Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory

NASA Astrophysics Data System (ADS)

Wattanasakulpong, Nuttawit; Chaikittiratana, Arisara; Pornpeerakeat, Sacharuck

2018-06-01

In this paper, vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory. The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs. The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams. The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle, which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions. Based on the numerical experiments, it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

Spectral methods for partial differential equations

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

Recent applications of spectral methods in fluid dynamics

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1985-01-01

Origins of spectral methods, especially their relation to the method of weighted residuals, are surveyed. Basic Fourier and Chebyshev 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 mixzed type. Fluid dynamical applications are emphasized.

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

A fast Chebyshev method for simulating flexible-wing propulsion

NASA Astrophysics Data System (ADS)

Moore, M. Nicholas J.

2017-09-01

We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (Nlog ⁡ N) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O (N2) cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, O (Nlog ⁡ N) , allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Membrane covered duct lining for high-frequency noise attenuation: prediction using a Chebyshev collocation method.

PubMed

Huang, Lixi

2008-11-01

A spectral method of Chebyshev collocation with domain decomposition is introduced for linear interaction between sound and structure in a duct lined with flexible walls backed by cavities with or without a porous material. The spectral convergence is validated by a one-dimensional problem with a closed-form analytical solution, and is then extended to the two-dimensional configuration and compared favorably against a previous method based on the Fourier-Galerkin procedure and a finite element modeling. The nonlocal, exact Dirichlet-to-Neumann boundary condition is embedded in the domain decomposition scheme without imposing extra computational burden. The scheme is applied to the problem of high-frequency sound absorption by duct lining, which is normally ineffective when the wavelength is comparable with or shorter than the duct height. When a tensioned membrane covers the lining, however, it scatters the incident plane wave into higher-order modes, which then penetrate the duct lining more easily and get dissipated. For the frequency range of f=0.3-3 studied here, f=0.5 being the first cut-on frequency of the central duct, the membrane cover is found to offer an additional 0.9 dB attenuation per unit axial distance equal to half of the duct height.

A conservative staggered-grid Chebyshev multidomain method for compressible flows

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Kolias, John H.

1995-01-01

We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

A conforming spectral collocation strategy for Stokes flow through a channel contraction

NASA Technical Reports Server (NTRS)

Phillips, Timothy N.; Karageorghis, Andreas

1989-01-01

A formula expressing the coefficients of an expansion of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

Fourier-Legendre spectral methods for incompressible channel flow

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1984-01-01

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

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

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Spectral simulation of unsteady compressible flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Gottlieb, David

1990-01-01

An unsteady compressible viscous wake flow past a circular cylinder was successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for periodic problems is introduced. It was further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It was been shown that the solution of a model problem has exponential growth in time if improper boundary conditions are used. A characteristic boundary condition, which is based on the characteristics of the Euler equations of gas dynamics, was derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

NASA Astrophysics Data System (ADS)

Auteri, F.; Quartapelle, L.; Vigevano, L.

2002-08-01

This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

NASA Technical Reports Server (NTRS)

Lin, Ray-Sing; Reed, Helen L.

1993-01-01

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

NASA Technical Reports Server (NTRS)

Shbeeb, N.; Binienda, W. K.; Kreider, K.

1999-01-01

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

Analysis of an Interface Crack for a Functionally Graded Strip Sandwiched between Two Homogeneous Layers of Finite Thickness

NASA Technical Reports Server (NTRS)

Shbeeh, N. I.; Binienda, W. K.

1999-01-01

The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a non-homogeneous interface was formulated for singular integral equations with Cauchy kernels and integrated using the Lobatto-Chebyshev collocation technique. Mixed-mode Stress Intensity Factors and Strain Energy Release Rates were calculated. The Stress Intensity Factors were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various non-homogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.

Parallel high-precision orbit propagation using the modified Picard-Chebyshev method

NASA Astrophysics Data System (ADS)

Koblick, Darin C.

2012-03-01

The modified Picard-Chebyshev method, when run in parallel, is thought to be more accurate and faster than the most efficient sequential numerical integration techniques when applied to orbit propagation problems. Previous experiments have shown that the modified Picard-Chebyshev method can have up to a one order magnitude speedup over the 12th order Runge-Kutta-Nystrom method. For this study, the evaluation of the accuracy and computational time of the modified Picard-Chebyshev method, using the Java Astrodynamics Toolkit high-precision force model, is conducted to assess its runtime performance. Simulation results of the modified Picard-Chebyshev method, implemented in MATLAB and the MATLAB Parallel Computing Toolbox, are compared against the most efficient first and second order Ordinary Differential Equation (ODE) solvers. A total of six processors were used to assess the runtime performance of the modified Picard-Chebyshev method. It was found that for all orbit propagation test cases, where the gravity model was simulated to be of higher degree and order (above 225 to increase computational overhead), the modified Picard-Chebyshev method was faster, by as much as a factor of two, than the other ODE solvers which were tested.

Application of two direct runoff prediction methods in Puerto Rico

USGS Publications Warehouse

Sepulveda, N.

1997-01-01

Two methods for predicting direct runoff from rainfall data were applied to several basins and the resulting hydrographs compared to measured values. The first method uses a geomorphology-based unit hydrograph to predict direct runoff through its convolution with the excess rainfall hyetograph. The second method shows how the resulting hydraulic routing flow equation from a kinematic wave approximation is solved using a spectral method based on the matrix representation of the spatial derivative with Chebyshev collocation and a fourth-order Runge-Kutta time discretization scheme. The calibrated Green-Ampt (GA) infiltration parameters are obtained by minimizing the sum, over several rainfall events, of absolute differences between the total excess rainfall volume computed from the GA equations and the total direct runoff volume computed from a hydrograph separation technique. The improvement made in predicting direct runoff using a geomorphology-based unit hydrograph with the ephemeral and perennial stream network instead of the strictly perennial stream network is negligible. The hydraulic routing scheme presented here is highly accurate in predicting the magnitude and time of the hydrograph peak although the much faster unit hydrograph method also yields reasonable results.

Analysis of the low gravity tolerance of Bridgman-Stockbarger crystal growth. I - Steady and impulse accelerations

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.; Ouazzani, Jalil; Rosenberger, Franz

1989-01-01

The effects of steady and impulse-type residual accelerations on dopant distributions during directional solidification in 2D and 3D 'generic' models of the Bridgman-Stockbarger technique are investigated using numerical methods. The calculations are based on the thermophysical properties of molten germanium doped with a low concentration of gallium. A Chebyshev collocation pseudospectral method is used for the solution of the governing momentum-, mass-, species-, and heat-transfer equations. Only convection caused by temperature gradients is considered. It is found that lateral nonuniformity in composition is very sensitive to the orientation of the steady component of the residual gravity vector and to the particular operating conditions under consideration. It is also found that laterally or radially averaged composition profiles are alone insufficient to describe the extent of residual convection in a spacecraft environment. The effects of impulse-type disturbances can be severe and can extend for times on the order of 1000 sec after the termination of the impulse.

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

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

PubMed

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

2016-01-01

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

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

On a generating mechanism for Yanai waves and the 25-day oscillation

NASA Technical Reports Server (NTRS)

Kelly, Brian G.; Meyers, Steven D.; O'Brien, James J.

1995-01-01

A spectral Chebyshev-collocation method applied to the linear, 1.5 layer reduced-gravity ocean model equations is used to study 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 the waves. 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 25 days and 1000 km respectively. These properties are also seen in the model results and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Viscous instabilities in the q-vortex at large swirl numbers

NASA Astrophysics Data System (ADS)

Fabre, David; Jacquin, Laurent

2002-11-01

This comunication deals with the temporal stability of the q-vortex trailing line vortex model. We describe a family of viscous instabilities existing in a range of parameters which is usually assumed to be stable, namely large swirl parameters (q>1.5) and large Reynolds numbers. These instabilities affect negative azimuthal wavenumbers (m < 0) and take the form of centre-modes (i.e. with a structure concentrated along the vortex centerline). They are related to a family of viscous modes described by Stewartson, Ng & Brown (1988) in swirling Poiseuille flow, and are the temporal counterparts of weakly amplified spatial modes recently computed by Olendraru & Sellier (2002). These instabilities are studied numerically using an original and highly accurate Chebyshev collocation method, which allows a mapping of the unstable regions up to Rey 10^6 and q 7. Our results indicate that in the limit of very large Reynolds numbers, trailing vortices are affected by this kind of instabilities whatever the value of the swirl number.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

A spectrally accurate boundary-layer code for infinite swept wings

NASA Technical Reports Server (NTRS)

Pruett, C. David

1994-01-01

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

NASA Astrophysics Data System (ADS)

Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

2013-03-01

Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

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

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

PubMed

Temel, Burcin; Mills, Greg; Metiu, Horia

2008-03-27

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

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

PubMed

Cvitaš, Marko T; Althorpe, Stuart C

2013-08-14

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

Numerical Modeling of Tidal Effects in Polytropic Accretion Disks

NASA Technical Reports Server (NTRS)

Godon, Patrick

1997-01-01

A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m = 1 eccentric instability in the disk. While the m = 2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m = 2 azimuthal mode), with an elliptic pattern rotating at about a fraction (approx. = 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r(Omega)/c(sub s) = M approx. = 40) we also find a critical value of the viscosity parameter (alpha approx. = 0.01), below which shock dissipation dominates and is balanced by the wave amplification due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number M(sub s) approx. = 1.3.

Collocation and Galerkin Time-Stepping Methods

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2011-01-01

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

New template family for the detection of gravitational waves from comparable-mass black hole binaries

NASA Astrophysics Data System (ADS)

Porter, Edward K.

2007-11-01

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various resummation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on reexpressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all post-Newtonian orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the last stable orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

NASA Astrophysics Data System (ADS)

Huang, Yi-Xin; Tian, Hao; Zhao, Yang

2017-10-01

The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

NASA Astrophysics Data System (ADS)

Warnez, M. T.; Johnsen, E.

2015-06-01

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

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

NASA Astrophysics Data System (ADS)

Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo

2014-04-01

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

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

NASA Astrophysics Data System (ADS)

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

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

Best quadrature formula on Sobolev class with Chebyshev weight

NASA Astrophysics Data System (ADS)

Xie, Congcong

2008-05-01

Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

NASA Astrophysics Data System (ADS)

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

2014-10-01

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

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

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

Miniaturized dielectric waveguide filters

NASA Astrophysics Data System (ADS)

Sandhu, Muhammad Y.; Hunter, Ian C.

2016-10-01

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

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

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

Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Javaloyes, J., E-mail: julien.javaloyes@uib.es; Balle, S.

2015-10-01

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allowmore » handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.« less

Comparison of the Chebyshev Method and the Generalized Crank-Nicholson Method for time Propagation in Quantum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Formanek, Martin; Vana, Martin; Houfek, Karel

2010-09-30

We compare efficiency of two methods for numerical solution of the time-dependent Schroedinger equation, namely the Chebyshev method and the recently introduced generalized Crank-Nicholson method. As a testing system the free propagation of a particle in one dimension is used. The space discretization is based on the high-order finite diferences to approximate accurately the kinetic energy operator in the Hamiltonian. We show that the choice of the more effective method depends on how many wave functions must be calculated during the given time interval to obtain relevant and reasonably accurate information about the system, i.e. on the choice of themore » time step.« less

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

NASA Astrophysics Data System (ADS)

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

2007-02-01

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

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

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

PubMed

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

2018-06-12

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

Cosmographic analysis with Chebyshev polynomials

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Movement of Landslide Triggered by Bedrock Exfiltration with Nonuniform Pore Pressure Distribution

NASA Astrophysics Data System (ADS)

Jan, C. D.; Jian, Z. K.

2014-12-01

Landslides are common phenomena of sediment movement in mountain areas and usually pose severe risks to people and infrastructure around those areas. The occurrence of landslides is influenced by groundwater dynamics and bedrock characteristics as well as by rainfall and soil-mass properties. The bedrock may drain or contribute to groundwater in the overlying soil mass, depending on the hydraulic conductivity, degree of fracturing, saturation, and hydraulic head. Our study here is based on the model proposed by Iverson (2005). The model describes the relation between landslide displacement and the shear-zone dilation/contraction of pore water pressure. To study landslide initiation and movement, a block soil mass sliding down an inclined beck-rock plane is governed by Newton's equation of motion, while both the bedrock exfiltration and excess pore pressure induced by dilatation or contraction of basal shear zone are described by diffusion equations. The Chebyshev collocation method was used to transform the governing equations to a system of first-order ordinary differential equations, without the need of iteration. Then a fourth-order Runge-Kutta scheme was used to solve these ordinary differential equations. The effects of nonuniform bedrock exfiltration pressure distributions, such as the delayed peak, central peak, and advanced peak distributions, on the time of landslide initiation and the speed of landslide movement were compared and discussed.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

PubMed Central

Warnez, M. T.; Johnsen, E.

2015-01-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller–Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin–Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time. PMID:26130967

DOE Office of Scientific and Technical Information (OSTI.GOV)

Versino, Daniele; Bronkhorst, Curt Allan

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

NASA Astrophysics Data System (ADS)

Chen, C.; Aubry, S.; Oppelstrup, T.; Arsenlis, A.; Darve, E.

2018-06-01

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). We implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.

47 CFR 51.321 - Methods of obtaining interconnection and access to unbundled elements under section 251 of the Act.

Code of Federal Regulations, 2010 CFR

2010-10-01

... elements include, but are not limited to: (1) Physical collocation and virtual collocation at the premises... seeking a particular collocation arrangement, either physical or virtual, is entitled to a presumption... incumbent LEC shall be required to provide virtual collocation, except at points where the incumbent LEC...

Phase-field modeling of switchable diode-like current-voltage characteristics in ferroelectric BaTiO{sub 3}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Y., E-mail: yxc238@psu.edu; Randall, C. A.; Chen, L. Q.

2014-05-05

A self-consistent model has been proposed to study the switchable current-voltage (I-V) characteristics in Cu/BaTiO{sub 3}/Cu sandwiched structure combining the phase-field model of ferroelectric domains and diffusion equations for ionic/electronic transport. The electrochemical transport equations and Ginzburg-Landau equations are solved using the Chebyshev collocation algorithm. We considered a single parallel plate capacitor configuration which consists of a single layer BaTiO{sub 3} containing a single tetragonal domain orientated normal to the plate electrodes (Cu) and is subject to a sweep of ac bias from −1.0 to 1.0 V at 25 °C. Our simulation clearly shows rectifying I-V response with rectification ratios amount tomore » 10{sup 2}. The diode characteristics are switchable with an even larger rectification ratio after the polarization direction is flipped. The effects of interfacial polarization charge, dopant concentration, and dielectric constant on current responses were investigated. The switchable I-V behavior is attributed to the polarization bound charges that modulate the bulk conduction.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borzov, V. V., E-mail: borzov.vadim@yandex.ru; Damaskinsky, E. V., E-mail: evd@pdmi.ras.ru

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

Single scattering from nonspherical Chebyshev particles: A compendium of calculations

NASA Technical Reports Server (NTRS)

Wiscombe, W. J.; Mugnai, A.

1986-01-01

A large set of exact calculations of the scattering from a class of nonspherical particles known as Chebyshev particles' has been performed. Phase function and degree of polarization in random orientation, and parallel and perpendicular intensities in fixed orientations, are plotted for a variety of particles shapes and sizes. The intention is to furnish a data base against which both experimental data, and the predictions of approximate methods, can be tested. The calculations are performed with the widely-used Extended Boundary Condition Method. An extensive discussion of this method is given, including much material that is not easily available elsewhere (especially the analysis of its convergence properties). An extensive review is also given of all extant methods for nonspherical scattering calculations, as well as of the available pool of experimental data.

New algorithms for solving high even-order differential equations using third and fourth Chebyshev-Galerkin methods

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Bassuony, M. A.

2013-03-01

This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made.

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

NASA Technical Reports Server (NTRS)

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

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.

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

NASA Technical Reports Server (NTRS)

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

2013-01-01

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

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

Synthesis and optimization of four bar mechanism with six design parameters

NASA Astrophysics Data System (ADS)

Jaiswal, Ankur; Jawale, H. P.

2018-04-01

Function generation is synthesis of mechanism for specific task, involves complexity for specially synthesis above five precision of coupler points. Thus pertains to large structural error. The methodology for arriving to better precision solution is to use the optimization technique. Work presented herein considers methods of optimization of structural error in closed kinematic chain with single degree of freedom, for generating functions like log(x), ex, tan(x), sin(x) with five precision points. The equation in Freudenstein-Chebyshev method is used to develop five point synthesis of mechanism. The extended formulation is proposed and results are obtained to verify existing results in literature. Optimization of structural error is carried out using least square approach. Comparative structural error analysis is presented on optimized error through least square method and extended Freudenstein-Chebyshev method.

Dynamic response analysis of structure under time-variant interval process model

NASA Astrophysics Data System (ADS)

Xia, Baizhan; Qin, Yuan; Yu, Dejie; Jiang, Chao

2016-10-01

Due to the aggressiveness of the environmental factor, the variation of the dynamic load, the degeneration of the material property and the wear of the machine surface, parameters related with the structure are distinctly time-variant. Typical model for time-variant uncertainties is the random process model which is constructed on the basis of a large number of samples. In this work, we propose a time-variant interval process model which can be effectively used to deal with time-variant uncertainties with limit information. And then two methods are presented for the dynamic response analysis of the structure under the time-variant interval process model. The first one is the direct Monte Carlo method (DMCM) whose computational burden is relative high. The second one is the Monte Carlo method based on the Chebyshev polynomial expansion (MCM-CPE) whose computational efficiency is high. In MCM-CPE, the dynamic response of the structure is approximated by the Chebyshev polynomials which can be efficiently calculated, and then the variational range of the dynamic response is estimated according to the samples yielded by the Monte Carlo method. To solve the dependency phenomenon of the interval operation, the affine arithmetic is integrated into the Chebyshev polynomial expansion. The computational effectiveness and efficiency of MCM-CPE is verified by two numerical examples, including a spring-mass-damper system and a shell structure.

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere

NASA Astrophysics Data System (ADS)

Blakely, Christopher D.

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.

The transverse instability in a differentially heated vertical cavity filled with molecular radiating gases. I. Linear stability analysis

NASA Astrophysics Data System (ADS)

Borget, V.; Bdéoui, F.; Soufiani, A.; Le Quéré, P.

2001-05-01

Radiation effects on the onset of the transverse instability in a differentially heated vertical cavity containing molecular emitting and absorbing gases in the so-called conduction regime is studied theoretically. Radiative transfer is treated using the full integro-differential formulation. The neutral stability curves are determined using a combined Galerkin-collocation method based on Chebyshev polynomials. A modified correlated-k model and the absorption distribution function model are used in order to take into account the spectral structure of the absorption coefficient for radiating molecules such as H2O and CO2. For transparent media, perfect agreement is found with the available data reported in the literature and, particularly, the principle of exchange of stability is found to hold for Prandtl number values less than 12.46. The study of gray media allows us to examine the basic mechanisms that yield to the onset of transverse instability as traveling waves. For real radiating gases, a parametric study for H2O and CO2 is reported. It is shown that the radiative transfer delays the onset of the transverse instability and this delay increases with temperature and decreases with boundary emissivities, while layer depth effects depend on the level of saturation of the gas active absorption bands. Whatever the gas considered, it is found that neither radiation effect on the basic flow nor the radiative power disturbances can be neglected.

Global stability analysis of axisymmetric boundary layer over a circular cylinder

NASA Astrophysics Data System (ADS)

Bhoraniya, Ramesh; Vinod, Narayanan

2018-05-01

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

A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities

DOE PAGES

Versino, Daniele; Bronkhorst, Curt Allan

2018-01-31

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

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

2003-01-01

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.

Factorized Runge-Kutta-Chebyshev Methods

NASA Astrophysics Data System (ADS)

O'Sullivan, Stephen

2017-05-01

The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) explicit schemes for the integration of large systems of PDEs with diffusive terms are presented. The schemes are simple to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures. Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability for acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The extent of the stability domain is approximately the same as that of RKC schemes, and a third longer than in the case of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is also discussed. A publicly available implementation of FRKC2 schemes may be obtained from maths.dit.ie/frkc

Spectral collocation methods

NASA Technical Reports Server (NTRS)

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

1987-01-01

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.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Iranian Pre-University Student's Retention of Collocations: Implicit Exposure or Explicit Instruction

ERIC Educational Resources Information Center

Gheisari, Nouzar; Yousofi, Nouroldin

2016-01-01

The effectiveness of different teaching methods of collocational expressions in ESL/EFL contexts of education has been a point of debate for more than two decades, with some believing in explicit and the others in implicit instruction of collocations. In this regard, the present study aimed at finding about which kind of instruction is more…

Data compression using Chebyshev transform

NASA Technical Reports Server (NTRS)

Cheng, Andrew F. (Inventor); Hawkins, III, S. Edward (Inventor); Nguyen, Lillian (Inventor); Monaco, Christopher A. (Inventor); Seagrave, Gordon G. (Inventor)

2007-01-01

The present invention is a method, system, and computer program product for implementation of a capable, general purpose compression algorithm that can be engaged on the fly. This invention has particular practical application with time-series data, and more particularly, time-series data obtained form a spacecraft, or similar situations where cost, size and/or power limitations are prevalent, although it is not limited to such applications. It is also particularly applicable to the compression of serial data streams and works in one, two, or three dimensions. The original input data is approximated by Chebyshev polynomials, achieving very high compression ratios on serial data streams with minimal loss of scientific information.

Time-variant random interval natural frequency analysis of structures

NASA Astrophysics Data System (ADS)

Wu, Binhua; Wu, Di; Gao, Wei; Song, Chongmin

2018-02-01

This paper presents a new robust method namely, unified interval Chebyshev-based random perturbation method, to tackle hybrid random interval structural natural frequency problem. In the proposed approach, random perturbation method is implemented to furnish the statistical features (i.e., mean and standard deviation) and Chebyshev surrogate model strategy is incorporated to formulate the statistical information of natural frequency with regards to the interval inputs. The comprehensive analysis framework combines the superiority of both methods in a way that computational cost is dramatically reduced. This presented method is thus capable of investigating the day-to-day based time-variant natural frequency of structures accurately and efficiently under concrete intrinsic creep effect with probabilistic and interval uncertain variables. The extreme bounds of the mean and standard deviation of natural frequency are captured through the embedded optimization strategy within the analysis procedure. Three particularly motivated numerical examples with progressive relationship in perspective of both structure type and uncertainty variables are demonstrated to justify the computational applicability, accuracy and efficiency of the proposed method.

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

PubMed

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

2017-10-10

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

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

NASA Technical Reports Server (NTRS)

Gyekenyesi, G. S.; Mendelson, A.

1972-01-01

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

2013-09-01

In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

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

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

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

Specific CT 3D rendering of the treatment zone after Irreversible Electroporation (IRE) in a pig liver model: the “Chebyshev Center Concept” to define the maximum treatable tumor size

PubMed Central

2014-01-01

Background Size and shape of the treatment zone after Irreversible electroporation (IRE) can be difficult to depict due to the use of multiple applicators with complex spatial configuration. Exact geometrical definition of the treatment zone, however, is mandatory for acute treatment control since incomplete tumor coverage results in limited oncological outcome. In this study, the “Chebyshev Center Concept” was introduced for CT 3d rendering to assess size and position of the maximum treatable tumor at a specific safety margin. Methods In seven pig livers, three different IRE protocols were applied to create treatment zones of different size and shape: Protocol 1 (n = 5 IREs), Protocol 2 (n = 5 IREs), and Protocol 3 (n = 5 IREs). Contrast-enhanced CT was used to assess the treatment zones. Technique A consisted of a semi-automated software prototype for CT 3d rendering with the “Chebyshev Center Concept” implemented (the “Chebyshev Center” is the center of the largest inscribed sphere within the treatment zone) with automated definition of parameters for size, shape and position. Technique B consisted of standard CT 3d analysis with manual definition of the same parameters but position. Results For Protocol 1 and 2, short diameter of the treatment zone and diameter of the largest inscribed sphere within the treatment zone were not significantly different between Technique A and B. For Protocol 3, short diameter of the treatment zone and diameter of the largest inscribed sphere within the treatment zone were significantly smaller for Technique A compared with Technique B (41.1 ± 13.1 mm versus 53.8 ± 1.1 mm and 39.0 ± 8.4 mm versus 53.8 ± 1.1 mm; p < 0.05 and p < 0.01). For Protocol 1, 2 and 3, sphericity of the treatment zone was significantly larger for Technique A compared with B. Conclusions Regarding size and shape of the treatment zone after IRE, CT 3d rendering with the “Chebyshev Center Concept” implemented provides significantly different results compared with standard CT 3d analysis. Since the latter overestimates the size of the treatment zone, the “Chebyshev Center Concept” could be used for a more objective acute treatment control. PMID:24410997

Recent advances in (soil moisture) triple collocation analysis

USDA-ARS?s Scientific Manuscript database

To date, triple collocation (TC) analysis is one of the most important methods for the global scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method....

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

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.

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

Possibility-based robust design optimization for the structural-acoustic system with fuzzy parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2018-03-01

The conventional engineering optimization problems considering uncertainties are based on the probabilistic model. However, the probabilistic model may be unavailable because of the lack of sufficient objective information to construct the precise probability distribution of uncertainties. This paper proposes a possibility-based robust design optimization (PBRDO) framework for the uncertain structural-acoustic system based on the fuzzy set model, which can be constructed by expert opinions. The objective of robust design is to optimize the expectation and variability of system performance with respect to uncertainties simultaneously. In the proposed PBRDO, the entropy of the fuzzy system response is used as the variability index; the weighted sum of the entropy and expectation of the fuzzy response is used as the objective function, and the constraints are established in the possibility context. The computations for the constraints and objective function of PBRDO are a triple-loop and a double-loop nested problem, respectively, whose computational costs are considerable. To improve the computational efficiency, the target performance approach is introduced to transform the calculation of the constraints into a double-loop nested problem. To further improve the computational efficiency, a Chebyshev fuzzy method (CFM) based on the Chebyshev polynomials is proposed to estimate the objective function, and the Chebyshev interval method (CIM) is introduced to estimate the constraints, thereby the optimization problem is transformed into a single-loop one. Numerical results on a shell structural-acoustic system verify the effectiveness and feasibility of the proposed methods.

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-02-01

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod-Patterson-Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.

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

NASA Technical Reports Server (NTRS)

Manson, S. S.

1979-01-01

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.

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

NASA Astrophysics Data System (ADS)

Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

NASA Astrophysics Data System (ADS)

Hu, Jun; Hadid, Hamda Ben; Henry, Daniel; Mojtabi, Abdelkader

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, ) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (0), and oscillatory for =0 remains so for >0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow.

PubMed

Priede, Jānis; Gerbeth, Gunter

2009-04-01

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number (Pr_{m}=0) . The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie; Hernandez, Kevin; Probe, Austin; Junkins, John L.

2018-03-01

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require "shooting" but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

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

PubMed

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

2008-11-01

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

An empirical understanding of triple collocation evaluation measure

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Understanding a reference-free impedance method using collocated piezoelectric transducers

NASA Astrophysics Data System (ADS)

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

2010-03-01

A new concept of a reference-free impedance method, which does not require direct comparison with a baseline impedance signal, is proposed for damage detection in a plate-like structure. A single pair of piezoelectric (PZT) wafers collocated on both surfaces of a plate are utilized for extracting electro-mechanical signatures (EMS) associated with mode conversion due to damage. A numerical simulation is conducted to investigate the EMS of collocated PZT wafers in the frequency domain at the presence of damage through spectral element analysis. Then, the EMS due to mode conversion induced by damage are extracted using the signal decomposition technique based on the polarization characteristics of the collocated PZT wafers. The effects of the size and the location of damage on the decomposed EMS are investigated as well. Finally, the applicability of the decomposed EMS to the reference-free damage diagnosis is discussed.

Stochastic collocation using Kronrod-Patterson-Hermite quadrature with moderate delay for subsurface flow and transport

NASA Astrophysics Data System (ADS)

Liao, Q.; Tchelepi, H.; Zhang, D.

2015-12-01

Uncertainty quantification aims at characterizing the impact of input parameters on the output responses and plays an important role in many areas including subsurface flow and transport. In this study, a sparse grid collocation approach, which uses a nested Kronrod-Patterson-Hermite quadrature rule with moderate delay for Gaussian random parameters, is proposed to quantify the uncertainty of model solutions. The conventional stochastic collocation method serves as a promising non-intrusive approach and has drawn a great deal of interests. The collocation points are usually chosen to be Gauss-Hermite quadrature nodes, which are naturally unnested. The Kronrod-Patterson-Hermite nodes are shown to be more efficient than the Gauss-Hermite nodes due to nestedness. We propose a Kronrod-Patterson-Hermite rule with moderate delay to further improve the performance. Our study demonstrates the effectiveness of the proposed method for uncertainty quantification through subsurface flow and transport examples.

A novel algorithm for thermal image encryption.

PubMed

Hussain, Iqtadar; Anees, Amir; Algarni, Abdulmohsen

2018-04-16

Thermal images play a vital character at nuclear plants, Power stations, Forensic labs biological research, and petroleum products extraction. Safety of thermal images is very important. Image data has some unique features such as intensity, contrast, homogeneity, entropy and correlation among pixels that is why somehow image encryption is trickier as compare to other encryptions. With conventional image encryption schemes it is normally hard to handle these features. Therefore, cryptographers have paid attention to some attractive properties of the chaotic maps such as randomness and sensitivity to build up novel cryptosystems. That is why, recently proposed image encryption techniques progressively more depends on the application of chaotic maps. This paper proposed an image encryption algorithm based on Chebyshev chaotic map and S8 Symmetric group of permutation based substitution boxes. Primarily, parameters of chaotic Chebyshev map are chosen as a secret key to mystify the primary image. Then, the plaintext image is encrypted by the method generated from the substitution boxes and Chebyshev map. By this process, we can get a cipher text image that is perfectly twisted and dispersed. The outcomes of renowned experiments, key sensitivity tests and statistical analysis confirm that the proposed algorithm offers a safe and efficient approach for real-time image encryption.

Geometrical effects on western intensification of wind-driven ocean currents: The rotated-channel Stommel model, coastal orientation, and curvature

NASA Astrophysics Data System (ADS)

Boyd, John P.; Sanjaya, Edwin

2014-03-01

We revisit early models of steady western boundary currents [Gulf Stream, Kuroshio, etc.] to explore the role of irregular coastlines on jets, both to advance the research frontier and to illuminate for education. In the framework of a steady-state, quasigeostrophic model with viscosity, bottom friction and nonlinearity, we prove that rotating a straight coastline, initially parallel to the meridians, significantly thickens the western boundary layer. We analyze an infinitely long, straight channel with arbitrary orientation and bottom friction using an exact solution and singular perturbation theory, and show that the model, though simpler than Stommel's, nevertheless captures both the western boundary jet (“Gulf Stream”) and the “orientation effect”. In the rest of the article, we restrict attention to the Stommel flow (that is, linear and inviscid except for bottom friction) and apply matched asymptotic expansions, radial basis function, Fourier-Chebyshev and Chebyshev-Chebyshev pseudospectral methods to explore the effects of coastal geometry in a variety of non-rectangular domains bounded by a circle, parabolas and squircles. Although our oceans are unabashedly idealized, the narrow spikes, broad jets and stationary points vividly illustrate the power and complexity of coastal control of western boundary layers.

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, Qinzhuo, E-mail: liaoqz@pku.edu.cn; Zhang, Dongxiao; Tchelepi, Hamdi

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiencymore » of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.« less

Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Some spectral approximation of one-dimensional fourth-order problems

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Maday, Yvon

1989-01-01

Some spectral type collocation method well suited for the approximation of fourth-order systems are proposed. The model problem is the biharmonic equation, in one and two dimensions when the boundary conditions are periodic in one direction. It is proved that the standard Gauss-Lobatto nodes are not the best choice for the collocation points. Then, a new set of nodes related to some generalized Gauss type quadrature formulas is proposed. Also provided is a complete analysis of these formulas including some new issues about the asymptotic behavior of the weights and we apply these results to the analysis of the collocation method.

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

NASA Astrophysics Data System (ADS)

Hu, Shou-Cun; Ji, Jiang-Hui

2017-12-01

In asteroid rendezvous missions, the dynamical environment near an asteroid’s surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped near-Earth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

NASA Technical Reports Server (NTRS)

Kousen, Kenneth A.

1999-01-01

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

Spectral multigrid methods for elliptic equations 2

NASA Technical Reports Server (NTRS)

Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

1983-01-01

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Algorithm for Compressing Time-Series Data

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

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

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

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.

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

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.

Evaluation of assumptions in soil moisture triple collocation analysis

USDA-ARS?s Scientific Manuscript database

Triple collocation analysis (TCA) enables estimation of error variances for three or more products that retrieve or estimate the same geophysical variable using mutually-independent methods. Several statistical assumptions regarding the statistical nature of errors (e.g., mutual independence and ort...

Ocean Striations Detecting and Its Features

NASA Astrophysics Data System (ADS)

Guan, Y. P.; Zhang, Y.; Chen, Z.; Liu, H.; Yu, Y.; Huang, R. X.

2016-02-01

Over the past 10 years or so, ocean striations has been one of the research frontiers as reported in many investigators. With suitable filtering subroutines, striations can be revealed from many different types of ocean datasets. It is clear that striations are some types of meso-scale phenomena in the large-scale circulation system, which in the form of alternating band-like structure. We present a comprehensive study on the effectiveness of the different detection approaches to unveiling the striations. Three one-dimensional filtering methods: Gaussian smoothing, Hanning and Chebyshev high-pass filtering. Our results show that all three methods can reveal ocean banded structures, but the Chebyshev filtering is the best choice. The Gaussian smoothing is not a high pass filter, and it can merely bring regional striations, such as those in the Eastern Pacific, to light. The Hanning high pass filter can introduce a northward shifting of stripes, so it is not as good as the Chebyshev filter. On the other hand, striations in the open ocean are mostly zonally oriented; however, there are always exceptions. In particular, in coastal ocean, due to topography constraint and along shore currents, striations can titled in the meridional direction. We examined the band-like structure of striation for some selected regions of the open ocean and the semi-closed sub-basins, such as the South China sea, the Gulf of Mexico, the Mediterranean Sea and the Japan Sea. A reasonable interpretation is given here.

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

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

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

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

NASA Astrophysics Data System (ADS)

Vu, Q. H.; Brenner, R.; Castelnau, O.; Moulinec, H.; Suquet, P.

2012-03-01

The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599-1606) have shown the equivalence between the collocation method used to invert Laplace-Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

PubMed Central

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

2008-01-01

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method. PMID:18956462

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

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

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

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

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

Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

2011-01-01

This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

A collocation-shooting method for solving fractional boundary value problems

NASA Astrophysics Data System (ADS)

Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M. N.

2010-12-01

In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

PubMed Central

Ando, Tadashi; Chow, Edmond; Saad, Yousef; Skolnick, Jeffrey

2012-01-01

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N2) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the “block” version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions. PMID:22897254

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Reducing the cost of using collocation to compute vibrational energy levels: Results for CH2NH.

PubMed

Avila, Gustavo; Carrington, Tucker

2017-08-14

In this paper, we improve the collocation method for computing vibrational spectra that was presented in the work of Avila and Carrington, Jr. [J. Chem. Phys. 143, 214108 (2015)]. Known quadrature and collocation methods using a Smolyak grid require storing intermediate vectors with more elements than points on the Smolyak grid. This is due to the fact that grid labels are constrained among themselves and basis labels are constrained among themselves. We show that by using the so-called hierarchical basis functions, one can significantly reduce the memory required. In this paper, the intermediate vectors have only as many elements as the Smolyak grid. The ideas are tested by computing energy levels of CH 2 NH.

Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim.

PubMed

Porsa, Sina; Lin, Yi-Chung; Pandy, Marcus G

2016-08-01

The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.

Secure Image Transmission over DFT-precoded OFDM-VLC systems based on Chebyshev Chaos scrambling

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Qiu, Weiwei

2017-08-01

This paper proposes a physical layer image secure transmission scheme for discrete Fourier transform (DFT) precoded OFDM-based visible light communication systems by using Chebyshev chaos maps. In the proposed scheme, 256 subcarriers and QPSK modulation are employed. The transmitted digital signal of the image is encrypted with a Chebyshev chaos sequence. The encrypted signal is then transformed by a DFT precoding matrix to reduce the PAPR of the OFDM signal. After that, the encrypted and DFT-precoded OFDM are transmitted over a VLC channel. The simulation results show that the proposed image security transmission scheme can not only protect the DFT-precoded OFDM-based VLC from eavesdroppers but also improve BER performance.

Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

DOE PAGES

Isotalo, Aarno; Pusa, Maria

2016-05-01

The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant sub-steps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. Themore » improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.« less

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

NASA Technical Reports Server (NTRS)

Phillips, J. R.

1996-01-01

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

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

Control of magnetic bearing systems via the Chebyshev polynomial-based unified model (CPBUM) neural network.

PubMed

Jeng, J T; Lee, T T

2000-01-01

A Chebyshev polynomial-based unified model (CPBUM) neural network is introduced and applied to control a magnetic bearing systems. First, we show that the CPBUM neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural network. It turns out that the CPBUM neural network is more suitable in the design of controller than the conventional feedforward/recurrent neural network. Second, we propose the inverse system method, based on the CPBUM neural networks, to control a magnetic bearing system. The proposed controller has two structures; namely, off-line and on-line learning structures. We derive a new learning algorithm for each proposed structure. The experimental results show that the proposed neural network architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

Best uniform approximation to a class of rational functions

NASA Astrophysics Data System (ADS)

Zheng, Zhitong; Yong, Jun-Hai

2007-10-01

We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/(x-c)2+K(a,b,c,n)/(x-c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n-1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle [eta] in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.

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

NASA Technical Reports Server (NTRS)

Solomonoff, A.; Turkel, E.

1986-01-01

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.

Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J.; Golberg, M.

1978-01-01

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

NASA Astrophysics Data System (ADS)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

A Christoffel function weighted least squares algorithm for collocation approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avila, Gustavo, E-mail: Gustavo-Avila@telefonica.net; Carrington, Tucker, E-mail: Tucker.Carrington@queensu.ca

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

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

ERIC Educational Resources Information Center

Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

2006-01-01

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Spacecraft stability and control using new techniques for periodic and time-delayed systems

NASA Astrophysics Data System (ADS)

NAzari, Morad

This dissertation addresses various problems in spacecraft stability and control using specialized theoretical and numerical techniques for time-periodic and time-delayed systems. First, the effects of energy dissipation are considered in the dual-spin spacecraft, where the damper masses in the platform (?) and the rotor (?) cause energy loss in the system. Floquet theory is employed to obtain stability charts for different relative spin rates of the subsystem [special characters omitted] with respect to the subsystem [special characters omitted]. Further, the stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Next, the dynamics of a rigid spacecraft with nonlinear delayed multi-actuator feedback control are studied, where a nonlinear feedback controller using an inverse dynamics approach is sought for the controlled system to have the desired linear delayed closed-loop dynamics (CLD). Later, three linear state feedback control strategies based on Chebyshev spectral collocation and the Lyapunov Floquet transformation (LFT) are explored for regulation control of linear periodic time delayed systems. First , a delayed feedback control law with discrete delay is implemented and the stability of the closed-loop response is investigated in the parameter space of available control gains using infinite-dimensional Floquet theory. Second, the delay differential equation (DDE) is discretized into a large set of ordinary differential equations (ODEs) using the Chebyshev spectral continuous time approximation (CSCTA) and delayed feedback with distributed delay is applied. The third strategy involves use of both CSCTA and the reduced Lyapunov Floquet transformation (RLFT) in order to design a non-delayed feedback control law. The delayed Mathieu equation is used as an illustrative example in which the closed-loop response and control effort are compared for all three control strategies. Finally, three example applications of control of time-periodic astrodynamic systems, i.e. formation flying control for an elliptic Keplerian chief orbit, body-fixed hovering control over a tumbling asteroid, and stationkeeping in Earth-Moon L1 halo orbits, are shown using versions of the control strategies introduced above. These applications employ a mixture of feedforward and non-delayed periodic-gain state feedback for tracking control of natural and non-natural motions in these systems. A major conclusion is that control effort is minimized by employing periodic-gain (rather than constant-gain) feedback control in such systems.

A Fourier collocation time domain method for numerically solving Maxwell's equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1991-01-01

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

A comparison of companion matrix methods to find roots of a trigonometric polynomial

NASA Astrophysics Data System (ADS)

Boyd, John P.

2013-08-01

A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements, the ECM algorithm is noticeably inferior to the complex-valued companion matrix in simplicity, ease of programming, and accuracy.

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

NASA Astrophysics Data System (ADS)

Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang

2017-12-01

Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

Improved particle position accuracy from off-axis holograms using a Chebyshev model.

PubMed

Öhman, Johan; Sjödahl, Mikael

2018-01-01

Side scattered light from micrometer-sized particles is recorded using an off-axis digital holographic setup. From holograms, a volume is reconstructed with information about both intensity and phase. Finding particle positions is non-trivial, since poor axial resolution elongates particles in the reconstruction. To overcome this problem, the reconstructed wavefront around a particle is used to find the axial position. The method is based on the change in the sign of the curvature around the true particle position plane. The wavefront curvature is directly linked to the phase response in the reconstruction. In this paper we propose a new method of estimating the curvature based on a parametric model. The model is based on Chebyshev polynomials and is fit to the phase anomaly and compared to a plane wave in the reconstructed volume. From the model coefficients, it is possible to find particle locations. Simulated results show increased performance in the presence of noise, compared to the use of finite difference methods. The standard deviation is decreased from 3-39 μm to 6-10 μm for varying noise levels. Experimental results show a corresponding improvement where the standard deviation is decreased from 18 μm to 13 μm.

Learning Collocations: Do the Number of Collocates, Position of the Node Word, and Synonymy Affect Learning?

ERIC Educational Resources Information Center

Webb, Stuart; Kagimoto, Eve

2011-01-01

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

Simplex-stochastic collocation method with improved scalability

NASA Astrophysics Data System (ADS)

Edeling, W. N.; Dwight, R. P.; Cinnella, P.

2016-04-01

The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

Spectral methods for time dependent problems

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1990-01-01

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

Galerkin-collocation domain decomposition method for arbitrary binary black holes

NASA Astrophysics Data System (ADS)

Barreto, W.; Clemente, P. C. M.; de Oliveira, H. P.; Rodriguez-Mueller, B.

2018-05-01

We present a new computational framework for the Galerkin-collocation method for double domain in the context of ADM 3 +1 approach in numerical relativity. This work enables us to perform high resolution calculations for initial sets of two arbitrary black holes. We use the Bowen-York method for binary systems and the puncture method to solve the Hamiltonian constraint. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show convergence of our code for the conformal factor and the ADM mass. Thus, we display features of the conformal factor for different masses, spins and linear momenta.

Electrochemistry of Anilines. II. Oxidation to Dications, Electrochemical and uv/vis Spectroelectrochemical Investigation.

DTIC Science & Technology

1984-01-06

NO-1 ARCUASSII 004-3K-40F /G74N L 2874 Lj6l 1.0= = aM22 1.2 1.1 1. 1. MICROCOP ’ RP’-OLLI’ION liT[* CHART %".NA. H~.Nt I -’AN, All - ,- A t$ CUeavr...The cyclic voltammogram of the methoxy compound -has been simulated by the orthogonal collocation method. Products of bulk electrolysis have been...spectroelectrochemical means. The cyclic volta-mocra. of the methoxy compound has been simulated by the orthoccna. collocation method. Products of bulk

The Use of Verb Noun Collocations in Writing Stories among Iranian EFL Learners

ERIC Educational Resources Information Center

Bazzaz, Fatemeh Ebrahimi; Samad, Arshad Abd

2011-01-01

An important aspect of native speakers' communicative competence is collocational competence which involves knowing which words usually come together and which do not. This paper investigates the possible relationship between knowledge of collocations and the use of verb noun collocation in writing stories because collocational knowledge…

Developing and Evaluating a Chinese Collocation Retrieval Tool for CFL Students and Teachers

ERIC Educational Resources Information Center

Chen, Howard Hao-Jan; Wu, Jian-Cheng; Yang, Christine Ting-Yu; Pan, Iting

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Liang, Conghui; Ceccarelli, Marco; Takeda, Yukio

2012-12-01

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

Enhancing Critical Thinking Skills for Army Leaders Using Blended-Learning Methods

DTIC Science & Technology

2013-01-01

delivering, and evaluating leader education and those who develop and implement distributed learning courses that incorporate group collaboration on topics...Circumstances Numerous studies comparing outcomes of collocated and virtual groups show that collocated groups perform better on interdependent tasks, such as...in class or “cold call” on students to answer questions. Third, using small (rather than large) groups for interactive activities can alleviate free

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

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

ERIC Educational Resources Information Center

Chen, Lidan

2017-01-01

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

Perceptions on L2 Lexical Collocation Translation with a Focus on English-Arabic

ERIC Educational Resources Information Center

Alqaed, Mai Abdullah

2017-01-01

This paper aims to shed light on recent research concerning translating English-Arabic lexical collocations. It begins with a brief overview of English and Arabic lexical collocations with reference to specialized dictionaries. Research views on translating lexical collocations are presented, with the focus on English-Arabic collocations. These…

Legendre spectral-collocation method for solving some types of fractional optimal control problems

PubMed Central

Sweilam, Nasser H.; Al-Ajami, Tamer M.

2014-01-01

In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937

High resolution wind measurements for offshore wind energy development

NASA Technical Reports Server (NTRS)

Nghiem, Son Van (Inventor); Neumann, Gregory (Inventor)

2013-01-01

A method, apparatus, system, article of manufacture, and computer readable storage medium provide the ability to measure wind. Data at a first resolution (i.e., low resolution data) is collected by a satellite scatterometer. Thin slices of the data are determined. A collocation of the data slices are determined at each grid cell center to obtain ensembles of collocated data slices. Each ensemble of collocated data slices is decomposed into a mean part and a fluctuating part. The data is reconstructed at a second resolution from the mean part and a residue of the fluctuating part. A wind measurement is determined from the data at the second resolution using a wind model function. A description of the wind measurement is output.

Investigating ESL Learners' Lexical Collocations: The Acquisition of Verb + Noun Collocations by Japanese Learners of English

ERIC Educational Resources Information Center

Miyakoshi, Tomoko

2009-01-01

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…

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1986-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, Claudio; Quarteroni, Alfio

1987-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

A Multi-domain Spectral Method for Supersonic Reactive Flows

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper has a dual purpose: it presents a multidomain Chebyshev method for the solution of the two-dimensional reactive compressible Navier-Stokes equations, and it reports the results of the application of this code to the numerical simulations of high Mach number reactive flows in recessed cavity. The computational method utilizes newly derived interface boundary conditions as well as an adaptive filtering technique to stabilize the computations. The results of the simulations are relevant to recessed cavity flameholders.

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

NASA Astrophysics Data System (ADS)

Wang, Che; Wang, Hong

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

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

Are Nonadjacent Collocations Processed Faster?

ERIC Educational Resources Information Center

Vilkaite, Laura

2016-01-01

Numerous studies have shown processing advantages for collocations, but they only investigated processing of adjacent collocations (e.g., "provide information"). However, in naturally occurring language, nonadjacent collocations ("provide" some of the "information") are equally, if not more frequent. This raises the…

Mars Mission Optimization Based on Collocation of Resources

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2009-01-01

attenuation and mass transport of a water -mud system due to a solitary wave on the free surface has been modeled by using the Chebyshev-Chebyshev...in Lagrangian coordinates and perturbation equations for shallow water waves were 3 derived. An iteration-by-subdomain technique was introduced to...found. Although the model is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves

Techniques for increasing the efficiency of Earth gravity calculations for precision orbit determination

NASA Technical Reports Server (NTRS)

Smith, R. L.; Lyubomirsky, A. S.

1981-01-01

Two techniques were analyzed. The first is a representation using Chebyshev expansions in three-dimensional cells. The second technique employs a temporary file for storing the components of the nonspherical gravity force. Computer storage requirements and relative CPU time requirements are presented. The Chebyshev gravity representation can provide a significant reduction in CPU time in precision orbit calculations, but at the cost of a large amount of direct-access storage space, which is required for a global model.

A Two-Timescale Discretization Scheme for Collocation

NASA Technical Reports Server (NTRS)

Desai, Prasun; Conway, Bruce A.

2004-01-01

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.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Min; Kollias, Pavlos; Feng, Zhe

The motivation for this research is to develop a precipitation classification and rain rate estimation method using cloud radar-only measurements for Atmospheric Radiation Measurement (ARM) long-term cloud observation analysis, which are crucial and unique for studying cloud lifecycle and precipitation features under different weather and climate regimes. Based on simultaneous and collocated observations of the Ka-band ARM zenith radar (KAZR), two precipitation radars (NCAR S-PolKa and Texas A&M University SMART-R), and surface precipitation during the DYNAMO/AMIE field campaign, a new cloud radar-only based precipitation classification and rain rate estimation method has been developed and evaluated. The resulting precipitation classification ismore » equivalent to those collocated SMART-R and S-PolKa observations. Both cloud and precipitation radars detected about 5% precipitation occurrence during this period. The convective (stratiform) precipitation fraction is about 18% (82%). The 2-day collocated disdrometer observations show an increased number concentration of large raindrops in convective rain compared to dominant concentration of small raindrops in stratiform rain. The composite distributions of KAZR reflectivity and Doppler velocity also show two distinct structures for convective and stratiform rain. These indicate that the method produces physically consistent results for two types of rain. The cloud radar-only rainfall estimation is developed based on the gradient of accumulative radar reflectivity below 1 km, near-surface Ze, and collocated surface rainfall (R) measurement. The parameterization is compared with the Z-R exponential relation. The relative difference between estimated and surface measured rainfall rate shows that the two-parameter relation can improve rainfall estimation.« less

Parallel/Vector Integration Methods for Dynamical Astronomy

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

1999-01-01

This paper reviews three recent works on the numerical methods to integrate ordinary differential equations (ODE), which are specially designed for parallel, vector, and/or multi-processor-unit(PU) computers. The first is the Picard-Chebyshev method (Fukushima, 1997a). It obtains a global solution of ODE in the form of Chebyshev polynomial of large (> 1000) degree by applying the Picard iteration repeatedly. The iteration converges for smooth problems and/or perturbed dynamics. The method runs around 100-1000 times faster in the vector mode than in the scalar mode of a certain computer with vector processors (Fukushima, 1997b). The second is a parallelization of a symplectic integrator (Saha et al., 1997). It regards the implicit midpoint rules covering thousands of timesteps as large-scale nonlinear equations and solves them by the fixed-point iteration. The method is applicable to Hamiltonian systems and is expected to lead an acceleration factor of around 50 in parallel computers with more than 1000 PUs. The last is a parallelization of the extrapolation method (Ito and Fukushima, 1997). It performs trial integrations in parallel. Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3.5 by using several PUs. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators (Makino and Aarseth, 1992), (Hut et al., 1995) or the implicit symmetric multistep methods (Fukushima, 1998), (Fukushima, 1999).

Collocations: A Neglected Variable in EFL.

ERIC Educational Resources Information Center

Farghal, Mohammed; Obiedat, Hussein

1995-01-01

Addresses the issue of collocations as an important and neglected variable in English-as-a-Foreign-Language classes. Two questionnaires, in English and Arabic, involving common collocations relating to food, color, and weather were administered to English majors and English language teachers. Results show both groups deficient in collocations. (36…

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2010 CFR

2010-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2014 CFR

2014-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2011 CFR

2011-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2013 CFR

2013-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2012 CFR

2012-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

Novel two-way artificial boundary condition for 2D vertical water wave propagation modelled with Radial-Basis-Function Collocation Method

NASA Astrophysics Data System (ADS)

Mueller, A.

2018-04-01

A new transparent artificial boundary condition for the two-dimensional (vertical) (2DV) free surface water wave propagation modelled using the meshless Radial-Basis-Function Collocation Method (RBFCM) as boundary-only solution is derived. The two-way artificial boundary condition (2wABC) works as pure incidence, pure radiation and as combined incidence/radiation BC. In this work the 2wABC is applied to harmonic linear water waves; its performance is tested against the analytical solution for wave propagation over horizontal sea bottom, standing and partially standing wave as well as wave interference of waves with different periods.

Acoustic ranging of small arms fire using a single sensor node collocated with the target.

PubMed

Lo, Kam W; Ferguson, Brian G

2015-06-01

A ballistic model-based method, which builds upon previous work by Lo and Ferguson [J. Acoust. Soc. Am. 132, 2997-3017 (2012)], is described for ranging small arms fire using a single acoustic sensor node collocated with the target, without a priori knowledge of the muzzle speed and ballistic constant of the bullet except that they belong to a known two-dimensional parameter space. The method requires measurements of the differential time of arrival and differential angle of arrival of the muzzle blast and ballistic shock wave at the sensor node. Its performance is evaluated using both simulated and real data.

Simulation of Edge Effects in Electroanalytical Experiments by Orthogonal Collocation. Part I. Two Dimensional Collocation and Theory for Chronoamperometry.

DTIC Science & Technology

1982-08-18

cselixataan has been shown to Pro, imonedimie. FIN SMCS10 tam we m Vp assuma threry. In lacd. it has been shown lor difeent oide a pouwerful method to simulate...Afortd meaden 11. ’by)W~itl 116.ttousol =odimra She delade Ia~c Ul - by she Oa SWISS INaolder 10 wAce shem. re’te" s s m rnb -bute r~ 6 X-06 CSc a I

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

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

ERIC Educational Resources Information Center

Nguyen, Thi My Hang; Webb, Stuart

2017-01-01

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

Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map

PubMed Central

2014-01-01

We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10113 key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970

Tensorial Basis Spline Collocation Method for Poisson's Equation

NASA Astrophysics Data System (ADS)

Plagne, Laurent; Berthou, Jean-Yves

2000-01-01

This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation. In the case of a localized 3D charge distribution in vacuum, this direct method based on a tensorial decomposition of the differential operator is shown to be competitive with both iterative BSCM and FFT-based methods. We emphasize the O(h4) and O(h6) convergence of TBSCM for cubic and quintic splines, respectively. We describe the implementation of this method on a distributed memory parallel machine. Performance measurements on a Cray T3E are reported. Our code exhibits high performance and good scalability: As an example, a 27 Gflops performance is obtained when solving Poisson's equation on a 2563 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Fuzzy interval Finite Element/Statistical Energy Analysis for mid-frequency analysis of built-up systems with mixed fuzzy and interval parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2016-10-01

This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.

English Learners' Knowledge of Prepositions: Collocational Knowledge or Knowledge Based on Meaning?

ERIC Educational Resources Information Center

Mueller, Charles M.

2011-01-01

Second language (L2) learners' successful performance in an L2 can be partly attributed to their knowledge of collocations. In some cases, this knowledge is accompanied by knowledge of the semantic and/or grammatical patterns that motivate the collocation. At other times, collocational knowledge may serve a compensatory role. To determine the…

Frequency of Input and L2 Collocational Processing: A Comparison of Congruent and Incongruent Collocations

ERIC Educational Resources Information Center

Wolter, Brent; Gyllstad, Henrik

2013-01-01

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…

Corpus-Based versus Traditional Learning of Collocations

ERIC Educational Resources Information Center

Daskalovska, Nina

2015-01-01

One of the aspects of knowing a word is the knowledge of which words it is usually used with. Since knowledge of collocations is essential for appropriate and fluent use of language, learning collocations should have a central place in the study of vocabulary. There are different opinions about the best ways of learning collocations. This study…

Collocations in Corpus-Based Language Learning Research: Identifying, Comparing, and Interpreting the Evidence

ERIC Educational Resources Information Center

Gablasova, Dana; Brezina, Vaclav; McEnery, Tony

2017-01-01

This article focuses on the use of collocations in language learning research (LLR). Collocations, as units of formulaic language, are becoming prominent in our understanding of language learning and use; however, while the number of corpus-based LLR studies of collocations is growing, there is still a need for a deeper understanding of factors…

Maximum of the modulus of kernels in Gauss-Turan quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.

2008-06-01

We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32

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

PubMed

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

2018-02-01

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

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

An effective pseudospectral method for constraint dynamic optimisation problems with characteristic times

NASA Astrophysics Data System (ADS)

Xiao, Long; Liu, Xinggao; Ma, Liang; Zhang, Zeyin

2018-03-01

Dynamic optimisation problem with characteristic times, widely existing in many areas, is one of the frontiers and hotspots of dynamic optimisation researches. This paper considers a class of dynamic optimisation problems with constraints that depend on the interior points either fixed or variable, where a novel direct pseudospectral method using Legendre-Gauss (LG) collocation points for solving these problems is presented. The formula for the state at the terminal time of each subdomain is derived, which results in a linear combination of the state at the LG points in the subdomains so as to avoid the complex nonlinear integral. The sensitivities of the state at the collocation points with respect to the variable characteristic times are derived to improve the efficiency of the method. Three well-known characteristic time dynamic optimisation problems are solved and compared in detail among the reported literature methods. The research results show the effectiveness of the proposed method.

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

47 CFR 69.121 - Connection charges for expanded interconnection.

Code of Federal Regulations, 2010 CFR

2010-10-01

... separations. (2) Charges for subelements associated with physical collocation or virtual collocation, other... of the virtual collocation equipment described in § 64.1401(e)(1) of this chapter, may reasonably...

Interpolation of Superconducting Gravity Observations Using Least-Squares Collocation Method

NASA Astrophysics Data System (ADS)

Habel, Branislav; Janak, Juraj

2014-05-01

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.

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

On Bernstein type inequalities and a weighted Chebyshev approximation problem on ellipses

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

A classical inequality due to Bernstein which estimates the norm of polynomials on any given ellipse in terms of their norm on any smaller ellipse with the same foci is examined. For the uniform and a certain weighted uniform norm, and for the case that the two ellipses are not too close, sharp estimates of this type were derived and the corresponding extremal polynomials were determined. These Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Some new results were also presented for a weighted approximation problem of this type.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Leung, Martin S. K.

1995-01-01

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Noise reduction in long‐period seismograms by way of array summing

USGS Publications Warehouse

Ringler, Adam; Wilson, David; Storm, Tyler; Marshall, Benjamin T.; Hutt, Charles R.; Holland, Austin

2016-01-01

Long‐period (>100  s period) seismic data can often be dominated by instrumental noise as well as local site noise. When multiple collocated sensors are installed at a single site, it is possible to improve the overall station noise levels by applying stacking methods to their traces. We look at the noise reduction in long‐period seismic data by applying the time–frequency phase‐weighted stacking method of Schimmel and Gallart (2007) as well as the phase‐weighted stacking (PWS) method of Schimmel and Paulssen (1997) to four collocated broadband sensors installed in the quiet Albuquerque Seismological Laboratory underground vault. We show that such stacking methods can improve vertical noise levels by as much as 10 dB over the mean background noise levels at 400 s period, suggesting that greater improvements could be achieved with an array involving multiple sensors. We also apply this method to reduce local incoherent noise on horizontal seismic records of the 2 March 2016 Mw 7.8 Sumatra earthquake, where the incoherent noise levels at very long periods are similar in amplitude to the earthquake signal. To maximize the coherency, we apply the PWS method to horizontal data where relative azimuths between collocated sensors are estimated and compared with a simpler linear stack with no azimuthal rotation. Such methods could help reduce noise levels at various seismic stations where multiple high‐quality sensors have been deployed. Such small arrays may also provide a solution to improving long‐period noise levels at Global Seismographic Network stations.

Regularization and computational methods for precise solution of perturbed orbit transfer problems

NASA Astrophysics Data System (ADS)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these individual algorithms. Following this discussion, the combined parallel algorithm, known as the unified Lambert tool, is presented and an explanation is given as to how it automatically selects which of the three perturbed solvers to compute the perturbed solution for a particular orbit transfer. The unified Lambert tool may be used to determine a single orbit transfer or for generating of an extremal field map. A case study is presented for a mission that is required to rendezvous with two pieces of orbit debris (spent rocket boosters). The unified Lambert tool software developed in this dissertation is already being utilized by several industrial partners and we are confident that it will play a significant role in practical applications, including solution of Lambert problems that arise in the current applications focused on enhanced space situational awareness.

Global statistics of liquid water content and effective number concentration of water clouds over ocean derived from combined CALIPSO and MODIS measurements

NASA Astrophysics Data System (ADS)

Hu, Y.; Vaughan, M.; McClain, C.; Behrenfeld, M.; Maring, H.; Anderson, D.; Sun-Mack, S.; Flittner, D.; Huang, J.; Wielicki, B.; Minnis, P.; Weimer, C.; Trepte, C.; Kuehn, R.

2007-06-01

This study presents an empirical relation that links the volume extinction coefficients of water clouds, the layer integrated depolarization ratios measured by lidar, and the effective radii of water clouds derived from collocated passive sensor observations. Based on Monte Carlo simulations of CALIPSO lidar observations, this method combines the cloud effective radius reported by MODIS with the lidar depolarization ratios measured by CALIPSO to estimate both the liquid water content and the effective number concentration of water clouds. The method is applied to collocated CALIPSO and MODIS measurements obtained during July and October of 2006, and January 2007. Global statistics of the cloud liquid water content and effective number concentration are presented.

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Spectral methods on arbitrary grids

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David

1995-01-01

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

Isogeometric Collocation for Elastostatics and Explicit Dynamics

DTIC Science & Technology

2012-01-25

ICES REPORT 12-07 January 2012 Isogeometric collocation for elastostatics and explicit dynamics by F. Auricchio, L. Beirao da Veiga , T.J.R. Hughes, A...Auricchio, L. Beirao da Veiga , T.J.R. Hughes, A. Reali, G. Sangalli, Isogeometric collocation for elastostatics and explicit dynamics, ICES REPORT 12-07...Isogeometric collocation for elastostatics and explicit dynamics F. Auricchio a,c, L. Beirão da Veiga b,c, T.J.R. Hughes d, A. Reali a,c,∗, G

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

2014-12-01

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Nordstrom, Jan; Gottlieb, David

2007-01-01

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

Design of a Synthetic Aperture Array to Support Experiments in Active Control of Scattering

DTIC Science & Technology

1990-06-01

becomes necessary to validate the theory and test the control system algorithms . While experiments in open water would be most like the anticipated...mathematical development of the beamforming algorithms used as well as an estimate of their applicability to the specifics of beamforming in a reverberant...Chebyshev array have been proposed. The method used in ARRAY, a nested product algorithm , proposed by Bresler [21] is recommended by Pozar [19] and

Collocation and Pattern Recognition Effects on System Failure Remediation

NASA Technical Reports Server (NTRS)

Trujillo, Anna C.; Press, Hayes N.

2007-01-01

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.

[Spatio-Temporal Bioelectrical Brain Activity Organization during Reading Syntagmatic and Paradigmatic Collocations by Students with Different Foreign Language Proficiency].

PubMed

Sokolova, L V; Cherkasova, A S

2015-01-01

Texts or words/pseudowords are often used as stimuli for human verbal activity research. Our study pays attention to decoding processes of grammatical constructions consisted of two-three words--collocations. Russian and English collocation sets without any narrative were presented to Russian-speaking students with different English language skill. Stimulus material had two types of collocations: paradigmatic and syntagmatic. 30 students (average age--20.4 ± 0.22) took part in the study, they were divided into two equal groups depending on their English language skill (linguists/nonlinguists). During reading brain bioelectrical activity of cortex has been registered from 12 electrodes in alfa-, beta-, theta-bands. Coherent function reflecting cooperation of different cortical areas during reading collocations has been analyzed. Increase of interhemispheric and diagonal connections while reading collocations in different languages in the group of students with low knowledge of foreign language testifies of importance of functional cooperation between the hemispheres. It has been found out that brain bioelectrical activity of students with good foreign language knowledge during reading of all collocation types in Russian and English is characterized by economization of nervous substrate resources compared to nonlinguists. Selective activation of certain cortical areas has also been observed (depending on the grammatical construction type) in nonlinguists group that is probably related to special decoding system which processes presented stimuli. Reading Russian paradigmatic constructions by nonlinguists entailed increase between left cortical areas, reading of English syntagmatic collocations--between right ones.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

NASA Astrophysics Data System (ADS)

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

2017-03-01

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.

Learning L2 Collocations Incidentally from Reading

ERIC Educational Resources Information Center

Pellicer-Sánchez, Ana

2017-01-01

Previous studies have shown that intentional learning through explicit instruction is effective for the acquisition of collocations in a second language (L2) (e.g. Peters, 2014, 2015), but relatively little is known about the effectiveness of incidental approaches for the acquisition of L2 collocations. The present study examined the incidental…

Incidental Learning of Collocation

ERIC Educational Resources Information Center

Webb, Stuart; Newton, Jonathan; Chang, Anna

2013-01-01

This study investigated the effects of repetition on the learning of collocation. Taiwanese university students learning English as a foreign language simultaneously read and listened to one of four versions of a modified graded reader that included different numbers of encounters (1, 5, 10, and 15 encounters) with a set of 18 target collocations.…

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

Code of Federal Regulations, 2011 CFR

2011-10-01

... accessible by both the incumbent LEC and the collocating telecommunications carrier, at which the fiber optic... technically feasible, the incumbent LEC shall provide the connection using copper, dark fiber, lit fiber, or... that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems...

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

Code of Federal Regulations, 2010 CFR

2010-10-01

... accessible by both the incumbent LEC and the collocating telecommunications carrier, at which the fiber optic... technically feasible, the incumbent LEC shall provide the connection using copper, dark fiber, lit fiber, or... that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems...

Usability Study of Two Collocated Prototype System Displays

NASA Technical Reports Server (NTRS)

Trujillo, Anna C.

2007-01-01

Currently, most of the displays in control rooms can be categorized as status screens, alerts/procedures screens (or paper), or control screens (where the state of a component is changed by the operator). The primary focus of this line of research is to determine which pieces of information (status, alerts/procedures, and control) should be collocated. Two collocated displays were tested for ease of understanding in an automated desktop survey. This usability study was conducted as a prelude to a larger human-in-the-loop experiment in order to verify that the 2 new collocated displays were easy to learn and usable. The results indicate that while the DC display was preferred and yielded better performance than the MDO display, both collocated displays can be easily learned and used.

Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Duckeman, Gregory A.

1994-01-01

In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Youssri, Y. H.

2013-10-01

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane-Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.

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

ERIC Educational Resources Information Center

Macis, Marijana; Schmitt, Norbert

2017-01-01

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

Teaching and Learning Collocation in Adult Second and Foreign Language Learning

ERIC Educational Resources Information Center

Boers, Frank; Webb, Stuart

2018-01-01

Perhaps the greatest challenge to creating a research timeline on teaching and learning collocation is deciding how wide to cast the net in the search for relevant publications. For one thing, the term "collocation" does not have the same meaning for all (applied) linguists and practitioners (Barfield & Gyllstad 2009) (see timeline).…

Supporting Collocation Learning with a Digital Library

ERIC Educational Resources Information Center

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

2010-01-01

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

Cross-Linguistic Influence: Its Impact on L2 English Collocation Production

ERIC Educational Resources Information Center

Phoocharoensil, Supakorn

2013-01-01

This research study investigated the influence of learners' mother tongue on their acquisition of English collocations. Having drawn the linguistic data from two groups of Thai EFL learners differing in English proficiency level, the researcher found that the native language (L1) plays a significant role in the participants' collocation learning…

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

ERIC Educational Resources Information Center

Liu, Dilin

2010-01-01

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,…

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

ERIC Educational Resources Information Center

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

2012-01-01

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

The Effect of Error Correction Feedback on the Collocation Competence of Iranian EFL Learners

ERIC Educational Resources Information Center

Jafarpour, Ali Akbar; Sharifi, Abolghasem

2012-01-01

Collocations are one of the most important elements in language proficiency but the effect of error correction feedback of collocations has not been thoroughly examined. Some researchers report the usefulness and importance of error correction (Hyland, 1990; Bartram & Walton, 1991; Ferris, 1999; Chandler, 2003), while others showed that error…

Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks

ERIC Educational Resources Information Center

Menon, Sujatha; Mukundan, Jayakaran

2012-01-01

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

The Effect of Grouping and Presenting Collocations on Retention

ERIC Educational Resources Information Center

Akpinar, Kadriye Dilek; Bardakçi, Mehmet

2015-01-01

The aim of this study is two-fold. Firstly, it attempts to determine the role of presenting collocations by organizing them based on (i) the keyword, (ii) topic related and (iii) grammatical aspect on retention of collocations. Secondly, it investigates the relationship between participants' general English proficiency and the presentation types…

Temi firthiani di linguistica applicata: "Restricted Languages" e "Collocation" (Firthian Themes in Applied Linguistics: "Restricted Languages" and "Collocation")

ERIC Educational Resources Information Center

Leonardi, Magda

1977-01-01

Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in…

Corpora and Collocations in Chinese-English Dictionaries for Chinese Users

ERIC Educational Resources Information Center

Xia, Lixin

2015-01-01

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

Three-dimensional wave field modeling by a collocated-grid finite-difference method in the anelastic model with surface topography

NASA Astrophysics Data System (ADS)

Wang, N.; Li, J.; Borisov, D.; Gharti, H. N.; Shen, Y.; Zhang, W.; Savage, B. K.

2016-12-01

We incorporate 3D anelastic attenuation into the collocated-grid finite-difference method on curvilinear grids (Zhang et al., 2012), using the rheological model of the generalized Maxwell body (Emmerich and Korn, 1987; Moczo and Kristek, 2005; Käser et al., 2007). We follow a conventional procedure to calculate the anelastic coefficients (Emmerich and Korn, 1987) determined by the Q(ω)-law, with a modification in the choice of frequency band and thus the relaxation frequencies that equidistantly cover the logarithmic frequency range. We show that such an optimization of anelastic coefficients is more accurate when using a fixed number of relaxation mechanisms to fit the frequency independent Q-factors. We use curvilinear grids to represent the surface topography. The velocity-stress form of the 3D isotropic anelastic wave equation is solved with a collocated-grid finite-difference method. Compared with the elastic case, we need to solve additional material-independent anelastic functions (Kristek and Moczo, 2003) for the mechanisms at each relaxation frequency. Based on the stress-strain relation, we calculate the spatial partial derivatives of the anelastic functions indirectly thereby saving computational storage and improving computational efficiency. The complex-frequency-shifted perfectly matched layer (CFS-PML) is used for the absorbing boundary condition based on the auxiliary difference equation (Zhang and Shen, 2010). The traction image method (Zhang and Chen, 2006) is employed for the free-surface boundary condition. We perform several numerical experiments including homogeneous full-space models and layered half-space models, considering both flat and 3D Gaussian-shape hill surfaces. The results match very well with those of the spectral-element method (Komatitisch and Tromp, 2002; Savage et al., 2010), verifying the simulations by our method in the anelastic model with surface topography.

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1977-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

On the Effect of Gender and Years of Instruction on Iranian EFL Learners' Collocational Competence

ERIC Educational Resources Information Center

Ganji, Mansoor

2012-01-01

This study investigates the Iranian EFL learners' Knowledge of Lexical Collocation at three academic levels: freshmen, sophomores, and juniors. The participants were forty three English majors doing their B.A. in English Translation studies in Chabahar Maritime University. They took a 50-item fill-in-the-blank test of lexical collocations. The…

Formulaic Language and Collocations in German Essays: From Corpus-Driven Data to Corpus-Based Materials

ERIC Educational Resources Information Center

Krummes, Cedric; Ensslin, Astrid

2015-01-01

Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…

Symmetrical and Asymmetrical Scaffolding of L2 Collocations in the Context of Concordancing

ERIC Educational Resources Information Center

Rezaee, Abbas Ali; Marefat, Hamideh; Saeedakhtar, Afsaneh

2015-01-01

Collocational competence is recognized to be integral to native-like L2 performance, and concordancing can be of assistance in gaining this competence. This study reports on an investigation into the effect of symmetrical and asymmetrical scaffolding on the collocational competence of Iranian intermediate learners of English in the context of…

Profiling the Collocation Use in ELT Textbooks and Learner Writing

ERIC Educational Resources Information Center

Tsai, Kuei-Ju

2015-01-01

The present study investigates the collocational profiles of (1) three series of graded textbooks for English as a foreign language (EFL) commonly used in Taiwan, (2) the written productions of EFL learners, and (3) the written productions of native speakers (NS) of English. These texts were examined against a purpose-built collocation list. Based…

Learning and Teaching L2 Collocations: Insights from Research

ERIC Educational Resources Information Center

Szudarski, Pawel

2017-01-01

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

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cameron, M.K.; Fomel, S.B.; Sethian, J.A.

2009-01-01

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approachmore » is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.« less

A perturbation method to the tent map based on Lyapunov exponent and its application

NASA Astrophysics Data System (ADS)

Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu

2015-10-01

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

Model-free simulations of turbulent reactive flows

NASA Technical Reports Server (NTRS)

Givi, Peyman

1989-01-01

The current computational methods for solving transport equations of turbulent reacting single-phase flows are critically reviewed, with primary attention given to those methods that lead to model-free simulations. In particular, consideration is given to direct numerical simulations using spectral (Galerkin) and pseudospectral (collocation) methods, spectral element methods, and Lagrangian methods. The discussion also covers large eddy simulations and turbulence modeling.

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

ERIC Educational Resources Information Center

Ying, Yang

2015-01-01

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

An Automatic Collocation Writing Assistant for Taiwanese EFL Learners: A Case of Corpus-Based NLP Technology

ERIC Educational Resources Information Center

Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin

2008-01-01

Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation…

First and Second Generation New York City Bilinguals: What Is the Role of Input in Their Collocational Knowledge of English and Spanish?

ERIC Educational Resources Information Center

Heidrick, Ingrid T.

2017-01-01

This study compares monolinguals and different kinds of bilinguals with respect to their knowledge of the type of lexical phenomenon known as collocation. Collocations are word combinations that speakers use recurrently, forming the basis of conventionalized lexical patterns that are shared by a linguistic community. Examples of collocations…

Mapping implicit spectral methods to distributed memory architectures

NASA Technical Reports Server (NTRS)

Overman, Andrea L.; Vanrosendale, John

1991-01-01

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

State-to-state quantum dynamics of the F + HCl (vi = 0, ji = 0) → HF(vf, jf) + Cl reaction on the ground state potential energy surface.

PubMed

Li, Anyang; Guo, Hua; Sun, Zhigang; Kłos, Jacek; Alexander, Millard H

2013-10-07

The state-to-state reaction dynamics of the title reaction is investigated on the ground electronic state potential energy surface using two quantum dynamical methods. The results obtained using the Chebyshev real wave packet method are in excellent agreement with those obtained using the time-independent method, except at low translational energies. It is shown that this exothermic hydrogen abstraction reaction is direct, resulting in a strong back-scattered bias in the product angular distribution. The HF product is highly excited internally. Agreement with available experimental data is only qualitative. We discuss several possible causes of disagreement with experiment.

Asymptotic formulae for the zeros of orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badkov, V M

2012-09-30

Let p{sub n}(t) be an algebraic polynomial that is orthonormal with weight p(t) on the interval [-1, 1]. When p(t) is a perturbation (in certain limits) of the Chebyshev weight of the first kind, the zeros of the polynomial p{sub n}( cos {tau}) and the differences between pairs of (not necessarily consecutive) zeros are shown to satisfy asymptotic formulae as n{yields}{infinity}, which hold uniformly with respect to the indices of the zeros. Similar results are also obtained for perturbations of the Chebyshev weight of the second kind. First, some preliminary results on the asymptotic behaviour of the difference between twomore » zeros of an orthogonal trigonometric polynomial, which are needed, are established. Bibliography: 15 titles.« less

Nonlinear adaptive inverse control via the unified model neural network

NASA Astrophysics Data System (ADS)

Jeng, Jin-Tsong; Lee, Tsu-Tian

1999-03-01

In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

Edge gradients evaluation for 2D hybrid finite volume method model

USDA-ARS?s Scientific Manuscript database

In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Tayl...

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

NASA Astrophysics Data System (ADS)

Ophaug, Vegard; Gerlach, Christian

2017-11-01

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

Collocational Links in the L2 Mental Lexicon and the Influence of L1 Intralexical Knowledge

ERIC Educational Resources Information Center

Wolter, Brent; Gyllstad, Henrik

2011-01-01

This article assesses the influence of L1 intralexical knowledge on the formation of L2 intralexical collocations. Two tests, a primed lexical decision task (LDT) and a test of receptive collocational knowledge, were administered to a group of non-native speakers (NNSs) (L1 Swedish), with native speakers (NSs) of English serving as controls on the…

A Corpus-Driven Design of a Test for Assessing the ESL Collocational Competence of University Students

ERIC Educational Resources Information Center

Jaen, Maria Moreno

2007-01-01

This paper reports an assessment of the collocational competence of students of English Linguistics at the University of Granada. This was carried out to meet a two-fold purpose. On the one hand, we aimed to establish a solid corpus-driven approach based upon a systematic and reliable framework for the evaluation of collocational competence in…

On estimating gravity anomalies: A comparison of least squares collocation with least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1976-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

Vibration and Control of Flexible Rotor Supported by Magnetic Bearings

NASA Technical Reports Server (NTRS)

Nonami, Kenzou

1988-01-01

Active vibration control of flexible rotors supported by magnetic bearings is discussed. Using a finite-element method for a mathematical model of the flexible rotor, the eigenvalue problem is formulated taking into account the interaction between a mechanical system of the flexible rotor and an electrical system of the magnetic bearings and the controller. However, for the sake of simplicity, gyroscopic effects are disregarded. It is possible to adapt this formulation to a general flexible rotor-magnetic bearing system. Controllability with and without collocation sensors and actuators located at the same distance along the rotor axis is discussed for the higher order flexible modes of the test rig. In conclusion, it is proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then it is possible to stabilize for the case of uncollocation by means of this method.

Optimization of Low-Thrust Spiral Trajectories by Collocation

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Dankanich, John W.

2012-01-01

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

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Spectral analysis of GEOS-3 altimeter data and frequency domain collocation. [to estimate gravity anomalies

NASA Technical Reports Server (NTRS)

Eren, K.

1980-01-01

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.

Potential applications of skip SMV with thrust engine

NASA Astrophysics Data System (ADS)

Wang, Weilin; Savvaris, Al

2016-11-01

This paper investigates the potential applications of Space Maneuver Vehicles (SMV) with skip trajectory. Due to soaring space operations over the past decades, the risk of space debris has considerably increased such as collision risks with space asset, human property on ground and even aviation. Many active debris removal methods have been investigated and in this paper, a debris remediation method is first proposed based on skip SMV. The key point is to perform controlled re-entry. These vehicles are expected to achieve a trans-atmospheric maneuver with thrust engine. If debris is released at altitude below 80 km, debris could be captured by the atmosphere drag force and re-entry interface prediction accuracy is improved. Moreover if the debris is released in a cargo at a much lower altitude, this technique protects high value space asset from break up by the atmosphere and improves landing accuracy. To demonstrate the feasibility of this concept, the present paper presents the simulation results for two specific mission profiles: (1) descent to predetermined altitude; (2) descent to predetermined point (altitude, longitude and latitude). The evolutionary collocation method is adopted for skip trajectory optimization due to its global optimality and high-accuracy. This method is actually a two-step optimization approach based on the heuristic algorithm and the collocation method. The optimal-control problem is transformed into a nonlinear programming problem (NLP) which can be efficiently and accurately solved by the sequential quadratic programming (SQP) procedure. However, such a method is sensitive to initial values. To reduce the sensitivity problem, genetic algorithm (GA) is adopted to refine the grids and provide near optimum initial values. By comparing the simulation data from different scenarios, it is found that skip SMV is feasible in active debris removal and the evolutionary collocation method gives a truthful re-entry trajectory that satisfies the path and boundary constraints.

Three-Dimensional Solution of the Free Vibration Problem for Metal-Ceramic Shells Using the Method of Sampling Surfaces

NASA Astrophysics Data System (ADS)

Kulikov, G. M.; Plotnikova, S. V.

2017-03-01

The possibility of using the method of sampling surfaces (SaS) for solving the free vibration problem of threedimensional elasticity for metal-ceramic shells is studied. According to this method, in the shell body, an arbitrary number of SaS parallel to its middle surface are selected in order to take displacements of these surfaces as unknowns. The SaS pass through the nodes of a Chebyshev polynomial, which improves the convergence of the SaS method significantly. As a result, the SaS method can be used to obtain analytical solutions of the vibration problem for metal-ceramic plates and cylindrical shells that asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

Combline designs improve mm-wave filter performance

NASA Astrophysics Data System (ADS)

Hey-Shipton, Gregory L.

1990-10-01

Combline filters with 2- to 75-percent bandwidths and orders up to 19 are discussed. They are realized as coupled rectangular coaxial transmission lines, since this type of transmission line is characterized by machinability and the wide variation in coupling coefficients that can be realized with rectangular bars. A broadband combline filter designed as a 19th-order, 0.01-dB equal-ripple Chebyshev type is presented, along with a third-order 0.001-dB equal-ripple Chebyshev filter with a 200-MHz bandwidth centered at 8.0 GHz. Interfaces to standard 50-ohm coaxial lines, as well as structures for waveguide interfaces are described, and focus is placed on a two-step impedance transformer matching a 538-ohm waveguide characteristic impedance to a 95-ohm filter terminal impedance.

Frequency modulation television analysis: Distortion analysis

NASA Technical Reports Server (NTRS)

Hodge, W. H.; Wong, W. H.

1973-01-01

Computer simulation is used to calculate the time-domain waveform of standard T-pulse-and-bar test signal distorted in passing through an FM television system. The simulator includes flat or preemphasized systems and requires specification of the RF predetection filter characteristics. The predetection filters are modeled with frequency-symmetric Chebyshev (0.1-db ripple) and Butterworth filters. The computer was used to calculate distorted output signals for sixty-four different specified systems, and the output waveforms are plotted for all sixty-four. Comparison of the plotted graphs indicates that a Chebyshev predetection filter of four poles causes slightly more signal distortion than a corresponding Butterworth filter and the signal distortion increases as the number of poles increases. An increase in the peak deviation also increases signal distortion. Distortion also increases with the addition of preemphasis.

Finite length Taylor Couette flow

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

Deterministic analysis of extrinsic and intrinsic noise in an epidemiological model.

PubMed

Bayati, Basil S

2016-05-01

We couple a stochastic collocation method with an analytical expansion of the canonical epidemiological master equation to analyze the effects of both extrinsic and intrinsic noise. It is shown that depending on the distribution of the extrinsic noise, the master equation yields quantitatively different results compared to using the expectation of the distribution for the stochastic parameter. This difference is incident to the nonlinear terms in the master equation, and we show that the deviation away from the expectation of the extrinsic noise scales nonlinearly with the variance of the distribution. The method presented here converges linearly with respect to the number of particles in the system and exponentially with respect to the order of the polynomials used in the stochastic collocation calculation. This makes the method presented here more accurate than standard Monte Carlo methods, which suffer from slow, nonmonotonic convergence. In epidemiological terms, the results show that extrinsic fluctuations should be taken into account since they effect the speed of disease breakouts and that the gamma distribution should be used to model the basic reproductive number.

A Probabilistic Collocation Based Iterative Kalman Filter for Landfill Data Assimilation

NASA Astrophysics Data System (ADS)

Qiang, Z.; Zeng, L.; Wu, L.

2016-12-01

Due to the strong spatial heterogeneity of landfill, uncertainty is ubiquitous in gas transport process in landfill. To accurately characterize the landfill properties, the ensemble Kalman filter (EnKF) has been employed to assimilate the measurements, e.g., the gas pressure. As a Monte Carlo (MC) based method, the EnKF usually requires a large ensemble size, which poses a high computational cost for large scale problems. In this work, we propose a probabilistic collocation based iterative Kalman filter (PCIKF) to estimate permeability in a liquid-gas coupling model. This method employs polynomial chaos expansion (PCE) to represent and propagate the uncertainties of model parameters and states, and an iterative form of Kalman filter to assimilate the current gas pressure data. To further reduce the computation cost, the functional ANOVA (analysis of variance) decomposition is conducted, and only the first order ANOVA components are remained for PCE. Illustrated with numerical case studies, this proposed method shows significant superiority in computation efficiency compared with the traditional MC based iterative EnKF. The developed method has promising potential in reliable prediction and management of landfill gas production.

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

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

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

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

Leapfrog variants of iterative methods for linear algebra equations

NASA Technical Reports Server (NTRS)

Saylor, Paul E.

1988-01-01

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

NASA Astrophysics Data System (ADS)

Izaac, Josh A.; Wang, Jingbo B.

2015-01-01

In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

DOE PAGES

Isotalo, Aarno E.; Wieselquist, William A.

2015-05-15

A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Lastly, in most cases, the new solver is upmore » to several times faster due to not requiring similar substepping as the original one.« less

Martian resource locations: Identification and optimization

NASA Astrophysics Data System (ADS)

Chamitoff, Gregory; James, George; Barker, Donald; Dershowitz, Adam

2005-04-01

The identification and utilization of in situ Martian natural resources is the key to enable cost-effective long-duration missions and permanent human settlements on Mars. This paper presents a powerful software tool for analyzing Martian data from all sources, and for optimizing mission site selection based on resource collocation. This program, called Planetary Resource Optimization and Mapping Tool (PROMT), 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. Preliminary optimization results are shown for a number of mission scenarios.

[A particular anthropometric method for the study of accessibility of a workstation].

PubMed

Molinaro, V; Del Ferraro, S

2008-01-01

One of the main factors which can involve musculo-skeletal disorders is the assumption of awkward postures. These lasts can be caused, in some cases, by a no-suitable collocation of some devices which are indispensable for the work. It is possible to evaluate if the chosen collocation is adequate or not by studying the accessibility of the workstation with a special regard for the accessibility of the devices placed inside the workstation. EN ISO 14738:2002 is a specific standard which has been adopted in Italy as UNI EN ISO 14738:2004. This standard gives some useful requirements, in terms of accessibility, to design a workstation at no-mobile machinery. In this study, the authors have analyzed a check out workstation by following the requirements described in UNI EN ISO 14738:2004. Critical aspects, related to the organization both of the work activities either of the workstation, have been highlighted taking into account standard criteria. Finally the authors make a new design of the check out workstation trying to optimize device collocation in order to reduce awkward postures. The new configuration has been investigated by applying the criteria mentioned in the standard.

Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Direct Numerical Simulation of Turbulent Flow Over Complex Bathymetry

NASA Astrophysics Data System (ADS)

Yue, L.; Hsu, T. J.

2017-12-01

Direct numerical simulation (DNS) is regarded as a powerful tool in the investigation of turbulent flow featured with a wide range of time and spatial scales. With the application of coordinate transformation in a pseudo-spectral scheme, a parallelized numerical modeling system was created aiming at simulating flow over complex bathymetry with high numerical accuracy and efficiency. The transformed governing equations were integrated in time using a third-order low-storage Runge-Kutta method. For spatial discretization, the discrete Fourier expansion was adopted in the streamwise and spanwise direction, enforcing the periodic boundary condition in both directions. The Chebyshev expansion on Chebyshev-Gauss-Lobatto points was used in the wall-normal direction, assuming there is no-slip on top and bottom walls. The diffusion terms were discretized with a Crank-Nicolson scheme, while the advection terms dealiased with the 2/3 rule were discretized with an Adams-Bashforth scheme. In the prediction step, the velocity was calculated in physical domain by solving the resulting linear equation directly. However, the extra terms introduced by coordinate transformation impose a strict limitation to time step and an iteration method was applied to overcome this restriction in the correction step for pressure by solving the Helmholtz equation. The numerical solver is written in object-oriented C++ programing language utilizing Armadillo linear algebra library for matrix computation. Several benchmarking cases in laminar and turbulent flow were carried out to verify/validate the numerical model and very good agreements are achieved. Ongoing work focuses on implementing sediment transport capability for multiple sediment classes and parameterizations for flocculation processes.

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

DOE PAGES

Banerjee, Amartya S.; Lin, Lin; Hu, Wei; ...

2016-10-21

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) canmore » be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.« less

Stability of streamwise vortices

NASA Technical Reports Server (NTRS)

Khorrami, M. K.; Grosch, C. E.; Ash, R. L.

1987-01-01

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

47 CFR 51.501 - Scope.

Code of Federal Regulations, 2010 CFR

2010-10-01

... FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Pricing of Elements § 51.501 Scope. (a) The rules in this subpart apply to the pricing of network elements, interconnection, and methods of obtaining access to unbundled elements, including physical collocation and virtual...

Performance of FFT methods in local gravity field modelling

NASA Technical Reports Server (NTRS)

Forsberg, Rene; Solheim, Dag

1989-01-01

Fast Fourier transform (FFT) methods provide a fast and efficient means of processing large amounts of gravity or geoid data in local gravity field modelling. The FFT methods, however, has a number of theoretical and practical limitations, especially the use of flat-earth approximation, and the requirements for gridded data. In spite of this the method often yields excellent results in practice when compared to other more rigorous (and computationally expensive) methods, such as least-squares collocation. The good performance of the FFT methods illustrate that the theoretical approximations are offset by the capability of taking into account more data in larger areas, especially important for geoid predictions. For best results good data gridding algorithms are essential. In practice truncated collocation approaches may be used. For large areas at high latitudes the gridding must be done using suitable map projections such as UTM, to avoid trivial errors caused by the meridian convergence. The FFT methods are compared to ground truth data in New Mexico (xi, eta from delta g), Scandinavia (N from delta g, the geoid fits to 15 cm over 2000 km), and areas of the Atlantic (delta g from satellite altimetry using Wiener filtering). In all cases the FFT methods yields results comparable or superior to other methods.

Spectral methods in time for a class of parabolic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ierley, G.; Spencer, B.; Worthing, R.

1992-09-01

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time.more » 14 refs., 9 figs.« less

A review of spectral methods

NASA Technical Reports Server (NTRS)

Lustman, L.

1984-01-01

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

Orbit and uncertainty propagation: a comparison of Gauss-Legendre-, Dormand-Prince-, and Chebyshev-Picard-based approaches

NASA Astrophysics Data System (ADS)

Aristoff, Jeffrey M.; Horwood, Joshua T.; Poore, Aubrey B.

2014-01-01

We present a new variable-step Gauss-Legendre implicit-Runge-Kutta-based approach for orbit and uncertainty propagation, VGL-IRK, which includes adaptive step-size error control and which collectively, rather than individually, propagates nearby sigma points or states. The performance of VGL-IRK is compared to a professional (variable-step) implementation of Dormand-Prince 8(7) (DP8) and to a fixed-step, optimally-tuned, implementation of modified Chebyshev-Picard iteration (MCPI). Both nearly-circular and highly-elliptic orbits are considered using high-fidelity gravity models and realistic integration tolerances. VGL-IRK is shown to be up to eleven times faster than DP8 and up to 45 times faster than MCPI (for the same accuracy), in a serial computing environment. Parallelization of VGL-IRK and MCPI is also discussed.

Polynomial Chaos Based Acoustic Uncertainty Predictions from Ocean Forecast Ensembles

NASA Astrophysics Data System (ADS)

Dennis, S.

2016-02-01

Most significant ocean acoustic propagation occurs at tens of kilometers, at scales small compared basin and to most fine scale ocean modeling. To address the increased emphasis on uncertainty quantification, for example transmission loss (TL) probability density functions (PDF) within some radius, a polynomial chaos (PC) based method is utilized. In order to capture uncertainty in ocean modeling, Navy Coastal Ocean Model (NCOM) now includes ensembles distributed to reflect the ocean analysis statistics. Since the ensembles are included in the data assimilation for the new forecast ensembles, the acoustic modeling uses the ensemble predictions in a similar fashion for creating sound speed distribution over an acoustically relevant domain. Within an acoustic domain, singular value decomposition over the combined time-space structure of the sound speeds can be used to create Karhunen-Loève expansions of sound speed, subject to multivariate normality testing. These sound speed expansions serve as a basis for Hermite polynomial chaos expansions of derived quantities, in particular TL. The PC expansion coefficients result from so-called non-intrusive methods, involving evaluation of TL at multi-dimensional Gauss-Hermite quadrature collocation points. Traditional TL calculation from standard acoustic propagation modeling could be prohibitively time consuming at all multi-dimensional collocation points. This method employs Smolyak order and gridding methods to allow adaptive sub-sampling of the collocation points to determine only the most significant PC expansion coefficients to within a preset tolerance. Practically, the Smolyak order and grid sizes grow only polynomially in the number of Karhunen-Loève terms, alleviating the curse of dimensionality. The resulting TL PC coefficients allow the determination of TL PDF normality and its mean and standard deviation. In the non-normal case, PC Monte Carlo methods are used to rapidly establish the PDF. This work was sponsored by the Office of Naval Research

Revision of IRIS/IDA Seismic Station Metadata

NASA Astrophysics Data System (ADS)

Xu, W.; Davis, P.; Auerbach, D.; Klimczak, E.

2017-12-01

Trustworthy data quality assurance has always been one of the goals of seismic network operators and data management centers. This task is considerably complex and evolving due to the huge quantities as well as the rapidly changing characteristics and complexities of seismic data. Published metadata usually reflect instrument response characteristics and their accuracies, which includes zero frequency sensitivity for both seismometer and data logger as well as other, frequency-dependent elements. In this work, we are mainly focused studying the variation of the seismometer sensitivity with time of IRIS/IDA seismic recording systems with a goal to improve the metadata accuracy for the history of the network. There are several ways to measure the accuracy of seismometer sensitivity for the seismic stations in service. An effective practice recently developed is to collocate a reference seismometer in proximity to verify the in-situ sensors' calibration. For those stations with a secondary broadband seismometer, IRIS' MUSTANG metric computation system introduced a transfer function metric to reflect two sensors' gain ratios in the microseism frequency band. In addition, a simulation approach based on M2 tidal measurements has been proposed and proven to be effective. In this work, we compare and analyze the results from three different methods, and concluded that the collocated-sensor method is most stable and reliable with the minimum uncertainties all the time. However, for epochs without both the collocated sensor and secondary seismometer, we rely on the analysis results from tide method. For the data since 1992 on IDA stations, we computed over 600 revised seismometer sensitivities for all the IRIS/IDA network calibration epochs. Hopefully further revision procedures will help to guarantee that the data is accurately reflected by the metadata of these stations.

Study of the footprints of short-term variation in XCO2 observed by TCCON sites using NIES and FLEXPART atmospheric transport models

NASA Astrophysics Data System (ADS)

Belikov, Dmitry A.; Maksyutov, Shamil; Ganshin, Alexander; Zhuravlev, Ruslan; Deutscher, Nicholas M.; Wunch, Debra; Feist, Dietrich G.; Morino, Isamu; Parker, Robert J.; Strong, Kimberly; Yoshida, Yukio; Bril, Andrey; Oshchepkov, Sergey; Boesch, Hartmut; Dubey, Manvendra K.; Griffith, David; Hewson, Will; Kivi, Rigel; Mendonca, Joseph; Notholt, Justus; Schneider, Matthias; Sussmann, Ralf; Velazco, Voltaire A.; Aoki, Shuji

2017-01-01

The Total Carbon Column Observing Network (TCCON) is a network of ground-based Fourier transform spectrometers (FTSs) that record near-infrared (NIR) spectra of the sun. From these spectra, accurate and precise observations of CO2 column-averaged dry-air mole fractions (denoted XCO2) are retrieved. TCCON FTS observations have previously been used to validate satellite estimations of XCO2; however, our knowledge of the short-term spatial and temporal variations in XCO2 surrounding the TCCON sites is limited. In this work, we use the National Institute for Environmental Studies (NIES) Eulerian three-dimensional transport model and the FLEXPART (FLEXible PARTicle dispersion model) Lagrangian particle dispersion model (LPDM) to determine the footprints of short-term variations in XCO2 observed by operational, past, future and possible TCCON sites. We propose a footprint-based method for the collocation of satellite and TCCON XCO2 observations and estimate the performance of the method using the NIES model and five GOSAT (Greenhouse Gases Observing Satellite) XCO2 product data sets. Comparison of the proposed approach with a standard geographic method shows a higher number of collocation points and an average bias reduction up to 0.15 ppm for a subset of 16 stations for the period from January 2010 to January 2014. Case studies of the Darwin and Reunion Island sites reveal that when the footprint area is rather curved, non-uniform and significantly different from a geographical rectangular area, the differences between these approaches are more noticeable. This emphasises that the collocation is sensitive to local meteorological conditions and flux distributions.

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation.

PubMed

Lin, Yi-Chung; Pandy, Marcus G

2017-07-05

The aim of this study was to perform full-body three-dimensional (3D) dynamic optimization simulations of human locomotion by driving a neuromusculoskeletal model toward in vivo measurements of body-segmental kinematics and ground reaction forces. Gait data were recorded from 5 healthy participants who walked at their preferred speeds and ran at 2m/s. Participant-specific data-tracking dynamic optimization solutions were generated for one stride cycle using direct collocation in tandem with an OpenSim-MATLAB interface. The body was represented as a 12-segment, 21-degree-of-freedom skeleton actuated by 66 muscle-tendon units. Foot-ground interaction was simulated using six contact spheres under each foot. The dynamic optimization problem was to find the set of muscle excitations needed to reproduce 3D measurements of body-segmental motions and ground reaction forces while minimizing the time integral of muscle activations squared. Direct collocation took on average 2.7±1.0h and 2.2±1.6h of CPU time, respectively, to solve the optimization problems for walking and running. Model-computed kinematics and foot-ground forces were in good agreement with corresponding experimental data while the calculated muscle excitation patterns were consistent with measured EMG activity. The results demonstrate the feasibility of implementing direct collocation on a detailed neuromusculoskeletal model with foot-ground contact to accurately and efficiently generate 3D data-tracking dynamic optimization simulations of human locomotion. The proposed method offers a viable tool for creating feasible initial guesses needed to perform predictive simulations of movement using dynamic optimization theory. The source code for implementing the model and computational algorithm may be downloaded at http://simtk.org/home/datatracking. Copyright © 2017 Elsevier Ltd. All rights reserved.

Intercomparison of an Aerosol Chemical Speciation Monitor (ACSM) with ambient fine aerosol measurements in downtown Atlanta, Georgia

NASA Astrophysics Data System (ADS)

Budisulistiorini, S. H.; Canagaratna, M. R.; Croteau, P. L.; Baumann, K.; Edgerton, E. S.; Kollman, M. S.; Ng, N. L.; Verma, V.; Shaw, S. L.; Knipping, E. M.; Worsnop, D. R.; Jayne, J. T.; Weber, R. J.; Surratt, J. D.

2014-07-01

Currently, there are a limited number of field studies that evaluate the long-term performance of the Aerodyne Aerosol Chemical Speciation Monitor (ACSM) against established monitoring networks. In this study, we present seasonal intercomparisons of the ACSM with collocated fine aerosol (PM2.5) measurements at the Southeastern Aerosol Research and Characterization (SEARCH) Jefferson Street (JST) site near downtown Atlanta, GA, during 2011-2012. Intercomparison of two collocated ACSMs resulted in strong correlations (r2 > 0.8) for all chemical species, except chloride (r2 = 0.21) indicating that ACSM instruments are capable of stable and reproducible operation. In general, speciated ACSM mass concentrations correlate well (r2 > 0.7) with the filter-adjusted continuous measurements from JST, although the correlation for nitrate is weaker (r2 = 0.55) in summer. Correlations of the ACSM NR-PM1 (non-refractory particulate matter with aerodynamic diameter less than or equal to 1 μm) plus elemental carbon (EC) with tapered element oscillating microbalance (TEOM) PM2.5 and Federal Reference Method (FRM) PM1 mass are strong with r2 > 0.7 and r2 > 0.8, respectively. Discrepancies might be attributed to evaporative losses of semi-volatile species from the filter measurements used to adjust the collocated continuous measurements. This suggests that adjusting the ambient aerosol continuous measurements with results from filter analysis introduced additional bias to the measurements. We also recommend to calibrate the ambient aerosol monitoring instruments using aerosol standards rather than gas-phase standards. The fitting approach for ACSM relative ionization for sulfate was shown to improve the comparisons between ACSM and collocated measurements in the absence of calibrated values, suggesting the importance of adding sulfate calibration into the ACSM calibration routine.

The precision of wet atmospheric deposition data from national atmospheric deposition program/national trends network sites determined with collocated samplers

USGS Publications Warehouse

Nilles, M.A.; Gordon, J.D.; Schroder, L.J.

1994-01-01

A collocated, wet-deposition sampler program has been operated since October 1988 by the U.S. Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments at four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database. Sampling precision was determined from the absolute value of differences in the analytical results for the paired samples in terms of median relative and absolute difference. The median relative difference for Mg2+, Na+, K+ and NH4+ concentration and deposition was quite variable between sites and exceeded 10% at most sites. Relative error for analytes whose concentrations typically approached laboratory method detection limits were greater than for analytes that did not typically approach detection limits. The median relative difference for SO42- and NO3- concentration, specific conductance, and sample volume at all sites was less than 7%. Precision for H+ concentration and deposition ranged from less than 10% at sites with typically high levels of H+ concentration to greater than 30% at sites with low H+ concentration. Median difference for analyte concentration and deposition was typically 1.5-2-times greater for samples collected during the winter than during other seasons at two northern sites. Likewise, the median relative difference in sample volume for winter samples was more than double the annual median relative difference at the two northern sites. Bias accounted for less than 25% of the collocated variability in analyte concentration and deposition from weekly collocated precipitation samples at most sites.A collocated, wet-deposition sampler program has been operated since OCtober 1988 by the U.S Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database.

Extracting Useful Semantic Information from Large Scale Corpora of Text

ERIC Educational Resources Information Center

Mendoza, Ray Padilla, Jr.

2012-01-01

Extracting and representing semantic information from large scale corpora is at the crux of computer-assisted knowledge generation. Semantic information depends on collocation extraction methods, mathematical models used to represent distributional information, and weighting functions which transform the space. This dissertation provides a…

Triple collocation based merging of satellite soil moisture retrievals

USDA-ARS?s Scientific Manuscript database

We propose a method for merging soil moisture retrievals from space borne active and passive microwave instruments based on weighted averaging taking into account the error characteristics of the individual data sets. The merging scheme is parameterized using error variance estimates obtained from u...

A mass-conserving mixed Fourier-Galerkin B-Spline-collocation method for Direct Numerical Simulation of the variable-density Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Reuter, Bryan; Oliver, Todd; Lee, M. K.; Moser, Robert

2017-11-01

We present an algorithm for a Direct Numerical Simulation of the variable-density Navier-Stokes equations based on the velocity-vorticity approach introduced by Kim, Moin, and Moser (1987). In the current work, a Helmholtz decomposition of the momentum is performed. Evolution equations for the curl and the Laplacian of the divergence-free portion are formulated by manipulation of the momentum equations and the curl-free portion is reconstructed by enforcing continuity. The solution is expanded in Fourier bases in the homogeneous directions and B-Spline bases in the inhomogeneous directions. Discrete equations are obtained through a mixed Fourier-Galerkin and collocation weighted residual method. The scheme is designed such that the numerical solution conserves mass locally and globally by ensuring the discrete divergence projection is exact through the use of higher order splines in the inhomogeneous directions. The formulation is tested on multiple variable-density flow problems.

Nonparametric triple collocation

USDA-ARS?s Scientific Manuscript database

Triple collocation derives variance-covariance relationships between three or more independent measurement sources and an indirectly observed truth variable in the case where the measurement operators are linear-Gaussian. We generalize that theory to arbitrary observation operators by deriving nonpa...

Error analysis for spectral approximation of the Korteweg-De Vries equation

NASA Technical Reports Server (NTRS)

Maday, Y.; recent years.

1987-01-01

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

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

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

NASA Astrophysics Data System (ADS)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

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

Glucose control and medication adherence among veterans with diabetes and serious mental illness: does collocation of primary care and mental health care matter?

PubMed

Long, Judith A; Wang, Andrew; Medvedeva, Elina L; Eisen, Susan V; Gordon, Adam J; Kreyenbuhl, Julie; Marcus, Steven C

2014-08-01

Persons with serious mental illness (SMI) may benefit from collocation of medical and mental health healthcare professionals and services in attending to their chronic comorbid medical conditions. We evaluated and compared glucose control and diabetes medication adherence among patients with SMI who received collocated care to those not receiving collocated care (which we call usual care). We performed a cross-sectional, observational cohort study of 363 veteran patients with type 2 diabetes and SMI who received care from one of three Veterans Affairs medical facilities: two sites that provided both collocated and usual care and one site that provided only usual care. Through a survey, laboratory tests, and medical records, we assessed patient characteristics, glucose control as measured by a current HbA1c, and adherence to diabetes medication as measured by the medication possession ration (MPR) and self-report. In the sample, the mean HbA1c was 7.4% (57 mmol/mol), the mean MPR was 80%, and 51% reported perfect adherence to their diabetes medications. In both unadjusted and adjusted analyses, there were no differences in glucose control and medication adherence by collocation of care. Patients seen in collocated care tended to have better HbA1c levels (β = -0.149; P = 0.393) and MPR values (β = 0.34; P = 0.132) and worse self-reported adherence (odds ratio 0.71; P = 0.143), but these were not statistically significant. In a population of veterans with comorbid diabetes and SMI, patients on average had good glucose control and medication adherence regardless of where they received primary care. © 2014 by the American Diabetes Association. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered.

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Data assimilation for unsaturated flow models with restart adaptive probabilistic collocation based Kalman filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Man, Jun; Li, Weixuan; Zeng, Lingzao

2016-06-01

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

On the Stability of Collocated Controllers in the Presence or Uncertain Nonlinearities and Other Perils

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1985-01-01

Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Optimal control and Galois theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zelikin, M I; Kiselev, D D; Lokutsievskiy, L V

2013-11-30

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems ofmore » Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.« less

Numerical Analysis of Modeling Based on Improved Elman Neural Network

PubMed Central

Jie, Shao

2014-01-01

A modeling based on the improved Elman neural network (IENN) is proposed to analyze the nonlinear circuits with the memory effect. The hidden layer neurons are activated by a group of Chebyshev orthogonal basis functions instead of sigmoid functions in this model. The error curves of the sum of squared error (SSE) varying with the number of hidden neurons and the iteration step are studied to determine the number of the hidden layer neurons. Simulation results of the half-bridge class-D power amplifier (CDPA) with two-tone signal and broadband signals as input have shown that the proposed behavioral modeling can reconstruct the system of CDPAs accurately and depict the memory effect of CDPAs well. Compared with Volterra-Laguerre (VL) model, Chebyshev neural network (CNN) model, and basic Elman neural network (BENN) model, the proposed model has better performance. PMID:25054172

LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

PubMed Central

Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

2014-01-01

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

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

USGS Publications Warehouse

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

2013-01-01

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

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Gray, Justin S.; Naylor, Bret

2016-01-01

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

NASA Astrophysics Data System (ADS)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Performance Evaluation and Community Application of Low-Cost Sensors for Ozone and Nitrogen Dioxide

EPA Science Inventory

This study reports on the performance of electrochemical-based low-cost sensors and their use in a community application. CairClip sensors were collocated with federal reference and equivalent methods and operated in a network of sites by citizen scientists (community members) in...

Multi-fidelity stochastic collocation method for computation of statistical moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu; Linebarger, Erin M., E-mail: aerinline@sci.utah.edu; Xiu, Dongbin, E-mail: xiu.16@osu.edu

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

On the anomaly of velocity-pressure decoupling in collocated mesh solutions

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Vanoverbeke, Thomas

1991-01-01

The use of various pressure correction algorithms originally developed for fully staggered meshes can yield a velocity-pressure decoupled solution for collocated meshes. The mechanism that causes velocity-pressure decoupling is identified. It is shown that the use of a partial differential equation for the incremental pressure eliminates such a mechanism and yields a velocity-pressure coupled solution. Example flows considered are a three dimensional lid-driven cavity flow and a laminar flow through a 90 deg bend square duct. Numerical results obtained using the collocated mesh are in good agreement with the measured data and other numerical results.

Computational Electromagnetics Application to Small Geometric Anomalies and Associated Ucertainty Evaluation

DTIC Science & Technology

2010-02-28

implemented a fast method to enable the statistical characterization of electromagnetic interference and compatibility (EMI/EMC) phenomena on electrically...higher accuracy is needed, e.g., to compute higher moment statistics . To address this problem, we have developed adaptive stochastic collocation methods ...SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AF OFFICE OF SCIENTIFIC RESEARCH 875 N. RANDOLPH ST. ROOM 3112 ARLINGTON VA 22203 UA

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

PubMed

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

2012-07-01

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

Beyond triple collocation: Applications to satellite soil moisture

USDA-ARS?s Scientific Manuscript database

Triple collocation is now routinely used to resolve the exact (linear) relationships between multiple measurements and/or representations of a geophysical variable that are subject to errors. It has been utilized in the context of calibration, rescaling and error characterisation to allow comparison...

Evaluating Remotely-Sensed Surface Soil Moisture Estimates Using Triple Collocation

USDA-ARS?s Scientific Manuscript database

Recent work has demonstrated the potential of enhancing remotely-sensed surface soil moisture validation activities through the application of triple collocation techniques which compare time series of three mutually independent geophysical variable estimates in order to acquire the root-mean-square...

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

USGS Publications Warehouse

Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P and S waves. ?? 2011 Elsevier Ltd.

Discretization of the induced-charge boundary integral equation.

PubMed

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

2009-07-01

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

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Discretization of the induced-charge boundary integral equation

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Parallel/Vector Integration Methods for Dynamical Astronomy

NASA Astrophysics Data System (ADS)

Fukushima, T.

Progress of parallel/vector computers has driven us to develop suitable numerical integrators utilizing their computational power to the full extent while being independent on the size of system to be integrated. Unfortunately, the parallel version of Runge-Kutta type integrators are known to be not so efficient. Recently we developed a parallel version of the extrapolation method (Ito and Fukushima 1997), which allows variable timesteps and still gives an acceleration factor of 3-4 for general problems. While the vector-mode usage of Picard-Chebyshev method (Fukushima 1997a, 1997b) will lead the acceleration factor of order of 1000 for smooth problems such as planetary/satellites orbit integration. The success of multiple-correction PECE mode of time-symmetric implicit Hermitian integrator (Kokubo 1998) seems to enlighten Milankar's so-called "pipelined predictor corrector method", which is expected to lead an acceleration factor of 3-4. We will review these directions and discuss future prospects.

A Comparative Usage-Based Approach to the Reduction of the Spanish and Portuguese Preposition "Para"

ERIC Educational Resources Information Center

Gradoville, Michael Stephen

2013-01-01

This study examines the frequency effect of two-word collocations involving "para" "to," "for" (e.g. "fui para," "para que") on the reduction of "para" to "pa" (in Spanish) and "pra" (in Portuguese). Collocation frequency effects demonstrate that language speakers…

On pseudo-spectral time discretizations in summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Nordström, Jan

2018-05-01

Fully-implicit discrete formulations in summation-by-parts form for initial-boundary value problems must be invertible in order to provide well functioning procedures. We prove that, under mild assumptions, pseudo-spectral collocation methods for the time derivative lead to invertible discrete systems when energy-stable spatial discretizations are used.

Advances in Time and Frequency Transfer From Dual-Frequency GPS Pseudorange and Carrier-Phase Observations

DTIC Science & Technology

2008-12-01

collocated independent time transfer techniques such as Two-Way Satellite Time and Frequency Transfer ( TWSTFT ) [10,11]. The issue of pseudorange errors...transfer methods, e.g. TWSTFT . There is a side benefit that far exceeds just meeting the objective we have set. The new model explicitly reveals, on

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

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Parallel adaptive wavelet collocation method for PDEs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nejadmalayeri, Alireza, E-mail: Alireza.Nejadmalayeri@gmail.com; Vezolainen, Alexei, E-mail: Alexei.Vezolainen@Colorado.edu; Brown-Dymkoski, Eric, E-mail: Eric.Browndymkoski@Colorado.edu

2015-10-01

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allowsmore » fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.« less

Three-dimensional seismic depth migration

NASA Astrophysics Data System (ADS)

Zhou, Hongbo

1998-12-01

One-pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45sp° one-way wave equation (a third-order partial differential equation) with a pair of second and first order partial differential equations. Except for an extra correction term, the resulting second order equation has a form similar to Claerbout's 15sp° one-way wave equation, which is known to have a nearly circular horizontal impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second-order in accuracy and economical to solve. A modification of the Crank-Nicholson implementation maintains stability. Absorbing boundary conditions play an important role in one-way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist's 2-D absorbing boundary conditions for one-way wave extrapolation by depth-stepping in the frequency domain are extended to 3-D using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45sp° one-way wave equation. Frequency-space domain Butterworth and Chebyshev dip filters are implemented. By regrouping the product terms in the filter transfer function into summations, a cascaded (serial) Butterworth dip filter can be made parallel. A parallel Chebyshev dip filter can be similarly obtained, and has the same form as the Butterworth filter; but has different coeffcients. One of the advantages of the Chebyshev filter is that it has a sharper transition zone than that of Butterworth filter of the same order. Both filters are incorporated into 3-D one-way frequency-space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals. Synthetic examples illustrate the behavior of the parallel filters. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. A Chebyshev filter is more effective for phase compensation than the Butterworth filter of the same order, at the expense of some wavenumber-dependent amplitude ripples. An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis. Under this expression, geometrical spreading can be determined only by the anisotropic parameters in the first layer, the traveltime derivatives, and source-receiver offset. An explicit, numerically feasible expression for geometrical spreading can be further obtained by considering some of the special cases of transverse isotropy, such as weak anisotropy or elliptic anisotropy. Therefore, with the techniques of non-hyerbolic moveout for transverse isotropic media, geometrical spreading can be calculated by using picked traveltimes of primary P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading.

On the coefficients of differentiated expansions of ultraspherical polynomials

NASA Technical Reports Server (NTRS)

Karageorghis, Andreas; Phillips, Timothy N.

1989-01-01

A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

[On-orbit radiometric calibration accuracy of FY-3A MERSI thermal infrared channel].

PubMed

Xu, Na; Hu, Xiu-qing; Chen, Lin; Zhang, Yong; Hu, Ju-yang; Sun, Ling

2014-12-01

Accurate satellite radiance measurements are significant for data assimilations and quantitative retrieval applications. In the present paper, radiometric calibration accuracy of FungYun-3A (FY-3A) Medium Resolution Spectral Imager (MERSI) thermal infrared (TIR) channel was evaluated based on simultaneous nadir observation (SNO) intercalibration method. Hyperspectral and high-quality measurements of METOP-A/IASI were used as reference. Assessment uncertainty from intercalibration method was also investigated by examining the relation between BT bias against four main collocation factors, i. e. observation time difference, view geometric difference related to zenith angles and azimuth angles, and scene spatial homogeneity. It was indicated that the BT bias is evenly distributed across the collocation variables with no significant linear relationship in MERSI IR channel. Among the four collocation factors, the scene spatial homogeneity may be the most important factor with the uncertainty less than 2% of BT bias. Statistical analysis of monitoring biases during one and a half years indicates that the brightness temperature measured by MERSI is much warmer than that of IASI. The annual mean bias (MERSI-IASI) in 2012 is (3.18±0.34) K. Monthly averaged BT biases show a little seasonal variation character, and fluctuation range is less than 0.8 K. To further verify the reliability, our evaluation result was also compared with the synchronous experiment results at Dunhuang and Qinghai Lake sites, which showed excellent agreement. Preliminary analysis indicates that there are two reasons leading to the warm bias. One is the overestimation of blackbody emissivity, and the other is probably the incorrect spectral respond function which has shifted to window spectral. Considering the variation character of BT biases, SRF error seems to be the dominant factor.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Reports 10, The Yugoslav Serbo-Croatian-English Contrastive Project.

ERIC Educational Resources Information Center

Filipovic, Rudolf

The tenth volume in this series contains five articles dealing with various aspects of Serbo-Croatian-English contrastive analysis. They are: "The Infinitive as Subject in English and Serbo-Croatian," by Ljiljana Bibovic; "The Contrastive Analysis of Collocations: Collocational Ranges of "Make" and "Take" with Nouns and Their Serbo-Croatian…

No Silver Bullet: L2 Collocation Instruction in an Advanced Spanish Classroom

ERIC Educational Resources Information Center

Jensen, Eric Carl

2017-01-01

Many contemporary second language (L2) instructional materials feature collocation exercises; however, few studies have verified their effectiveness (Boers, Demecheleer, Coxhead, & Webb, 2014) or whether these exercises can be utilized for target languages beyond English (Higueras García, 2017). This study addresses these issues by…

Assessing Team Learning in Technology-Mediated Collaboration: An Experimental Study

ERIC Educational Resources Information Center

Andres, Hayward P.; Akan, Obasi H.

2010-01-01

This study examined the effects of collaboration mode (collocated versus non-collocated videoconferencing-mediated) on team learning and team interaction quality in a team-based problem solving context. Situated learning theory and the theory of affordances are used to provide a framework that describes how technology-mediated collaboration…

Collocation in Regional Development--The Peel Education and TAFE Response.

ERIC Educational Resources Information Center

Goff, Malcolm H.; Nevard, Jennifer

The collocation of services in regional Western Australia (WA) is an important strand of WA's regional development policy. The initiative is intended to foster working relationships among stakeholder groups with a view toward ensuring that regional WA communities have access to quality services. Clustering compatible services in smaller…

Interlanguage Development and Collocational Clash

ERIC Educational Resources Information Center

Shahheidaripour, Gholamabbass

2000-01-01

Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate…

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

Code of Federal Regulations, 2012 CFR

2012-10-01

... unbundled network element if and only if the primary purpose and function of the equipment, as the... nondiscriminatory access to that unbundled network element, including any of its features, functions, or... must be a logical nexus between the additional functions the equipment would perform and the...

Testing ESL Learners' Knowledge of Collocations.

ERIC Educational Resources Information Center

Bonk, William J.

This study reports on the development, administration, and analysis of a test of collocational knowledge for English-as-a-Second-Language (ESL) learners of a wide range of proficiency levels. Through native speaker item validation and pilot testing, three subtests were developed and administered to 98 ESL learners of low-intermediate to advanced…

Singularity Preserving Numerical Methods for Boundary Integral Equations

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki (Principal Investigator)

1996-01-01

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

An optimal filter for short photoplethysmogram signals

PubMed Central

Liang, Yongbo; Elgendi, Mohamed; Chen, Zhencheng; Ward, Rabab

2018-01-01

A photoplethysmogram (PPG) contains a wealth of cardiovascular system information, and with the development of wearable technology, it has become the basic technique for evaluating cardiovascular health and detecting diseases. However, due to the varying environments in which wearable devices are used and, consequently, their varying susceptibility to noise interference, effective processing of PPG signals is challenging. Thus, the aim of this study was to determine the optimal filter and filter order to be used for PPG signal processing to make the systolic and diastolic waves more salient in the filtered PPG signal using the skewness quality index. Nine types of filters with 10 different orders were used to filter 219 (2.1s) short PPG signals. The signals were divided into three categories by PPG experts according to their noise levels: excellent, acceptable, or unfit. Results show that the Chebyshev II filter can improve the PPG signal quality more effectively than other types of filters and that the optimal order for the Chebyshev II filter is the 4th order. PMID:29714722

Efficient characterization of phase space mapping in axially symmetric optical systems

NASA Astrophysics Data System (ADS)

Barbero, Sergio; Portilla, Javier

2018-01-01

Phase space mapping, typically between an object and image plane, characterizes an optical system within a geometrical optics framework. We propose a novel conceptual frame to characterize the phase mapping in axially symmetric optical systems for arbitrary object locations, not restricted to a specific object plane. The idea is based on decomposing the phase mapping into a set of bivariate equations corresponding to different values of the radial coordinate on a specific object surface (most likely the entrance pupil). These equations are then approximated through bivariate Chebyshev interpolation at Chebyshev nodes, which guarantees uniform convergence. Additionally, we propose the use of a new concept (effective object phase space), defined as the set of points of the phase space at the first optical element (typically the entrance pupil) that are effectively mapped onto the image surface. The effective object phase space provides, by means of an inclusion test, a way to avoid tracing rays that do not reach the image surface.

Collocational Processing in Light of the Phraseological Continuum Model: Does Semantic Transparency Matter?

ERIC Educational Resources Information Center

Gyllstad, Henrik; Wolter, Brent

2016-01-01

The present study investigates whether two types of word combinations (free combinations and collocations) differ in terms of processing by testing Howarth's Continuum Model based on word combination typologies from a phraseological tradition. A visual semantic judgment task was administered to advanced Swedish learners of English (n = 27) and…

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

Code of Federal Regulations, 2014 CFR

2014-10-01

... unbundled network elements. (1) Equipment is necessary for interconnection if an inability to deploy that... obtains within its own network or the incumbent provides to any affiliate, subsidiary, or other party. (2) Equipment is necessary for access to an unbundled network element if an inability to deploy that equipment...

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

Code of Federal Regulations, 2013 CFR

2013-10-01

... unbundled network elements. (1) Equipment is necessary for interconnection if an inability to deploy that... obtains within its own network or the incumbent provides to any affiliate, subsidiary, or other party. (2) Equipment is necessary for access to an unbundled network element if an inability to deploy that equipment...

Improving English Learners' Productive Collocation Knowledge: The Effects of Involvement Load, Spacing, and Intentionality

ERIC Educational Resources Information Center

Snoder, Per

2017-01-01

This article reports on a classroom-based experiment that tested the effects of three vocabulary teaching constructs (involvement load, spacing, and intentionality) on the learning of English verb-noun collocations--for example, "shelve a plan." Laufer and Hulstijn's (2001) "involvement load" predicts that the higher the…

Strategies in Translating Collocations in Religious Texts from Arabic into English

ERIC Educational Resources Information Center

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

2010-01-01

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

77 FR 60089 - Approval and Promulgation of Air Quality Implementation Plans; Delaware, New Jersey, and...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-02

... quarter substitution test. ``Collocated'' indicates that the collocated data was substituted for missing... 24-hour standard design value is greater than the level of the standard. EPA addresses missing data... substituted for the missing data. In the maximum quarter test, maximum recorded values are substituted for the...

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1994-01-01

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1994-01-01

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

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

USDA-ARS?s Scientific Manuscript database

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

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

ERIC Educational Resources Information Center

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

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…

Processing and Learning of Enhanced English Collocations: An Eye Movement Study

ERIC Educational Resources Information Center

Choi, Sungmook

2017-01-01

Research to date suggests that textual enhancement may positively affect the learning of multiword combinations known as collocations, but may impair recall of unenhanced text. However, the attentional mechanisms underlying such effects remain unclear. In this study, 38 undergraduate students were divided into two groups: one read a text…

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Eigenmodes of Multilayer Slit Structures

NASA Astrophysics Data System (ADS)

Kovalenko, A. N.

2017-12-01

We generalize the high-efficiency numerical-analytical method of calculating the eigenmodes of a microstrip line, which was proposed in [1], to multilayer slit structures. The obtained relationships make it possible to allow for the multilayer nature of the medium on the basis of solving the electrodynamic problem for a two-layer structure. The algebraic models of a single line and coupled slit lines in a multilayer dielectric medium are constructed. The matrix elements of the system of linear algebraic equations, which is used to determine the expansion coefficients of the electric field inside the slits in a Chebyshev basis, are converted to rapidly convergent series. The constructed models allow one to use computer simulation to obtain numerical results with high speed and accuracy, regardless of the number of dielectric layers. The presented results of a numerical study of the method convergence confirm high efficiency of the method.

Photoexcitation and ionization in carbon dioxide - Theoretical studies in the separated-channel static-exchange approximation

NASA Technical Reports Server (NTRS)

Padial, N.; Csanak, G.; Mckoy, B. V.; Langhoff, P. W.

1981-01-01

Vertical-electronic static-exchange photoexcitation and ionization cross sections are reported which provide a first approximation to the complete dipole spectrum of CO2. Separated-channel static-exchange calculations of vertical-electronic transition energies and oscillator strengths, and Stieltjes-Chebyshev moment methods were used in the development. Detailed comparisons were made of the static-exchange excitation and ionization spectra with photoabsorption, electron-impact excitation, and quantum-defect estimates of discrete transition energies and intensities, and with partial-channel photoionization cross sections obtained from fluorescence measurements and from tunable-source and (e, 2e) photoelectron spectroscopy. Results show that the separate-channel static-exchange approximation is generally satisfactory in CO2.

Factors Impacting Recognition of False Collo­cations by Speakers of English as L1 and L2

ERIC Educational Resources Information Center

Makinina, Olga

2017-01-01

Currently there is a general uncertainty about what makes collocations (i.e., fixed word combinations with specific, not easily interpreted relations between their components) hard for ESL learners to master, and about how to improve collocation recognition and learning process. This study explored and designed a comparative classification of…

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

ERIC Educational Resources Information Center

Nkemleke, Daniel

2009-01-01

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

Geostationary Collocation: Case Studies for Optimal Maneuvers

DTIC Science & Technology

2016-03-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release; distribution is unlimited GEOSTATIONARY ...DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE GEOSTATIONARY COLLOCATION: CASE STUDIES FOR OPTIMAL MANEUVERS 5. FUNDING NUMBERS 6...The geostationary belt is considered a natural resource, and as time goes by, the physical spaces for geostationary satellites will run out. The

The Effect of Critical Reading Strategies on EFL Learners' Recall and Retention of Collocations

ERIC Educational Resources Information Center

NematTabrizi, Amir Reza; Saber, Mehrnoush Akhavan

2016-01-01

The study was an attempt to measure the effect of critical reading strategies, namely; re-reading, questioning and annotating on recall and retention of collocations by intermediate Iranian EFL learners. To this end, Nelson proficiency test was administered to ninety (n = 90) Iranian EFL learners studying at Zaban Sara language institute in…

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

ERIC Educational Resources Information Center

Sadeghi, Karim

2009-01-01

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…

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

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

The dynamics and control of large flexible asymmetric spacecraft

NASA Astrophysics Data System (ADS)

Humphries, T. T.

1991-02-01

This thesis develops the equations of motion for a large flexible asymmetric Earth observation satellite and finds the characteristics of its motion under the influence of control forces. The mathematical model of the structure is produced using analytical methods. The equations of motion are formed using an expanded momentum technique which accounts for translational motion of the spacecraft hub and employs orthogonality relations between appendage and vehicle modes. The controllability and observability conditions of the full spacecraft motions using force and torque actuators are defined. A three axis reaction wheel control system is implemented for both slewing the spacecraft and controlling its resulting motions. From minor slew results it is shown that the lowest frequency elastic mode of the spacecraft is more important than higher frequency modes, when considering the effects of elastic motion on instrument pointing from the hub. Minor slews of the spacecraft configurations considered produce elastic deflections resulting in rotational attitude motions large enough to contravene pointing accuracy requirements of instruments aboard the spacecraft hub. Active vibration damping is required to reduce these hub motions to acceptable bounds in sufficiently small time. A comparison between hub mounted collocated and hub/appendage mounted non-collocated control systems verifies that provided the non-collocated system is stable, it can more effectively damp elastic modes whilst maintaining adequate damping of rigid modes. Analysis undertaken shows that the reaction wheel controller could be replaced by a thruster control system which decouples the modes of the spacecraft motion, enabling them to be individually damped.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Cubication of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

2009-01-01

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

PubMed

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

Mode 1 stress intensity factors for round compact specimens

NASA Technical Reports Server (NTRS)

Gross, B.

1976-01-01

The mode 1 stress intensity factors were computed for round compact specimens by the boundary collocation method. Results are presented for ratios A sub T/R sub 0 in the range 0.3 to 0.8, where A sub t is the distance from the specimen center to the crack tip for a specimen of diameter 2R sub 0.

Sketching Muslims: A Corpus Driven Analysis of Representations around the Word "Muslim" in the British Press 1998-2009

ERIC Educational Resources Information Center

Baker, Paul; Gabrielatos, Costas; McEnery, Tony

2013-01-01

This article uses methods from corpus linguistics and critical discourse analysis to examine patterns of representation around the word "Muslim" in a 143 million word corpus of British newspaper articles published between 1998 and 2009. Using the analysis tool Sketch Engine, an analysis of noun collocates of "Muslim" found that the following…

Impact of WhatsAPP on Learning and Retention of Collocation Knowledge among Iranian EFL Learners

ERIC Educational Resources Information Center

Ashiyan, Zahra; Salehi, Hadi

2016-01-01

During the recent technological years, language learning has been attempted to transform its path from the conventional methods to instrumental applications. Mobile phone provides people to reach and exchange information through chats (WhatsApp). It is a tool or mode that means the facilities are used for main purposes. The unique features of the…

Two-Dimensional DOA and Polarization Estimation for a Mixture of Uncorrelated and Coherent Sources with Sparsely-Distributed Vector Sensor Array

PubMed Central

Si, Weijian; Zhao, Pinjiao; Qu, Zhiyu

2016-01-01

This paper presents an L-shaped sparsely-distributed vector sensor (SD-VS) array with four different antenna compositions. With the proposed SD-VS array, a novel two-dimensional (2-D) direction of arrival (DOA) and polarization estimation method is proposed to handle the scenario where uncorrelated and coherent sources coexist. The uncorrelated and coherent sources are separated based on the moduli of the eigenvalues. For the uncorrelated sources, coarse estimates are acquired by extracting the DOA information embedded in the steering vectors from estimated array response matrix of the uncorrelated sources, and they serve as coarse references to disambiguate fine estimates with cyclical ambiguity obtained from the spatial phase factors. For the coherent sources, four Hankel matrices are constructed, with which the coherent sources are resolved in a similar way as for the uncorrelated sources. The proposed SD-VS array requires only two collocated antennas for each vector sensor, thus the mutual coupling effects across the collocated antennas are reduced greatly. Moreover, the inter-sensor spacings are allowed beyond a half-wavelength, which results in an extended array aperture. Simulation results demonstrate the effectiveness and favorable performance of the proposed method. PMID:27258271

Stretched Verb Collocations with "Give": Their Use and Translation into Spanish Using the BNC and CREA Corpora

ERIC Educational Resources Information Center

Molina-Plaza, Silvia; de Gregorio-Godeo, Eduardo

2010-01-01

Within the context of on-going research, this paper explores the pedagogical implications of contrastive analyses of multiword units in English and Spanish based on electronic corpora as a CALL resource. The main tenets of collocations from a contrastive perspective--and the points of contact and departure between both languages--are discussed…

Action Research: Applying a Bilingual Parallel Corpus Collocational Concordancer to Taiwanese Medical School EFL Academic Writing

ERIC Educational Resources Information Center

Reynolds, Barry Lee

2016-01-01

Lack of knowledge in the conventional usage of collocations in one's respective field of expertise cause Taiwanese students to produce academic writing that is markedly different than more competent writing. This is because Taiwanese students are first and foremost English as a Foreign language (EFL) readers and may have difficulties picking up on…

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

ERIC Educational Resources Information Center

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

2010-01-01

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…

The Effect of Corpus-Based Activities on Verb-Noun Collocations in EFL Classes

ERIC Educational Resources Information Center

Ucar, Serpil; Yükselir, Ceyhun

2015-01-01

This current study sought to reveal the impacts of corpus-based activities on verb-noun collocation learning in EFL classes. This study was carried out on two groups--experimental and control groups- each of which consists of 15 students. The students were preparatory class students at School of Foreign Languages, Osmaniye Korkut Ata University.…

A Study of Learners' Usage of a Mobile Learning Application for Learning Idioms and Collocations

ERIC Educational Resources Information Center

Amer, Mahmoud

2014-01-01

This study explored how four groups of language learners used a mobile software application developed by the researcher for learning idiomatic expressions and collocations. A total of 45 participants in the study used the application for a period of one week. Data for this study was collected from the application, a questionnaire, and follow-up…

Retention and Use of Lexical Collocations (Verb + Noun and Adjective + Noun) by Applying Lexical Approach in a Reading Course

ERIC Educational Resources Information Center

Ördem, Eser; Paker, Turan

2016-01-01

The purpose of this study was to investigate whether teaching vocabulary via collocations would contribute to retention and use of foreign language, English. A quasi-experimental design was formed to see whether there would be a significant difference between the treatment and control groups. Three instruments developed were conducted to 60…

A Comparative Study on the Effects of Negative Evidence and Enriched Input on Learning of Verb-Noun Collocations

ERIC Educational Resources Information Center

Okyar, Hatice; Yangin Eksi, Gonca

2017-01-01

This study compared the effectiveness of negative evidence and enriched input on learning the verb-noun collocations. There were 52 English as Foreign Language (EFL) learners in this research study and they were randomly assigned to the negative evidence or enriched input groups. While the negative evidence group (n = 27) was provided with…

The Effects of Utilizing Corpus Resources to Correct Collocation Errors in L2 Writing--Students' Performance, Corpus Use and Perceptions

ERIC Educational Resources Information Center

Wu, Yi-ju

2016-01-01

Data-Driven Learning (DDL), in which learners "confront [themselves] directly with the corpus data" (Johns, 2002, p. 108), has shown to be effective in collocation learning in L2 writing. Nevertheless, there have been only few research studies of this type examining the relationship between English proficiency and corpus consultation.…

Radiation energy budget studies using collocated AVHRR and ERBE observations

NASA Technical Reports Server (NTRS)

Ackerman, Steven A.; Inoue, Toshiro

1994-01-01

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.

Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions

NASA Astrophysics Data System (ADS)

Leclerc, Arnaud; Thomas, Phillip S.; Carrington, Tucker

2017-08-01

Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analysed and the numerical results are compared with those obtained with the reduced rank block power method. Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank SOP functions, is noticeable in terms of CPU time.

Optimal reorientation of asymmetric underactuated spacecraft using differential flatness and receding horizon control

NASA Astrophysics Data System (ADS)

Cai, Wei-wei; Yang, Le-ping; Zhu, Yan-wei

2015-01-01

This paper presents a novel method integrating nominal trajectory optimization and tracking for the reorientation control of an underactuated spacecraft with only two available control torque inputs. By employing a pseudo input along the uncontrolled axis, the flatness property of a general underactuated spacecraft is extended explicitly, by which the reorientation trajectory optimization problem is formulated into the flat output space with all the differential constraints eliminated. Ultimately, the flat output optimization problem is transformed into a nonlinear programming problem via the Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques to overcome the side effects of the differential matrix's ill-conditions on numerical accuracy. Treating the trajectory tracking control as a state regulation problem, we develop a robust closed-loop tracking control law using the receding-horizon control method, and compute the feedback control at each control cycle rapidly via the differential transformation method. Numerical simulation results show that the proposed control scheme is feasible and effective for the reorientation maneuver.

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

NASA Technical Reports Server (NTRS)

Funaro, Daniele; Gottlieb, David

1989-01-01

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Decentralized model reference adaptive control of large flexible structures

NASA Technical Reports Server (NTRS)

Lee, Fu-Ming; Fong, I-Kong; Lin, Yu-Hwan

1988-01-01

A decentralized model reference adaptive control (DMRAC) method is developed for large flexible structures (LFS). The development follows that of a centralized model reference adaptive control for LFS that have been shown to be feasible. The proposed method is illustrated using a simply supported beam with collocated actuators and sensors. Results show that the DMRAC can achieve either output regulation or output tracking with adequate convergence, provided the reference model inputs and their time derivatives are integrable, bounded, and approach zero as t approaches infinity.

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

New Bernstein type inequalities for polynomials on ellipses

NASA Technical Reports Server (NTRS)

Freund, Roland; Fischer, Bernd

1990-01-01

New and sharp estimates are derived for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Also presented are some new results for approximation problems of this type.

Accuracy improvement of the H-drive air-levitating wafer inspection stage based on error analysis and compensation

NASA Astrophysics Data System (ADS)

Zhang, Fan; Liu, Pinkuan

2018-04-01

In order to improve the inspection precision of the H-drive air-bearing stage for wafer inspection, in this paper the geometric error of the stage is analyzed and compensated. The relationship between the positioning errors and error sources are initially modeled, and seven error components are identified that are closely related to the inspection accuracy. The most effective factor that affects the geometric error is identified by error sensitivity analysis. Then, the Spearman rank correlation method is applied to find the correlation between different error components, aiming at guiding the accuracy design and error compensation of the stage. Finally, different compensation methods, including the three-error curve interpolation method, the polynomial interpolation method, the Chebyshev polynomial interpolation method, and the B-spline interpolation method, are employed within the full range of the stage, and their results are compared. Simulation and experiment show that the B-spline interpolation method based on the error model has better compensation results. In addition, the research result is valuable for promoting wafer inspection accuracy and will greatly benefit the semiconductor industry.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Dynamics of a new family of iterative processes for quadratic polynomials

NASA Astrophysics Data System (ADS)

Gutiérrez, J. M.; Hernández, M. A.; Romero, N.

2010-03-01

In this work we show the presence of the well-known Catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations. In fact, we introduce a family of methods, depending on a parameter . These methods reach the order of convergence m+2 when they are applied to quadratic polynomials with different roots. Newton's and Chebyshev's methods appear as particular choices of the family appear for m=0 and m=1, respectively. We make both analytical and graphical studies of these methods, which give rise to rational functions defined in the extended complex plane. Firstly, we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers. Secondly, we make an incursion into its dynamical behavior. In fact, we show that the rational maps related to these methods can be written in terms of the entries of the Catalan triangle. Next we analyze its general convergence, by including some computer plots showing the intricate structure of the Universal Julia sets associated with the methods.

Sobolev-orthogonal systems of functions associated with an orthogonal system

NASA Astrophysics Data System (ADS)

Sharapudinov, I. I.

2018-02-01

For every system of functions \\{\\varphi_k(x)\\} which is orthonormal on (a,b) with weight ρ(x) and every positive integer r we construct a new associated system of functions \\{\\varphir,k(x)\\}k=0^∞ which is orthonormal with respect to a Sobolev-type inner product of the form \\displaystyle < f,g >=\\sumν=0r-1f(ν)(a)g(ν)(a)+\\intab f(r)(t)g(r)(t)ρ(t) dt. We study the convergence of Fourier series in the systems \\{\\varphir,k(x)\\}k=0^∞. In the important particular cases of such systems generated by the Haar functions and the Chebyshev polynomials T_n(x)=\\cos(n\\arccos x), we obtain explicit representations for the \\varphir,k(x) that can be used to study their asymptotic properties as k\\to∞ and the approximation properties of Fourier sums in the system \\{\\varphir,k(x)\\}k=0^∞. Special attention is paid to the study of approximation properties of Fourier series in systems of type \\{\\varphir,k(x)\\}k=0^∞ generated by Haar functions and Chebyshev polynomials.

On uniform constants of strong uniqueness in Chebyshev approximations and fundamental results of N. G. Chebotarev

NASA Astrophysics Data System (ADS)

Marinov, Anatolii V.

2011-06-01

In the problem of the best uniform approximation of a continuous real-valued function f\\in C(Q) in a finite-dimensional Chebyshev subspace M\\subset C(Q), where Q is a compactum, one studies the positivity of the uniform strong uniqueness constant \\gamma(N)=\\inf\\{\\gamma(f)\\colon f\\in N\\}. Here \\gamma(f) stands for the strong uniqueness constant of an element f_M\\in M of best approximation of f, that is, the largest constant \\gamma>0 such that the strong uniqueness inequality \\Vert f-\\varphi\\Vert\\ge\\Vert f-f_M\\Vert+\\gamma\\Vert f_M-\\varphi\\Vert holds for any \\varphi\\in M. We obtain a characterization of the subsets N\\subset C(Q) for which there is a neighbourhood O(N) of N satisfying the condition \\gamma(O(N))>0. The pioneering results of N. G. Chebotarev were published in 1943 and concerned the sharpness of the minimum in minimax problems and the strong uniqueness of algebraic polynomials of best approximation. They seem to have been neglected by the specialists, and we discuss them in detail.

Algorithms for Maneuvering Spacecraft Around Small Bodies

NASA Technical Reports Server (NTRS)

Acikmese, A. Bechet; Bayard, David

2006-01-01

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Development of a Multicenter Density Functional Tight Binding Model for Plutonium Surface Hydriding.

PubMed

Goldman, Nir; Aradi, Bálint; Lindsey, Rebecca K; Fried, Laurence E

2018-05-08

We detail the creation of a multicenter density functional tight binding (DFTB) model for hydrogen on δ-plutonium, using a framework of new Slater-Koster interaction parameters and a repulsive energy based on the Chebyshev Interaction Model for Efficient Simulation (ChIMES), where two- and three-center atomic interactions are represented by linear combinations of Chebyshev polynomials. We find that our DFTB/ChIMES model yields a total electron density of states for bulk δ-Pu that compares well to that from Density Functional Theory, as well as to a grid of energy calculations representing approximate H 2 dissociation paths on the δ-Pu (100) surface. We then perform molecular dynamics simulations and minimum energy pathway calculations to determine the energetics of surface dissociation and subsurface diffusion on the (100) and (111) surfaces. Our approach allows for the efficient creation of multicenter repulsive energies with a relatively small investment in initial DFT calculations. Our efforts are particularly pertinent to studies that rely on quantum calculations for interpretation and validation, such as experimental determination of chemical reactivity both on surfaces and in condensed phases.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down-channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

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

ERIC Educational Resources Information Center

Addison, James C., Jr.

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…

The Impact of Length of Study Abroad on Collocational Knowledge: The Case of Saudi Students in Australia

ERIC Educational Resources Information Center

Alqarni, Ibrahim R.

2017-01-01

This study investigates the impact that study in Australia has on the lexical knowledge of Saudi Arabian students. It focuses on: 1) the effects that the length of study in Australia has on the acquisition of lexical collocations, as reflected by lexical knowledge tests, and 2) whether there is a significant gender difference in the acquisition of…

Data-Driven Learning and the Acquisition of Italian Collocations: From Design to Student Evaluation

ERIC Educational Resources Information Center

Forti, Luciana

2017-01-01

This paper looks at how corpus data was used to design an Italian as an L2 language learning programme and how it was evaluated by students. The study focuses on the acquisition of Italian verb-noun collocations by Chinese native students attending a ten month long Italian language course before enrolling at an Italian university. It describes how…

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Liu, Bocheng; Hu, Hanping; Miao, Suoxia

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Scalable collaborative risk management technology for complex critical systems

NASA Technical Reports Server (NTRS)

Campbell, Scott; Torgerson, Leigh; Burleigh, Scott; Feather, Martin S.; Kiper, James D.

2004-01-01

We describe here our project and plans to develop methods, software tools, and infrastructure tools to address challenges relating to geographically distributed software development. Specifically, this work is creating an infrastructure that supports applications working over distributed geographical and organizational domains and is using this infrastructure to develop a tool that supports project development using risk management and analysis techniques where the participants are not collocated.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

A kernel function method for computing steady and oscillatory supersonic aerodynamics with interference.

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1973-01-01

The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.

Oscillatory supersonic kernel function method for interfering surfaces

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1974-01-01

In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isotalo, Aarno

A method referred to as tally nuclides is presented for accurately and efficiently calculating the time-step averages and integrals of any quantities that are weighted sums of atomic densities with constant weights during the step. The method allows all such quantities to be calculated simultaneously as a part of a single depletion solution with existing depletion algorithms. Some examples of the results that can be extracted include step-average atomic densities and macroscopic reaction rates, the total number of fissions during the step, and the amount of energy released during the step. Furthermore, the method should be applicable with several depletionmore » algorithms, and the integrals or averages should be calculated with an accuracy comparable to that reached by the selected algorithm for end-of-step atomic densities. The accuracy of the method is demonstrated in depletion calculations using the Chebyshev rational approximation method. Here, we demonstrate how the ability to calculate energy release in depletion calculations can be used to determine the accuracy of the normalization in a constant-power burnup calculation during the calculation without a need for a reference solution.« less

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

A method superior to adding percentiles when only limited anthropometric data such as percentile tables are available for design models.

PubMed

Albin, Thomas J; Vink, Peter

2014-11-01

Designers and ergonomists may occasionally be limited to using tables of percentiles of anthropometric data to model users. Design models that add or subtract percentiles produce unreliable estimates of the proportion of users accommodated, in part because they assume a perfect correlation between variables. Percentile data do not allow the use of more reliable modeling methods such as Principle Component Analysis. A better method is needed. A new method for modeling with limited data is described. It uses measures of central tendency (median or mean) of the range of possible correlation values to estimate the combined variance is shown to reduce error compared to combining percentiles. Second, use of the Chebyshev inequality allows the designer to more reliably estimate the percent accommodation when the distributions of the underlying anthropometric data are unknown than does combining percentiles. This paper describes a modeling method that is more accurate than combining percentiles when only limited data are available. Copyright © 2014 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Calculating Time-Integral Quantities in Depletion Calculations

DOE PAGES

Isotalo, Aarno

2016-06-02

A method referred to as tally nuclides is presented for accurately and efficiently calculating the time-step averages and integrals of any quantities that are weighted sums of atomic densities with constant weights during the step. The method allows all such quantities to be calculated simultaneously as a part of a single depletion solution with existing depletion algorithms. Some examples of the results that can be extracted include step-average atomic densities and macroscopic reaction rates, the total number of fissions during the step, and the amount of energy released during the step. Furthermore, the method should be applicable with several depletionmore » algorithms, and the integrals or averages should be calculated with an accuracy comparable to that reached by the selected algorithm for end-of-step atomic densities. The accuracy of the method is demonstrated in depletion calculations using the Chebyshev rational approximation method. Here, we demonstrate how the ability to calculate energy release in depletion calculations can be used to determine the accuracy of the normalization in a constant-power burnup calculation during the calculation without a need for a reference solution.« less

The Effects of Repetition and Time of Post-Test Administration on EFL Learners' Form Recall of Single Words and Collocations

ERIC Educational Resources Information Center

Peters, Elke

2014-01-01

This article examines how form recall of target lexical items by learners of English as a foreign language (EFL) is affected (1) by repetition (1, 3 or 5 number of occurrences), (2) by the type of target item (single words versus collocations), and (3) by the time of post-test administration (immediately or one week after the learning session).…

Investigation of IPPD: A Case Study of the Marine Corps AAAV.

DTIC Science & Technology

1998-03-01

process. ( Rafii , 1995, p. 78) The United States Marine Corps is in the process of developing their next generation of Advanced Amphibious Assault...particular product or process. ( Rafii , 1995, p. 78) DiTrapani and Geither’s (1996) study of IPTs stressed the collocation of team members to the...School of Systems Management, Naval Postgraduate School, Monterey, CA, December 1996. Rafii , F., "How Important Is Physical Collocation to Product

Integrated High-Speed Torque Control System for a Robotic Joint

NASA Technical Reports Server (NTRS)

Davis, Donald R. (Inventor); Radford, Nicolaus A. (Inventor); Permenter, Frank Noble (Inventor); Valvo, Michael C. (Inventor); Askew, R. Scott (Inventor)

2013-01-01

A control system for achieving high-speed torque for a joint of a robot includes a printed circuit board assembly (PCBA) having a collocated joint processor and high-speed communication bus. The PCBA may also include a power inverter module (PIM) and local sensor conditioning electronics (SCE) for processing sensor data from one or more motor position sensors. Torque control of a motor of the joint is provided via the PCBA as a high-speed torque loop. Each joint processor may be embedded within or collocated with the robotic joint being controlled. Collocation of the joint processor, PIM, and high-speed bus may increase noise immunity of the control system, and the localized processing of sensor data from the joint motor at the joint level may minimize bus cabling to and from each control node. The joint processor may include a field programmable gate array (FPGA).

Geodesy and Cartography (Selected Articles),

DTIC Science & Technology

1979-08-10

C-OO/b73 GEODESY AND CARTOGRAPHY (SELECTED ARTICLES) English pages: 40 Source: GeodezJa i Kartografia, Vol. 27, Nr. 1, 1978, PP. 3-27 Country of...1976. 14) kledzixski, J., Zibek, Z., Czarnecki, K., Rogowski, J.B., Problems in Using Satellite Surveys in an Astronomical-Geodesic Network, Geodezja i...Based on Observations of Low-Low Satellites Using Collocation Methods, Geodezja i Kartografia, Vol. XXVI, No. 4, 1977. [-7. Krynski, J., Schwarz, K.P

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

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

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

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

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

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

NASA Technical Reports Server (NTRS)

Streett, C. L.

1987-01-01

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

Satellite altitude determination uncertainties

NASA Technical Reports Server (NTRS)

Siry, J. W.

1972-01-01

Satellite altitude determination uncertainties will be discussed from the standpoint of the GEOS-C satellite, from the longer range viewpoint afforded by the Geopause concept. Data are focused on methods for short-arc tracking which are essentially geometric in nature. One uses combinations of lasers and collocated cameras. The other method relies only on lasers, using three or more to obtain the position fix. Two typical locales are looked at, the Caribbean area, and a region associated with tracking sites at Goddard, Bermuda and Canada which encompasses a portion of the Gulf Stream in which meanders develop.

Approximating a retarded-advanced differential equation that models human phonation

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

Boundary-element modelling of dynamics in external poroviscoelastic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Litvinchuk, S. Yu; Ipatov, A. A.; Petrov, A. N.

2018-04-01

A problem of a spherical cavity in porous media is considered. Porous media are assumed to be isotropic poroelastic or isotropic poroviscoelastic. The poroviscoelastic formulation is treated as a combination of Biot’s theory of poroelasticity and elastic-viscoelastic correspondence principle. Such viscoelastic models as Kelvin–Voigt, Standard linear solid, and a model with weakly singular kernel are considered. Boundary field study is employed with the help of the boundary element method. The direct approach is applied. The numerical scheme is based on the collocation method, regularized boundary integral equation, and Radau stepped scheme.

An Extension of the Split Window Technique for the Retrieval of Precipitable Water: Experimental Verification

DTIC Science & Technology

1988-09-23

DOWNGRADING SCHEDULE D~istribution Unlimited 4. PERFORMING ORGANIZATiON REPORT NUMVBER(S) 5. MONITORiG ORGANIZATION REPORT NUMBER(S) AFGL-TR-88-0237...Collocations were performed on launch sites of the cloud contamination, aerosol problems, collocation 1200 UT radiosondes on 25 Aug 1987. Statistics were...al (1987) and Thomason, 1987). In this imagery opaque clouds to this problem appear white, low clouds and fog appear bright red against a brown

Precise control of flexible manipulators

NASA Technical Reports Server (NTRS)

Cannon, R. H., Jr.

1984-01-01

Experimental apparatus were developed for physically testing control systems for pointing flexible structures, such as limber spacecraft, for the case that control actuators cannot be collocated with sensors. Structural damping ratios are less than 0.003, each basic configuration of sensor/actuator noncollocation is available, and inertias can be halved or doubled abruptly during control maneuvers, thereby imposing, in particular, a sudden reversal in the plant's pole-zero sequence. First experimental results are presented, including stable control with both collocation and noncollocation.

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

Radiation Transport in Random Media With Large Fluctuations

NASA Astrophysics Data System (ADS)

Olson, Aaron; Prinja, Anil; Franke, Brian

2017-09-01

Neutral particle transport in media exhibiting large and complex material property spatial variation is modeled by representing cross sections as lognormal random functions of space and generated through a nonlinear memory-less transformation of a Gaussian process with covariance uniquely determined by the covariance of the cross section. A Karhunen-Loève decomposition of the Gaussian process is implemented to effciently generate realizations of the random cross sections and Woodcock Monte Carlo used to transport particles on each realization and generate benchmark solutions for the mean and variance of the particle flux as well as probability densities of the particle reflectance and transmittance. A computationally effcient stochastic collocation method is implemented to directly compute the statistical moments such as the mean and variance, while a polynomial chaos expansion in conjunction with stochastic collocation provides a convenient surrogate model that also produces probability densities of output quantities of interest. Extensive numerical testing demonstrates that use of stochastic reduced-order modeling provides an accurate and cost-effective alternative to random sampling for particle transport in random media.

Geophysical data integration, stochastic simulation and significance analysis of groundwater responses using ANOVA in the Chicot Aquifer system, Louisiana, USA

USGS Publications Warehouse

Rahman, A.; Tsai, F.T.-C.; White, C.D.; Carlson, D.A.; Willson, C.S.

2008-01-01

Data integration is challenging where there are different levels of support between primary and secondary data that need to be correlated in various ways. A geostatistical method is described, which integrates the hydraulic conductivity (K) measurements and electrical resistivity data to better estimate the K distribution in the Upper Chicot Aquifer of southwestern Louisiana, USA. The K measurements were obtained from pumping tests and represent the primary (hard) data. Borehole electrical resistivity data from electrical logs were regarded as the secondary (soft) data, and were used to infer K values through Archie's law and the Kozeny-Carman equation. A pseudo cross-semivariogram was developed to cope with the resistivity data non-collocation. Uncertainties in the auto-semivariograms and pseudo cross-semivariogram were quantified. The groundwater flow model responses by the regionalized and coregionalized models of K were compared using analysis of variance (ANOVA). The results indicate that non-collocated secondary data may improve estimates of K and affect groundwater flow responses of practical interest, including specific capacity and drawdown. ?? Springer-Verlag 2007.

A Novel L-Probe Proximity Fed Patch Antenna With Parasitic Patch and Its Utilization in Antenna Arrays

NASA Astrophysics Data System (ADS)

Sláma, Libor; Dobeš, Josef; Boštík, Tomáš; Vejražka, František

2018-03-01

An analysis of the L-probe fed patch antenna with an extraordinary parasitic patch is described. The element of the antenna is fed by the L-probe partially implemented in PCB. An excellent impedance matching is obtained (< ‑26 dB in the design frequency band 4.4–5 GHz). The radiation characteristics are also very good (gain > 10 dBi). For the numerical analyses, the Full Wave—CST Microwave Studio software was used in both frequency and time domains, and a very good agreement between the Time Domain Solver (TDS) and Frequency Domain Solver (FDS) was obtained. Real antenna samples have been created and measured as well as eight-element antenna arrays designed by the Dolph-Chebyshev method.

Control by model error estimation

NASA Technical Reports Server (NTRS)

Likins, P. W.; Skelton, R. E.

1976-01-01

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

Form finding in elastic gridshells.

PubMed

Baek, Changyeob; Sageman-Furnas, Andrew O; Jawed, Mohammad K; Reis, Pedro M

2018-01-02

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Form finding in elastic gridshells

NASA Astrophysics Data System (ADS)

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Investigation of advanced UQ for CRUD prediction with VIPRE.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eldred, Michael Scott

2011-09-01

This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. It demonstrates the application of 'advanced UQ,' in particular dimension-adaptive p-refinement for polynomial chaos and stochastic collocation. The study calculates statistics for several quantities of interest that are indicators for the formation of CRUD (Chalk River unidentified deposit), which can lead to CIPS (CRUD induced power shift). Stochastic expansion methods are attractive methods for uncertainty quantification due to their fast convergence properties. For smooth functions (i.e., analytic, infinitely-differentiable) in L{sup 2} (i.e., possessing finite variance), exponential convergence rates can be obtained under order refinementmore » for integrated statistical quantities of interest such as mean, variance, and probability. Two stochastic expansion methods are of interest: nonintrusive polynomial chaos expansion (PCE), which computes coefficients for a known basis of multivariate orthogonal polynomials, and stochastic collocation (SC), which forms multivariate interpolation polynomials for known coefficients. Within the DAKOTA project, recent research in stochastic expansion methods has focused on automated polynomial order refinement ('p-refinement') of expansions to support scalability to higher dimensional random input spaces [4, 3]. By preferentially refining only in the most important dimensions of the input space, the applicability of these methods can be extended from O(10{sup 0})-O(10{sup 1}) random variables to O(10{sup 2}) and beyond, depending on the degree of anisotropy (i.e., the extent to which randominput variables have differing degrees of influence on the statistical quantities of interest (QOIs)). Thus, the purpose of this study is to investigate the application of these adaptive stochastic expansion methods to the analysis of CRUD using the VIPRE simulation tools for two different plant models of differing random dimension, anisotropy, and smoothness.« less

Fully coupled methods for multiphase morphodynamics

NASA Astrophysics Data System (ADS)

Michoski, C.; Dawson, C.; Mirabito, C.; Kubatko, E. J.; Wirasaet, D.; Westerink, J. J.

2013-09-01

We present numerical methods for a system of equations consisting of the two dimensional Saint-Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge-Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge-Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.

Digital PI-PD controller design for arbitrary order systems: Dominant pole placement approach.

PubMed

Dincel, Emre; Söylemez, Mehmet Turan

2018-05-02

In this paper, a digital PI-PD controller design method is proposed for arbitrary order systems with or without time-delay to achieve desired transient response in the closed-loop via dominant pole placement approach. The digital PI-PD controller design problem is solved by converting the original problem to the digital PID controller design problem. Firstly, parametrization of the digital PID controllers which assign dominant poles to desired location is done. After that the subset of digital PID controller parameters in which the remaining poles are located away from the dominant pole pair is found via Chebyshev polynomials. The obtained PID controller parameters are then transformed into the PI-PD controller parameters by considering the closed-loop controller zero and the design is completed. Success of the proposed design method is firstly demonstrated on an example transfer function and compared with the well-known PID controller methods from the literature through simulations. After that the design method is implemented on the fan and plate laboratory system in a real environment. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

NASA Astrophysics Data System (ADS)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

The Shock and Vibration Digest, Volume 16, Number 10

DTIC Science & Technology

1984-10-01

shaped, arid a general polygonal-shaped membrane Fourier expansion -collocation method and the finite without symmetry They also derived, with the help...geometry is not applicable; therefore, a Fourier sine series expansion technique. The meth- not much work on the dynamic behavior of skew- od was applied...particular m.-de are obtained. This normal mode expansion form of deflection surface. The stability of motion approach has recently been used in a series of

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Spatial and temporal variability of the overall error of National Atmospheric Deposition Program measurements determined by the USGS collocated-sampler program, water years 1989-2001

USGS Publications Warehouse

Wetherbee, G.A.; Latysh, N.E.; Gordon, J.D.

2005-01-01

Data from the U.S. Geological Survey (USGS) collocated-sampler program for the National Atmospheric Deposition Program/National Trends Network (NADP/NTN) are used to estimate the overall error of NADP/NTN measurements. Absolute errors are estimated by comparison of paired measurements from collocated instruments. Spatial and temporal differences in absolute error were identified and are consistent with longitudinal distributions of NADP/NTN measurements and spatial differences in precipitation characteristics. The magnitude of error for calcium, magnesium, ammonium, nitrate, and sulfate concentrations, specific conductance, and sample volume is of minor environmental significance to data users. Data collected after a 1994 sample-handling protocol change are prone to less absolute error than data collected prior to 1994. Absolute errors are smaller during non-winter months than during winter months for selected constituents at sites where frozen precipitation is common. Minimum resolvable differences are estimated for different regions of the USA to aid spatial and temporal watershed analyses.

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

NASA Astrophysics Data System (ADS)

Tapimo, Romuald; Tagne Kamdem, Hervé Thierry; Yemele, David

2018-03-01

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions \\vert μ \\vert ≥0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.

A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis

2014-04-01

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

Attitude and vibration control of a large flexible space-based antenna

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1982-01-01

Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Least squares collocation applied to local gravimetric solutions from satellite gravity gradiometry data

NASA Technical Reports Server (NTRS)

Robbins, J. W.

1985-01-01

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.

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

NASA Astrophysics Data System (ADS)

Ocko, Ilissa B.; Ginoux, Paul A.

2017-04-01

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

Stress intensity and crack displacement for small edge cracks

NASA Technical Reports Server (NTRS)

Orange, Thomas W.

1988-01-01

The weight function method was used to derive stress intensity factors and crack mouth displacement coefficients for small edge cracks (less than 20 percent of the specimen width) in common fracture specimen configurations. Contact stresses due to point application of loads were found to be small but significant for three-point bending and insignificant for four-point bending. The results are compared with available equations and numerical solutions from the literature and with unpublished boundary collocation results.

Local Geoid Determination Using the Global Positioning System

DTIC Science & Technology

1988-09-01

Positioning System by Ma, Wei-Ming September 1988 Co-Advisor: Kandiah Jeyapalan Co-Advisor: Stevens P. Tucker Approved for public release; distribution is... Jeyapalan and Stevens P. Tucker, my thesis advisors, for their dedicated assistance and guidance during the study. Without their encouragement...method of collocation is [ Jeyapalan , 1977]: x = A*X+S +n +O.S q q P where x the vector of the observation (x = Ah - N0(X,Y,Z) - H) A a given rectangular

Visual Typo Correction by Collocative Optimization: A Case Study on Merchandize Images.

PubMed

Wei, Xiao-Yong; Yang, Zhen-Qun; Ngo, Chong-Wah; Zhang, Wei

2014-02-01

Near-duplicate retrieval (NDR) in merchandize images is of great importance to a lot of online applications on e-Commerce websites. In those applications where the requirement of response time is critical, however, the conventional techniques developed for a general purpose NDR are limited, because expensive post-processing like spatial verification or hashing is usually employed to compromise the quantization errors among the visual words used for the images. In this paper, we argue that most of the errors are introduced because of the quantization process where the visual words are considered individually, which has ignored the contextual relations among words. We propose a "spelling or phrase correction" like process for NDR, which extends the concept of collocations to visual domain for modeling the contextual relations. Binary quadratic programming is used to enforce the contextual consistency of words selected for an image, so that the errors (typos) are eliminated and the quality of the quantization process is improved. The experimental results show that the proposed method can improve the efficiency of NDR by reducing vocabulary size by 1000% times, and under the scenario of merchandize image NDR, the expensive local interest point feature used in conventional approaches can be replaced by color-moment feature, which reduces the time cost by 9202% while maintaining comparable performance to the state-of-the-art methods.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Viscoelastic stability in a single-screw channel flow

NASA Astrophysics Data System (ADS)

Agbessi, Y.; Bu, L. X.; Béreaux, Y.; Charmeau, J.-Y.

2018-05-01

In this work, we perform a linear stability analysis on pressure and drag flows of an Upper Convected Maxwell viscoelastic fluid. We use the well-recognised method of expanding the disturbances in Chebyschev polynomials and solve the resulting generalized eigenvalues problem with a collocation spectra method. Both the level of elasticity and the back-pressure vary. In a second stage, recent analytic solutions of viscoelastic fluid flows in slowly varying sections [1] are used to extend this stability analysis to flows in a compression or in a diverging section of a single screw channel, for example a wave mixing screw.

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

NASA Technical Reports Server (NTRS)

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.