equations in one space dimension by Hermitian collocation was used to calculate the unsteady velocity profiles for laminar flow in a circular tube. The code was tested for stability and accuracy for the problem for which an analytical solution exists prior to application to a like problem in which the initial and boundary conditions preclude the existence of analytical solutions. The test problem is one in which a pressure gradient is imposed on a fluid initially at rest in a circular tube; the fluid accelerates and at steady state has a parabolic velocity profile. A second example was constructed from the first; a pressure gradient equal but opposite in sign is imposed on the fluid with a fully developed parabolic velocity profile. At steady state, the velocity is again parabolic, but in the opposite direction to that at the initial conditions. Excellent agreement with the analytical solution was obtained in the first problem; in the second, the behavior was as expected.

Welch, James F.; Hurley, James A.; Glover, Michael P.; Nassimbene, Ryan D.; Yetzbacher, Marilyn R.

1991-05-01

485

NASA Astrophysics Data System (ADS)

The incompressible collocated mesh is often preferred over the staggered mesh scheme for turbulence simulation due to its slightly simpler form in curvilinear coordinates. Many researchers have used an upwind interpolation for the momentum, citing problems with numerical oscillations if centered interpolations are used. Analysis reveals that second order centered interpolations result in a kinetic energy conservation error, which can act as a source for numerical oscillations. Analysis also shows that a simple first order centered interpolation does not produce a kinetic energy conservation error. Various momentum interpolation operators are used in an inviscid simulation of the flow over an airfoil, as well as for simulations of turbulent channel flow. In the case of the airfoil, oscillations are present with the second order centered interpolation, but are absent for both the first order centered and the second order upwind schemes. The dissipative effects of the upwind interpolations degrade the results of the channel flow simulations, while both the first and second order centered interpolations yield good results. This work suggests that numerical oscillations can be controlled with a non-dissipative algorithm through the proper choice of the interpolation scheme.

Felten, Frederic; Lund, Thomas

2001-11-01

486

NASA Technical Reports Server (NTRS)

Cirrus clouds, particularly sub visual high thin cirrus with low optical thickness, are difficult to be screened in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to examine the susceptibility of operational aerosol products to thin cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the CALIPSO vertical feature mask (VFM) and the MODIS-derived thin cirrus screening parameters for the purpose of evaluating thin cirrus contamination. Key results of this study include: (1) Quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted. Although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons, (2) Challenges in matching up different data for analysis are highlighted and corresponding solutions proposed, and (3) Estimation of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.

Huang, Jingfeng; Hsu, N. Christina; Tsay, Si-Chee; Holben, Brent N.; Welton, Ellsworth J.; Smirnov, Alexander; Jeong, Myeong-Jae; Hansell, Richard A.; Berkoff, Timothy A.

2012-01-01

487

Optical coherence tomography (OCT) allows for non-invasive 3D visualization of biological tissue at cellular level resolution. Often hindered by speckle noise, the visualization of important biological tissue details in OCT that can aid disease diagnosis can be improved by speckle noise compensation. A challenge with handling speckle noise is its inherent non-stationary nature, where the underlying noise characteristics vary with the spatial location. In this study, an innovative speckle noise compensation method is presented for handling the non-stationary traits of speckle noise in OCT imagery. The proposed approach centers on a non-stationary spline-based speckle noise modeling strategy to characterize the speckle noise. The novel method was applied to ultra high-resolution OCT (UHROCT) images of the human retina and corneo-scleral limbus acquired in-vivo that vary in tissue structure and optical properties. Test results showed improved performance of the proposed novel algorithm compared to a number of previously published speckle noise compensation approaches in terms of higher signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and better overall visual assessment. PMID:24049697

Cameron, Andrew; Lui, Dorothy; Boroomand, Ameneh; Glaister, Jeffrey; Wong, Alexander; Bizheva, Kostadinka

2013-01-01

488

Optical coherence tomography (OCT) allows for non-invasive 3D visualization of biological tissue at cellular level resolution. Often hindered by speckle noise, the visualization of important biological tissue details in OCT that can aid disease diagnosis can be improved by speckle noise compensation. A challenge with handling speckle noise is its inherent non-stationary nature, where the underlying noise characteristics vary with the spatial location. In this study, an innovative speckle noise compensation method is presented for handling the non-stationary traits of speckle noise in OCT imagery. The proposed approach centers on a non-stationary spline-based speckle noise modeling strategy to characterize the speckle noise. The novel method was applied to ultra high-resolution OCT (UHROCT) images of the human retina and corneo-scleral limbus acquired in-vivo that vary in tissue structure and optical properties. Test results showed improved performance of the proposed novel algorithm compared to a number of previously published speckle noise compensation approaches in terms of higher signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and better overall visual assessment. PMID:24049697

Cameron, Andrew; Lui, Dorothy; Boroomand, Ameneh; Glaister, Jeffrey; Wong, Alexander; Bizheva, Kostadinka

2013-01-01

489

NASA Astrophysics Data System (ADS)

The National Ecological Observatory Network (NEON) is a continental-scale research platform currently in development to assess the causes of ecological change and biological responses to change across a projected 30-year timeframe. A suite of standardized sensor-based measurements (i.e., Terrestrial Instrument System (TIS) measurements) and in-situ field sampling and observations (i.e., Terrestrial Observation System (TOS) activities) will be conducted across 20 ecoclimatic domains in the U.S. where NEON is establishing 60 terrestrial research sites. NEON's TIS measurements and TOS activities are designed to observe the temporal and spatial dynamics of key drivers and ecological processes and responses to change within each of the 60 terrestrial research sites. The TIS measurements are non-destructive and designed to provide in-situ, continuous, and areally integrated observations of the surrounding ecosystem and environment, while TOS sampling and observation activities are designed to encompass a hierarchy of measurable biological states and processes including diversity, abundance, phenology, demography, infectious disease prevalence, ecohydrology, and biogeochemistry. To establish valid relationships between these drivers and site-specific responses, two contradicting requirements must be fulfilled: (i) both types of observations shall be representative of the same ecosystem, and (ii) they shall not significantly influence one another. Here we outline the theoretical background and algorithmic process for determining areas of mutual representativeness and exclusion around NEON's TIS measurements and develop a procedure which quantitatively optimizes this trade-off through: (i) quantifying the source area distributions of TIS measurements, (ii) determining the ratio of user-defined impact threshold to effective impact area for different TOS activities, and (iii) determining the range of feasible distances between TIS locations and TOS activities. This approach provides an evidence-based and repeatable method for combining sensor-based measurements and field sampling and observations at predefined levels of disturbance and spatial representativeness. The developed approach represents a general framework which is applicable to other environmental research sites where similar collocation is desired.

Zulueta, R. C.; Metzger, S.; Ayres, E.; Luo, H.; Meier, C. L.; Barnett, D.; Sanclements, M.; Elmendorf, S.

2013-12-01

490

Distributed lag and spline modeling for predicting energy expenditure from accelerometry in youth

Movement sensing using accelerometers is commonly used for the measurement of physical activity (PA) and estimating energy expenditure (EE) under free-living conditions. The major limitation of this approach is lack of accuracy and precision in estimating EE, especially in low-intensity activities. Thus the objective of this study was to investigate benefits of a distributed lag spline (DLS) modeling approach for the prediction of total daily EE (TEE) and EE in sedentary (1.01.5 metabolic equivalents; MET), light (1.53.0 MET), and moderate/vigorous (?3.0 MET) intensity activities in 10- to 17-year-old youth (n = 76). We also explored feasibility of the DLS modeling approach to predict physical activity EE (PAEE) and METs. Movement was measured by Actigraph accelerometers placed on the hip, wrist, and ankle. With whole-room indirect calorimeter as the reference standard, prediction models (Hip, Wrist, Ankle, Hip+Wrist, Hip+Wrist+Ankle) for TEE, PAEE, and MET were developed and validated using the fivefold cross-validation method. The TEE predictions by these DLS models were not significantly different from the room calorimeter measurements (all P > 0.05). The Hip+Wrist+Ankle predicted TEE better than other models and reduced prediction errors in moderate/vigorous PA for TEE, MET, and PAEE (all P < 0.001). The Hip+Wrist reduced prediction errors for the PAEE and MET at sedentary PA (P = 0.020 and 0.021) compared with the Hip. Models that included Wrist correctly classified time spent at light PA better than other models. The means and standard deviations of the prediction errors for the Hip+Wrist+Ankle and Hip were 0.4 144.0 and 1.5 164.7 kcal for the TEE, 0.0 84.2 and 1.3 104.7 kcal for the PAEE, and ?1.1 97.6 and ?0.1 108.6 MET min for the MET models. We conclude that the DLS approach for accelerometer data improves detailed EE prediction in youth. PMID:19959770

Chen, Kong Y.; Acra, Sari A.; Buchowski, Maciej S.

2010-01-01

491

NASA Astrophysics Data System (ADS)

Quantifying the uncertainty associated with predictions of mechanistic biospheric models remains an important problem, and is essential for accurately performing multi-model intercomparisons and syntheses. When individual simulations are computationally inexpensive, a simple Monte-Carlo approach can be adopted to quantify this uncertainity. However, this simple approach becomes intractable for mechanistic models with substantial computational costs. To overcome these computational bottlenecks, sparse sampling based methods that can capture the mechanistic model response using a small number of model simulations are required. Two such methods are explored in this study to quantify the uncertainity of the CASA-GFED mechanistic biosphere model. Random 'Latin hypercube' and deterministic 'polynomial chaos' sampling designs are used to construct Gaussian process (GP), and stochastic collocation (SC) surrogate models of the CASA-GFED biospheric model. With the aid of the GP model, we map the spatio-temporal impact of the uncertainty associated with temperature, precipitation, fraction of photosynthetically active radiation, and light use efficiency on estimates of the Net Primary Productivity produced by CASA-GFED. We find that both GP and SC models can accurately capture the mean and the variance of the mechanistic model output in substantially fewer simulations then a standard Monte-Carlo procedure. The GP model also provides additional details about the influence of uncertain variables on the mechanistic model output. However, this additional information comes with higher computational cost that is dependent on the parameterization of the covariance structure between the sampled variables used to model the response of the mechanistic model.

Yadav, V.; Michalak, A. M.

2013-12-01

492

NASA Astrophysics Data System (ADS)

A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in the rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy Elab = 6 MeV u-1. The charge transfer probabilities are calculated for different values of the impact parameter. The results obtained are compared with previous calculations (Tupitsyn et al 2010 Phys. Rev. A 82 042701), where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for the investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime.

Maltsev, I. A.; Deyneka, G. B.; Tupitsyn, I. I.; Shabaev, V. M.; Kozhedub, Y. S.; Plunien, G.; Sthlker, Th

2013-09-01

493

Supervised Scoring with Monotone Multidimensional Splines Abraham Othman

mathematically coherent scores. The method is used in practice to create the LEED Performance scores that gauge. On the whole, the USGBC is an organization with deep technical expertise about build- ings, but mathematical to create an appropriately complex but still inter- nally adaptable scoring function. This concrete

Gordon, Geoffrey J.

494

In 2001, the Norwegian Goat Health Service initiated the Healthier Goats program (HG), with the aim of eradicating caprine arthritis encephalitis, caseous lymphadenitis, and Johne's disease (caprine paratuberculosis) in Norwegian goat herds. The aim of the present study was to explore how control and eradication of the above-mentioned diseases by enrolling in HG affected milk yield by comparison with herds not enrolled in HG. Lactation curves were modeled using a multilevel cubic spline regression model where farm, goat, and lactation were included as random effect parameters. The data material contained 135,446 registrations of daily milk yield from 28,829 lactations in 43 herds. The multilevel cubic spline regression model was applied to 4 categories of data: enrolled early, control early, enrolled late, and control late. For enrolled herds, the early and late notations refer to the situation before and after enrolling in HG; for nonenrolled herds (controls), they refer to development over time, independent of HG. Total milk yield increased in the enrolled herds after eradication: the total milk yields in the fourth lactation were 634.2 and 873.3 kg in enrolled early and enrolled late herds, respectively, and 613.2 and 701.4 kg in the control early and control late herds, respectively. Day of peak yield differed between enrolled and control herds. The day of peak yield came on d 6 of lactation for the control early category for parities 2, 3, and 4, indicating an inability of the goats to further increase their milk yield from the initial level. For enrolled herds, on the other hand, peak yield came between d 49 and 56, indicating a gradual increase in milk yield after kidding. Our results indicate that enrollment in the HG disease eradication program improved the milk yield of dairy goats considerably, and that the multilevel cubic spline regression was a suitable model for exploring effects of disease control and eradication on milk yield. PMID:24819129

Nagel-Alne, G E; Krontveit, R; Bohlin, J; Valle, P S; Skjerve, E; Slverd, L S

2014-07-01

495

propose flexible high-accuracy practical techniques to perform 3D and 2D integral transformations from and that spline-based integration and differentiation are invertible. The cost of the in- crease in accuracyGeophysical Prospecting doi: 10.1111/j.1365-2478.2011.01026.x High-accuracy practical spline

Gao, Stephen Shangxing

496

NASA Astrophysics Data System (ADS)

A realization of a height system covering the south of Norway has been performed, based on least-squares collocation applied to differences between geometric and gravimetric quasigeoid heights, inhomogeneous and isotropic covariance modelling, and without prior information on the error sources of the involved data types. As a result, the derived normal heights were biased by the systematic errors of the GPS-levelling network. The important covariance properties were determined at every location from spatially differenced observations, and made it straightforward to evaluate the uncertainties of the biased height reference. The distribution of predictions followed a Gaussian shape, but extreme realizations were overrepresented.

Mysen, E.

2014-10-01

497

Modelling of reservoir-induced earthquakes: a multivariate adaptive regression spline

NASA Astrophysics Data System (ADS)

This paper employs a multivariate adaptive regression spline (MARS) for the prediction of the maximum magnitude (M) of reservoir-induced earthquakes based on reservoir parameters. MARS is a non-parametric adaptive regression procedure. It has the capability to determine the important sequence of inputs for the output. The comprehensive parameter (E) and maximum reservoir depth (H) are used as inputs for the MARS. The developed MARS gives an equation for the prediction of M. A comparative study is carried out between the developed MARS and other models and the results show that the developed MARS is a robust model for the prediction of M.

Samui, Pijush; Kim, Dookie

2012-10-01

498

Lack-of-fit Tests for Generalized Linear Models via Splines

Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the non-parametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use. PMID:23202300

LI, CHIN-SHANG

2012-01-01

499

NASA Astrophysics Data System (ADS)

A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic calculations of the excitation and charge-transfer probabilities in the low-energy U91 +(1 s)-U92+ collisions in two and three dimensional approaches are performed. The obtained results are compared with our previous calculations employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation.

Deyneka, Gennadiy B.; Maltsev, Ilia A.; Tupitsyn, Ilya I.; Shabaev, Vladimir M.; Bondarev, Andrey I.; Kozhedub, Yury S.; Plunien, Gnter; Sthlker, Thomas

2013-12-01

500

The key point to calculate augmentation index (AIx) related to cardiovascular diseases is the precise identification of the shoulder point. The commonly used method for extracting the shoulder point is to calculate the fourth derivative of the pulse waveform by numerical differentiation. However, this method has a poor anti-noise capability and is computationally intensive. The aims of this study were to develop a new method based on the 2nd-order B-spline wavelet for calculating AIx, and to compare it with numerical differentiation and Savitzky-Golay digital differentiator (SGDD). All the three methods were applied to pulse waveforms derived from 60 healthy subjects. There was a significantly high correlation between the proposed method and numerical differentiation (r=0.998 for carotid pulses, and r=0.997 for radial pulses), as well as between the proposed method and the SGDD (r=0.995 for carotid pulses, and r=0.993 for radial pulses). In addition, the anti-noise capability of the proposed method was evaluated by adding simulated noise (>10Hz) on pulse waveforms. The results showed that the proposed method was advantageous in noise tolerance than the other two methods. These findings indicate that the proposed method can quickly and accurately calculate AIx with a good anti-noise capability. PMID:24613502

He, Zijun; Zhang, Yongliang; Ma, Zuchang; Hu, Fusong; Sun, Yining

2014-06-01