The 3D Euler solutions using automated Cartesian grid generation
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.
NASA Astrophysics Data System (ADS)
Polkowski, Marcin
2016-04-01
Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.
Conversion of Cartesian coordinates from and to Generalized Balanced Ternary addresses
van Roessel, Jan W.
1988-01-01
Hexagonal grids have several advantages over square grids, such as a greater angular resolution and unambiguous connectivity. The Generalized Balanced Ternary (GBT) system is a spatial addressing method for hexagonal grids in which the hexagons are arranged in hierarchical aggregates, and which accommodates vector operations in GBT space. Efficient algorithms for converting Cartesian coordinates from and to GBT addresses are based on the dual representation of the hexagonal tessellation. The GBT-to-Cartesian algorithm is an order of magnitude faster than the Cartesian-to-GBT algorithm, the latter requiring interpolation and GBT addition for each digit of the generated GBT address.
Unstructured Cartesian/prismatic grid generation for complex geometries
NASA Technical Reports Server (NTRS)
Karman, Steve L., Jr.
1995-01-01
The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.
3D automatic Cartesian grid generation for Euler flows
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.
On differential transformations between Cartesian and curvilinear (geodetic) coordinates
NASA Technical Reports Server (NTRS)
Soler, T.
1976-01-01
Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.
Efficient Fluid Dynamic Design Optimization Using Cartesian Grids
NASA Technical Reports Server (NTRS)
Dadone, A.; Grossman, B.; Sellers, Bill (Technical Monitor)
2004-01-01
This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.
A Cartesian grid approach with hierarchical refinement for compressible flows
NASA Technical Reports Server (NTRS)
Quirk, James J.
1994-01-01
Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.
A general time element using Cartesian coordinates: Eccentric orbit integration
NASA Technical Reports Server (NTRS)
Janin, G.
1980-01-01
A general time element, valid with any arbitrary independent variables, and used with Cartesian coordinates for the integration of the elliptic motion in orbits, is examined. The derivation of the time element from a set of canonical elements of the Delaunay type, developed in the extended phase space, is presented. The application of the method using an example of a transfer orbit for a geosynchronous mission is presented. The eccentric and elliptic anomaly are utilized as the independent variable. The reduction of the in track error resulting from using Cartesian coordinates with the time element is reported.
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)
2002-01-01
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
NASA Astrophysics Data System (ADS)
Civicioglu, Pinar
2012-09-01
In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into geodetic coordinates or vice versa. It is very easy to solve the problem of transforming geodetic coordinates into geocentric cartesian coordinates. On the other hand, it is rather difficult to solve the problem of transforming geocentric cartesian coordinates into geodetic coordinates as it is very hard to define a mathematical relationship between the geodetic latitude (φ) and the geocentric cartesian coordinates (X, Y, Z). In this paper, a new algorithm, the Differential Search Algorithm (DS), is presented to solve the problem of transforming the geocentric cartesian coordinates into geodetic coordinates and its performance is compared with the performances of the classical methods (i.e., Borkowski, 1989; Bowring, 1976; Fukushima, 2006; Heikkinen, 1982; Jones, 2002; Zhang, 2005; Borkowski, 1987; Shu, 2010 and Lin, 1995) and Computational-Intelligence algorithms (i.e., ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES). The statistical tests realized for the comparison of performances indicate that the problem-solving success of DS algorithm in transforming the geocentric cartesian coordinates into geodetic coordinates is higher than those of all classical methods and Computational-Intelligence algorithms used in this paper.
GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows
NASA Technical Reports Server (NTRS)
2003-01-01
With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.
On NUFFT-based gridding for non-Cartesian MRI.
Fessler, Jeffrey A
2007-10-01
For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI. PMID:17689121
On NUFFT-based gridding for non-Cartesian MRI
NASA Astrophysics Data System (ADS)
Fessler, Jeffrey A.
2007-10-01
For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.
OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.
2000-06-27
This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.
Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
NASA Astrophysics Data System (ADS)
Giese, Guido
2009-11-01
Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic-plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
An adaptive discretization of compressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
Qiu, Linhai; Lu, Wenlong; Fedkiw, Ronald
2016-01-01
We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.
NASA Astrophysics Data System (ADS)
Rhee, Young Min
2000-10-01
A modified method to construct an accurate potential energy surface by interpolation is presented. The modification is based on the use of Cartesian coordinates in the weighting function. The translational and rotational invariance of the potential is incorporated by a proper definition of the distance between two Cartesian configurations. A numerical algorithm to find the distance is developed. It is shown that the present method is more exact in describing a planar system compared to the previous methods with weightings in internal coordinates. The applicability of the method to reactive systems is also demonstrated by performing classical trajectory simulations on the surface.
NASA Technical Reports Server (NTRS)
Finley, Dennis B.
1995-01-01
This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
NASA Astrophysics Data System (ADS)
Sanmiguel-Rojas, Enrique; Ortega-Casanova, Joaquin; del Pino, Carlos; Fernandez-Feria, Ramon
2004-11-01
A method for generating a non-uniform cartesian grid for irregular two-dimensional (2D) geometries such that all the boundary points are regular mesh points is given. The resulting non-uniform grid is used to discretize the Navier-Stokes equations for 2D incompressible viscous flows using finite difference approximations. To that end, finite-difference approximations of the derivatives on a non-uniform mesh are given. We test the method with two different examples: the shallow water flow on a lake with irregular contour, and the pressure driven flow through an irregular array of circular cylinders.
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
NASA Astrophysics Data System (ADS)
Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.
2013-06-01
The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Cartesian grid simulations of gas-solids flow systems with complex geometry
Dietiker, Jean-Francois; Li, Tingwen; Garg, Rahul; Shahnam, Mehrdad
2013-02-01
Complex geometries encountered in many applications of gas–solids flow need special treatment in most legacy multiphase flow solvers with Cartesian numerical grid. This paper briefly outlines the implementation of a cut cell technique in the open-source multiphase flow solver—MFIX for accurate representation of complex geometries. Specifically, applications of the Cartesian cut cell method to different gas–solids fluidization systems including a small scale bubbling fluidized bed with submerged tube bundle and a complete pilot-scale circulating fluidized bed will be presented. In addition to qualitative predictions on the general flow behaviors inside each system, quantitative comparison with the available experimental data will be presented. Furthermore, some results on extending the current cut-cell technique to Lagrangian–Eulerian simulations will be presented.
Grid-coordinate generation program
Cosner, Oliver J.; Horwich, Esther
1974-01-01
This program description of the grid-coordinate generation program is written for computer users who are familiar with digital aquifer models. The program computes the coordinates for a variable grid -used in the 'Pinder Model' (a finite-difference aquifer simulator), for input to the CalComp GPCP (general purpose contouring program). The program adjusts the y-value by a user-supplied constant in order to transpose the origin of the model grid from the upper left-hand corner to the lower left-hand corner of the grid. The user has the options of, (1.) choosing the boundaries of the plot; (2.) adjusting the z-values (altitudes) by a constant; (3.) deleting superfluous z-values and (4.) subtracting the simulated surfaces from each other to obtain the decline. Output of this program includes the fixed format CNTL data cards and the other data cards required for input to GPCP. The output from GPCP then is used to produce a potentiometric map or a decline map by means of the CalComp plotter.
Mackie, Cameron J; Candian, Alessandra; Huang, Xinchuan; Lee, Timothy J; Tielens, Alexander G G M
2015-06-28
A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D(+). PMID:26133410
A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains
Johansen, H.; Colella, P.
1997-01-31
The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
Khoromskij, B.N. Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-09-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h{sup 3}) convergence in the grid-size h=O(n{sup -1}). Moreover, this requires O(3rn+r{sup 3}) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH{sub 4} molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10{sup -6} hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
Cartesian-Grid Simulations of a Canard-Controlled Missile with a Free-Spinning Tail
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Kwak, Dochan (Technical Monitor)
2002-01-01
The proposed paper presents a series of simulations of a geometrically complex, canard-controlled, supersonic missile with free-spinning tail fins. Time-dependent simulations were performed using an inviscid Cartesian-grid-based method with results compared to both experimental data and high-resolution Navier-Stokes computations. At fixed free stream conditions and canard deflections, the tail spin rate was iteratively determined such that the net rolling moment on the empennage is zero. This rate corresponds to the time-asymptotic rate of the free-to-spin fin system. After obtaining spin-averaged aerodynamic coefficients for the missile, the investigation seeks a fixed-tail approximation to the spin-averaged aerodynamic coefficients, and examines the validity of this approximation over a variety of freestream conditions.
A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
Boschitsch, Alexander H; Fenley, Marcia O
2011-05-10
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous
NASA Astrophysics Data System (ADS)
Chen, XinJian
2012-12-01
This paper presents an application of a three-dimensional unstructured Cartesian grid model (Chen, 2011) to a real-world case, namely the Crystal River/Kings Bay system located on the Gulf coast of the Florida peninsula of the United States. Crystal River/Kings Bay is a spring-fed estuarine system which is believed to be the largest natural refuge in the United States for manatees during the coldest days in winter because of the existence of a large amount of discharge out of numerous spring vents at the bottom of Kings Bay. The unstructured Cartesian grid model was used to simulate hydrodynamics, including salinity transport processes and thermodynamics, in the estuary during a 34-month period from April 2007 to February 2010. Although there are some unidentified uncertainties in quantifying flow rates from the spring vents and salinity variations in spring flows, simulated water elevations, salinities, temperatures, and cross-sectional flux all match well or very well with measured real-time field data. This suggests that the unstructured Cartesian grid model can adequately simulate hydrodynamics in a complex shallow water system such as Crystal River/Kings Bay and the numerical theory for the unstructured Cartesian grid model works properly. The successful simulation of hydrodynamics in the estuarine system also suggests that an empirical formula that relates the spring discharge with the water level in Kings Bay and the groundwater level measured in a nearby well is reasonable.
NASA Technical Reports Server (NTRS)
Finley, Dennis B.; Karman, Steve L., Jr.
1996-01-01
The objective of the second phase of the Euler Technology Assessment program was to evaluate the ability of Euler computational fluid dynamics codes to predict compressible flow effects over a generic fighter wind tunnel model. This portion of the study was conducted by Lockheed Martin Tactical Aircraft Systems, using an in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaption of the volume grid during the solution to resolve high-gradient regions. The SPLITFLOW code predictions of configuration forces and moments are shown to be adequate for preliminary design, including predictions of sideslip effects and the effects of geometry variations at low and high angles-of-attack. The transonic pressure prediction capabilities of SPLITFLOW are shown to be improved over subsonic comparisons. The time required to generate the results from initial surface data is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2000-01-01
Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.; Nixon, David (Technical Monitor)
1998-01-01
The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.
NASA Astrophysics Data System (ADS)
Sato, Norikazu; Takeuchi, Shintaro; Kajishima, Takeo; Inagaki, Masahide; Horinouchi, Nariaki
2016-09-01
A new discretization scheme on Cartesian grids, namely, a "consistent direct discretization scheme", is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier-Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid-solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.
Modelling rapid mass movements using the shallow water equations in Cartesian coordinates
NASA Astrophysics Data System (ADS)
Hergarten, S.; Robl, J.
2015-03-01
We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application - an almost horizontal fluid table - is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open-source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. Testing the results against analytical solutions and the proprietary avalanche model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool for assisting regional-scale natural hazard studies.
Issack, Bilkiss B; Roy, Pierre-Nicholas
2005-08-22
An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.
Cartesian Methods for the Shallow Water Equations on a Sphere
Drake, J.B.
2000-02-14
The shallow water equations in a spherical geometry are solved using a 3-dimensional Cartesian method. Spatial discretization of the 2-dimensional, horizontal differential operators is based on the Cartesian form of the spherical harmonics and an icosahedral (spherical) grid. Computational velocities are expressed in Cartesian coordinates so that a problem with a singularity at the pole is avoided. Solution of auxiliary elliptic equations is also not necessary. A comparison is made between the standard form of the Cartesian equations and a rotational form using a standard set of test problems. Error measures and conservation properties of the method are reported for the test problems.
NASA Astrophysics Data System (ADS)
Miao, Sha; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad
2015-11-01
This work presents a novel and efficient Cartesian-grid based simulation capability for the study of an incompressible, turbulent gas layer over a liquid flow with disparate Reynolds numbers in two phases. This capability couples a turbulent gas-flow solver and a liquid-layer based on a second-order accurate Boundary Data Immersion Method (BDIM) at the deformable interface. The turbulent gas flow solver solves the incompressible Navier-Stokes equations via direct numerical simulation or through turbulence closure (unsteady Reynolds-Averaged Navier-Stokes Models) for Reynolds numbers O(106). In this application, a laminar liquid layer solution is obtained from depth-integrated Navier-Stokes equations utilizing shallow water wave assumptions. The immersed boundary method (BDIM) enforces the coupling at the deformable interface, the boundary conditions to turbulence closure equations and defines the domain geometry on the Cartesian grid. Validations are made for the turbulent gas channel flow over high-viscosity liquid. This simulation capability can be applied to problems in the oil and industrial sector such as channel and pipe flows with heavy oils as well as wind wave generation in shallow waters. Sponsored by the Chevron Energy Technology Company.
Cerezo, Javier; Zúñiga, José; Requena, Alberto; Ávila Ferrer, Francisco J; Santoro, Fabrizio
2013-11-12
When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.
NASA Astrophysics Data System (ADS)
Blanc, Emilie; Chiavassa, Guillaume; Lombard, Bruno
2014-10-01
A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, these coefficients introduce shifted fractional derivatives of order 1/2, involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation) model. The properties of both the Biot-JKD and the Biot-DA models are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, two approaches are analyzed: Gaussian quadratures and optimization methods in the frequency range of interest. The nonlinear optimization is shown to be the better way of determination. A splitting strategy is then applied to approximate numerically the Biot-DA equations. The propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. An immersed interface method is implemented to take into account heterogeneous media on a Cartesian grid and to discretize the jump conditions at interfaces. Numerical experiments are presented. Comparisons with analytical solutions show the efficiency and the accuracy of the approach, and some numerical experiments are performed to investigate wave phenomena in complex media, such as multiple scattering across a set of random scatterers.
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Bay, Yong Yi
2015-11-01
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods also introduce new challenges, in that the formulation of accurate and well-posed discrete operators is not trivial. A cut-cell method for the solution of the incompressible Navier-Stokes equation is proposed for staggered Cartesian grids. In both scalar and vector cases, the emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. This ensures mass, momentum and kinetic energy conservation. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The accuracy of method is finally assessed in standard test cases.
ERIC Educational Resources Information Center
Gawryszewski, Luiz G.; Carreiro, Luiz Renato R.; Magalhaes, Fabio V.
2005-01-01
A non-informative cue (C) elicits an inhibition of manual reaction time (MRT) to a visual target (T). We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7[degrees]) positions, the C-T angular distances (in polar…
NASA Astrophysics Data System (ADS)
Ma, Donglin; Feng, Zexin; Wang, Chengliang; Liang, Rongguang
2015-09-01
In this paper, we propose a new composite ray mapping method to design freeform total internal reflective (TIR) optics for LED illumination. We sample the ray intensity distribution into rectangular grids which have the best topological match to those rectangular grids on the target surface. With the multiple-to-one mapping relationships between the source intensity distribution and target irradiance distribution, we can construct the freeform TIR surfaces and freeform refractive surface using Snell's law. Compared to our previous design using uv-θϕ composite ray mapping method, this design approach is expected to have much less surface error and improve the illumination uniformity further because of the better topological match. In addition, due to the overlapping mechanism by multiple-to-one (composite) ray mapping, the method could lead to a more robust freeform optics compared to traditional freeform optics designs.
Relationship between Students' Understanding of Functions in Cartesian and Polar Coordinate Systems
ERIC Educational Resources Information Center
Montiel, Mariana; Vidakovic, Draga; Kabael, Tangul
2009-01-01
The present study was implemented as a prelude to a study on the generalization of the single variable function concept to multivariate calculus. In the present study we analyze students' mental processes and adjustments, as they are being exposed to single variable calculus with polar coordinates. The results show that there appears to be a…
Polynesian head form: an interpretation of a factor analysis of Cartesian co-ordinate data.
Buranarugsa, M; Houghton, P
1981-01-01
The three dimensional co-ordinates of a large number of landmarks on a series of Polynesian skulls have been obtained by means of a diagraph, and from standard lateral cephalograms. The method is accurate, and a very large amount of data is stored in the concise form of the standardized co-ordinates. A factor analysis of some of these data defines a number of distinct craniofacial segments showing independent variation in positioning, and therefore presumably growth, along defined axes. The segments thus defined relate well to the conclusions of other studies of skull growth and form, and support the view that the basis of cranial variation is the same for all Homo sapiens. It is suggested that the strict independence of the isolated craniofacial segments may be a consequence of the particular method, and may not truly reflect the situation in the growing skull. PMID:7328041
On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.
Dagdug, Leonardo; García-Chung, Angel A; Chacón-Acosta, Guillermo
2016-08-21
We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.
On the description of Brownian particles in confinement on a non-Cartesian coordinates basis
NASA Astrophysics Data System (ADS)
Dagdug, Leonardo; García-Chung, Angel A.; Chacón-Acosta, Guillermo
2016-08-01
We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.
On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.
Dagdug, Leonardo; García-Chung, Angel A; Chacón-Acosta, Guillermo
2016-08-21
We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical. PMID:27544085
Katz, Jessica; Denholm, Paul; Cochran, Jaquelin
2015-06-01
Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. Coordinating balancing area operation can promote more cost and resource efficient integration of variable renewable energy, such as wind and solar, into power systems. This efficiency is achieved by sharing or coordinating balancing resources and operating reserves across larger geographic boundaries.
A topological coordinate system for the diamond cubic grid.
Čomić, Lidija; Nagy, Benedek
2016-09-01
Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis. PMID:27580205
A topological coordinate system for the diamond cubic grid.
Čomić, Lidija; Nagy, Benedek
2016-09-01
Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.
Götze, Jan P; Karasulu, Bora; Thiel, Walter
2013-12-21
We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.
NASA Astrophysics Data System (ADS)
Lee, Y.-M.; Wu, J.-S.; Jiang, T.-F.; Chen, Y.-S.
2008-01-01
A parallelized three-dimensional Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for molecules with a single electron, assuming the motion of the nucleus is frozen, is presented in this paper. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternate times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using the domain decomposition method on distributed memory machines by applying a multilevel graph-partitioning technique. The solver is validated using a H2+ molecule system, both by observing the total electron probability and total energy conservation without laser interaction, and by comparing the ionization rates with previous two-dimensional axisymmetric simulation results with an aligned incident laser pulse. The parallel efficiency of this TDSE solver is presented and discussed; the parallel efficiency can be as high as 75% using 128 processors. Finally, examples of the temporal evolution of the probability distribution of laser incidence onto a H2+ molecule at inter-nuclear distance of 9a.u. ( χ=0° and 90°) and the spectral intensities of harmonic generation at internuclear distance of 2a.u. ( χ=0° , 30°, 60°, and 90°) are presented to demonstrate the powerful capability of the current TDSE solver. Future possible extensions of the present method are also outlined at the end of this paper.
Crockett, R.K.; Colella, P.; Graves, D.T.
2011-04-01
We present a method for solving Poisson and heat equations with discontinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in Johansen and Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10{sup 6}, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.
Crockett, Robert; Graves, Daniel; Colella, Phillip
2009-10-23
We present a method for solving Poisson and heat equations with discon- tinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materi- als, as described in Johansen& Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 106, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.
Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates
NASA Technical Reports Server (NTRS)
Deane, Anil E.
1996-01-01
Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.
NASA Astrophysics Data System (ADS)
Trost, Nico; Jiménez, Javier; Imke, Uwe; Sanchez, Victor
2014-06-01
TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.
Akçakaya, Mehmet; Nam, Seunghoon; Basha, Tamer A.; Kawaji, Keigo; Tarokh, Vahid; Nezafat, Reza
2014-01-01
Background Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability. Methods We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate. Results Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time. Conclusions The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity. PMID:25215945
An efficient game for vehicle-to-grid coordination problems in smart grids
NASA Astrophysics Data System (ADS)
Shi, Xingyu; Ma, Zhongjing
2015-11-01
Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey-Clarke-Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.
78 FR 70076 - Large Scale Networking (LSN)-Middleware and Grid Interagency Coordination (MAGIC) Team
Federal Register 2010, 2011, 2012, 2013, 2014
2013-11-22
... Large Scale Networking (LSN)--Middleware and Grid Interagency Coordination (MAGIC) Team AGENCY: The Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO... Networking (LSN) Coordinating Group (CG). Public Comments: The government seeks individual input;...
Federal Register 2010, 2011, 2012, 2013, 2014
2012-09-20
... Large Scale Networking (LSN); Middleware and Grid Interagency Coordination (MAGIC) Team AGENCY: The Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO... to the Large Scale Networking (LSN) Coordinating Group (CG). Public Comments: The government...
NASA Astrophysics Data System (ADS)
Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.
NASA Astrophysics Data System (ADS)
Kapahi, A.; Sambasivan, S.; Udaykumar, H. S.
2013-05-01
This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.
Concurrent negotiation and coordination for grid resource coallocation.
Sim, Kwang Mong; Shi, Benyun
2010-06-01
Bolstering resource coallocation is essential for realizing the Grid vision, because computationally intensive applications often require multiple computing resources from different administrative domains. Given that resource providers and consumers may have different requirements, successfully obtaining commitments through concurrent negotiations with multiple resource providers to simultaneously access several resources is a very challenging task for consumers. The impetus of this paper is that it is one of the earliest works that consider a concurrent negotiation mechanism for Grid resource coallocation. The concurrent negotiation mechanism is designed for 1) managing (de)commitment of contracts through one-to-many negotiations and 2) coordination of multiple concurrent one-to-many negotiations between a consumer and multiple resource providers. The novel contributions of this paper are devising 1) a utility-oriented coordination (UOC) strategy, 2) three classes of commitment management strategies (CMSs) for concurrent negotiation, and 3) the negotiation protocols of consumers and providers. Implementing these ideas in a testbed, three series of experiments were carried out in a variety of settings to compare the following: 1) the CMSs in this paper with the work of others in a single one-to-many negotiation environment for one resource where decommitment is allowed for both provider and consumer agents; 2) the performance of the three classes of CMSs in different resource market types; and 3) the UOC strategy with the work of others [e.g., the patient coordination strategy (PCS )] for coordinating multiple concurrent negotiations. Empirical results show the following: 1) the UOC strategy achieved higher utility, faster negotiation speed, and higher success rates than PCS for different resource market types; and 2) the CMS in this paper achieved higher final utility than the CMS in other works. Additionally, the properties of the three classes of CMSs in
Recognizing Patterns In Log-Polar Coordinates
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1992-01-01
Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.
Agent Concept for Intelligent Distributed Coordination in the Electric Power Grid
SMATHERS, DOUGLAS C.; GOLDSMITH, STEVEN Y.
2001-03-01
Intelligent agents and multi-agent systems promise to take information management for real-time control of the power grid to a new level. This report presents our concept for intelligent agents to mediate and coordinate communications between Control Areas and Security Coordinators for real-time control of the power grid. An appendix describes the organizations and publications that deal with agent technologies.
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1982-01-01
A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.
Oh, Aram; Baik, Hionsuck; Choi, Dong Shin; Cheon, Jae Yeong; Kim, Byeongyoon; Kim, Heejin; Kwon, Seong Jung; Joo, Sang Hoon; Jung, Yousung; Lee, Kwangyeol
2015-03-24
Catalytic properties of nanoparticles can be significantly enhanced by controlling nanoscale alloying and its structure. In this work, by using a facet-controlled Pt@Ni core-shell octahedron nanoparticle, we show that the nanoscale phase segregation can have directionality and be geometrically controlled to produce a Ni octahedron that is penetrated by Pt atoms along three orthogonal Cartesian axes and is coated by Pt atoms along its edges. This peculiar anisotropic diffusion of Pt core atoms along the ⟨100⟩ vertex, and then toward the ⟨110⟩ edges, is explained via the minimum strain energy for Ni-Ni pair interactions. The selective removal of the Ni-rich phase by etching then results in structurally fortified Pt-rich skeletal PtNi alloy framework nanostructures. Electrochemical evaluation of this hollow nanoframe suggests that the oxygen reduction reaction (ORR) activity is greatly improved compared to conventional Pt catalysts. PMID:25734892
Gai, Jiading; Obeid, Nady; Holtrop, Joseph L.; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P.; Hwu, Wen-mei W.; Liang, Zhi-Pei; Sutton, Bradley P.
2013-01-01
Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code. PMID:23682203
Gai, Jiading; Obeid, Nady; Holtrop, Joseph L; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P; Hwu, Wen-Mei W; Liang, Zhi-Pei; Sutton, Bradley P
2013-05-01
Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code. PMID:23682203
An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows
NASA Astrophysics Data System (ADS)
Wongwathanarat, A.; Hammer, N. J.; Müller, E.
2010-05-01
Aims: Three dimensional explicit hydrodynamic codes based on spherical polar coordinates using a single spherical polar grid suffer from a severe restriction of the time step size due to the convergence of grid lines near the poles of the coordinate system. More importantly, numerical artifacts are encountered at the symmetry axis of the grid where boundary conditions have to be imposed that flaw the flow near the axis. The first problem can be eased and the second one avoided by applying an overlapping grid technique. Methods: A type of overlapping grid in spherical coordinates is adopted. This so called “Yin-Yang” grid is a two-patch overset grid proposed by Kageyama and Sato for geophysical simulations. Its two grid patches contain only the low-latitude regions of the usual spherical polar grid and are combined together in a simple manner. This property of the Yin-Yang grid greatly simplifies its implementation into a 3D code already employing spherical polar coordinates. It further allows for a much larger time step in 3D simulations using high angular resolution (⪉1°) than that required in 3D simulations using a regular spherical grid with the same angular resolution. Results: The Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed several standard hydrodynamic tests producing results which are in very good agreement with analytic solutions. Moreover, the solutions obtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundary between the two grid patches. The code has also been successfully used to model astrophysically relevant situations, namely equilibrium polytropes, a Taylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to our results, the usage of the Yin-Yang grid greatly enhances the suitability and efficiency of 3D explicit Eulerian codes based on spherical polar coordinates for astrophysical
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
Peron, Stephanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
Hybrid optimal online-overnight charging coordination of plug-in electric vehicles in smart grid
NASA Astrophysics Data System (ADS)
Masoum, Mohammad A. S.; Nabavi, Seyed M. H.
2016-10-01
Optimal coordinated charging of plugged-in electric vehicles (PEVs) in smart grid (SG) can be beneficial for both consumers and utilities. This paper proposes a hybrid optimal online followed by overnight charging coordination of high and low priority PEVs using discrete particle swarm optimization (DPSO) that considers the benefits of both consumers and electric utilities. Objective functions are online minimization of total cost (associated with grid losses and energy generation) and overnight valley filling through minimization of the total load levels. The constraints include substation transformer loading, node voltage regulations and the requested final battery state of charge levels (SOCreq). The main challenge is optimal selection of the overnight starting time (toptimal-overnight,start) to guarantee charging of all vehicle batteries to the SOCreq levels before the requested plug-out times (treq) which is done by simultaneously solving the online and overnight objective functions. The online-overnight PEV coordination approach is implemented on a 449-node SG; results are compared for uncoordinated and coordinated battery charging as well as a modified strategy using cost minimizations for both online and overnight coordination. The impact of toptimal-overnight,start on performance of the proposed PEV coordination is investigated.
The adaptive, cut-cell Cartesian approach (warts and all)
NASA Astrophysics Data System (ADS)
Powell, Kenneth G.
1995-10-01
Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.
Multi-agent coordination algorithms for control of distributed energy resources in smart grids
NASA Astrophysics Data System (ADS)
Cortes, Andres
Sustainable energy is a top-priority for researchers these days, since electricity and transportation are pillars of modern society. Integration of clean energy technologies such as wind, solar, and plug-in electric vehicles (PEVs), is a major engineering challenge in operation and management of power systems. This is due to the uncertain nature of renewable energy technologies and the large amount of extra load that PEVs would add to the power grid. Given the networked structure of a power system, multi-agent control and optimization strategies are natural approaches to address the various problems of interest for the safe and reliable operation of the power grid. The distributed computation in multi-agent algorithms addresses three problems at the same time: i) it allows for the handling of problems with millions of variables that a single processor cannot compute, ii) it allows certain independence and privacy to electricity customers by not requiring any usage information, and iii) it is robust to localized failures in the communication network, being able to solve problems by simply neglecting the failing section of the system. We propose various algorithms to coordinate storage, generation, and demand resources in a power grid using multi-agent computation and decentralized decision making. First, we introduce a hierarchical vehicle-one-grid (V1G) algorithm for coordination of PEVs under usage constraints, where energy only flows from the grid in to the batteries of PEVs. We then present a hierarchical vehicle-to-grid (V2G) algorithm for PEV coordination that takes into consideration line capacity constraints in the distribution grid, and where energy flows both ways, from the grid in to the batteries, and from the batteries to the grid. Next, we develop a greedy-like hierarchical algorithm for management of demand response events with on/off loads. Finally, we introduce distributed algorithms for the optimal control of distributed energy resources, i
NASA Astrophysics Data System (ADS)
Milić, Ivan; Atanacković, Olga
2014-10-01
State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme.
Curvilinear grids for sinuous river channels
NASA Technical Reports Server (NTRS)
Tatom, F. B.; Waldrop, W. R.; Smith, S. R.
1980-01-01
In order to effectively analyze the flow in sinuous river channels, a curvilinear grid system was developed for use in the appropriate hydrodynamic code. The CENTERLINE program was designed to generate a two dimensional grid for this purpose. The Cartesian coordinates of a series of points along the boundaries of the sinuous channel represent the primary input to CENTERLINE. The program calculates the location of the river centerline, the distance downstream along the centerline, and both radius of curvature and channel width as a function of such distance downstream. These parameters form the basis for the generation of the curvilinear grid. Based on input values for longitudinal and lateral grid spacing, the corresponding grid system is generated and a file is created containing the appropriate parameters for use in the associated explicit finite difference hydrodynamic programs. Because of the option for a nonuniform grid, grid spacing can be concentrated in areas containing the largest flow gradients.
Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1980-01-01
The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations.
NASA Astrophysics Data System (ADS)
Takenaka, H.; Komatsu, M.; Toyokuni, G.; Nakamura, T.; Okamoto, T.
2015-12-01
A simple and efficient finite-difference scheme is developed to compute seismic wave propagation for a partial spherical shell model of a three-dimensionally (3-D) heterogeneous global earth structure. This new scheme solves the elastodynamic equations in the "quasi-Cartesian" coordinate system similar to a local Cartesian one, instead of the spherical coordinate system, with a staggered-grid finite-difference method in time domain (FDTD) which is one of the most popular numerical methods in seismic motion simulations for local to regional scale models. The proposed scheme may be useful for modeling seismic wave propagation in a very large region of sub-global scale beyond regional and less than global ones, where the effects of roundness of earth cannot be ignored. In "quasi-Cartesian" coordinates, x, y, and z are set to be locally in directions of latitude, longitude and depth, respectively. The stencil for each of the x-derivatives then depends on the depth coordinate at the evaluation point, while the stencil for each of the y-derivatives varies with both coordinates of the depth and latitude. In order to reduce lateral variations of the horizontal finite-difference stencils over the computational domain, we move the target area to a location around the equator of the computational spherical coordinate system using a way similar to the conversion from equatorial coordinates to ecliptic coordinates. The developed scheme can be easily implemented in 3-D Cartesian FDTD codes for local to regional scale modeling by changing a very small part of the codes. Our scheme may be able to open a window for multi-scale modeling of seismic wave propagation in scales from sub-global to local one.
Development and Applications of 3D Cartesian CFD Technology
NASA Technical Reports Server (NTRS)
Melton, John E.; Berger, Marsha J.; VanDalsem, William (Technical Monitor)
1994-01-01
The urgent need for dramatic reductions in aircraft design cycle time is focusing scrutiny upon all aspects of computational fluid dynamics (CFD). These reductions will most likely come not from increased reliance upon user-interactive (and therefore time-expensive) methods, but instead from methods that can be fully automated and incorporated into 'black box' solutions. In comparison with tetrahedral methods, three-dimensional Cartesian grid approaches are in relative infancy, but initial experiences with automated Cartesian techniques are quite promising. Our research is targeted at furthering the development of Cartesian methods so that they can become key elements of a completely automatic grid generation/flow solution procedure applicable to the Euler analysis of complex aircraft geometries.
Software for Automated Generation of Cartesian Meshes
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Melton, John E.; Berger, Marshal J.
2006-01-01
Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.
Flexible Two-Dimensional Square-Grid Coordination Polymers: Structures and Functions
Kajiro, Hiroshi; Kondo, Atsushi; Kaneko, Katsumi; Kanoh, Hirofumi
2010-01-01
Coordination polymers (CPs) or metal-organic frameworks (MOFs) have attracted considerable attention because of the tunable diversity of structures and functions. A 4,4′-bipyridine molecule, which is a simple, linear, exobidentate, and rigid ligand molecule, can construct two-dimensional (2D) square grid type CPs. Only the 2D-CPs with appropriate metal cations and counter anions exhibit flexibility and adsorb gas with a gate mechanism and these 2D-CPs are called elastic layer-structured metal-organic frameworks (ELMs). Such a unique property can make it possible to overcome the dilemma of strong adsorption and easy desorption, which is one of the ideal properties for practical adsorbents. PMID:21152303
Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.
Mathiowetz, A. M.; Goddard, W. A.
1995-01-01
Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better. PMID:7549885
A Cartesian embedded boundary method for hyperbolic conservation laws
Sjogreen, B; Petersson, N A
2006-12-04
The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
2006-01-01
A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.
ERIC Educational Resources Information Center
Planinsic, G.; Kos, M.; Jerman, R.
2004-01-01
It is quite easy to make a version of the well known Cartesian diver experiment that uses two immiscible liquids. This allows students to test their knowledge of density and pressure in explaining the diver's behaviour. Construction details are presented here together with a mathematical model to explain the observations.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Technical Reports Server (NTRS)
Chen, S. C.
1988-01-01
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Lalonde, R; Hayzoun, K; Selimi, F; Mariani, J; Strazielle, C
2003-11-01
Grid2(ho/ho) is a loss of function gene mutation resulting in abnormal dendritic arborizations of Purkinje cells. These mutants were compared in a series of motor coordination tests requiring balance and equilibrium to nonataxic controls (Grid2(ho/+)) and to a double mutant (Grid2(ho/Lc)) with an inserted Lc mutation. The performance of Grid2(ho/ho) mutant mice was poorer than that of controls on stationary beam, coat hanger, unsteady platform, and rotorod tests. Grid2(ho/Lc) did not differ from Grid2(Lc/+) mice. However, the insertion of the Lc mutation in Grid2(ho/Lc) potentiated the deficits found in Grid2(ho/ho) in stationary beam, unsteady platform, and rotorod tests. These results indicate a deleterious effect of the Lc mutation on Grid2-deficient mice.
SAR imagery in non-Cartesian geometries
NASA Astrophysics Data System (ADS)
Dendal, Didier
1995-11-01
The subject of the reported work is the improvement of geometrical models for a SAR scanning in pushbroom, spotlight, scansar or bistatic imaging modes. This research has been motivated by the planetary cornerstone mission of ESA's long term program for European Space Science ('rendezvous' with a comet, and fly-bys of asteroids). In this specific context, the synthetic aperture radar is destined for an important role, but the rules and standard backgrounds of the Cartesian geometry are no longer justified. Several new techniques are proposed to handle with an optimal precision the data relative to celestial bodies with a complex geometry (coherent and non-coherent imagery). On the basis of a mathematical rigor (singleness of solutions, convergence of processes, biunivocity of transformations and generalizations), a lot of scenarios are discussed with key relations established (plane and spherical models, bodies with a symmetry of revolution and general bodies, specific sensor(s) trajectories as fly-bys or flight into orbit with the possibility of an approaching probe). The four methods developed are the tomographic analogy of radar principles (only known, previously, in the usual case of a straight line flight at constant altitude over a plane surface) and Hilbertian techniques for a direct adaptation to the scanned surface geometry, an automated autofocusing which enhances the contrast resulting from a Cartesian reconstruction and the coordinates transformation where the real space is converted into a fictitious space where Cartesian algorithms are fully rigorous. Beyond the fact that an interpolation step is often unavoidable, the major conclusion of the research is that all the prospected techniques are complementary and that the choice between the methods has to be made according to geometry, objectives and time requirements (reconstruction on board or not). In particular, coordinates transformation techniques are worthy of commendation in the case of plane
Irreducible Cartesian tensors of highest weight, for arbitrary order
NASA Astrophysics Data System (ADS)
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
NASA Astrophysics Data System (ADS)
Zhang, Li; Jabbari, Faryar; Brown, Tim; Samuelsen, Scott
2014-12-01
Plug-in electric vehicles (PEVs) shift energy consumption from petroleum to electricity for the personal transportation sector. This work proposes a decentralized charging protocol for PEVs with grid operators updating the cost signal. Each PEV calculates its own optimal charging profile only once based on the cost signal, after it is plugged in, and sends the result back to the grid operators. Grid operators only need to aggregate charging profiles and update the load and cost. The existing PEV characteristics, national household travel survey (NHTS), California Independent System Operator (CAISO) demand, and estimates for future renewable generation in California are used to simulate PEV operation, PEV charging profiles, grid demand, and grid net load (demand minus renewable). Results show the proposed protocol has good performance for overnight net load valley filling if the costs to be minimized are proportional to the net load. Annual results are shown in terms of overnight load variation and comparisons are made with grid level valley filling results. Further, a target load can be approached in the same manner by using the gap between current load and the target load as the cost. The communication effort involved is quite modest.
Sink or Swim: The Cartesian Diver.
ERIC Educational Resources Information Center
Pinkerton, K. David
2001-01-01
Presents the activity of Cartesian divers which demonstrates the relationship between pressure, temperature, volume, and buoyancy. Includes both instructor information and student activity sheet. (YDS)
Tao, Liang; McCurdy, C.W.; Rescigno, T.N.
2008-11-25
We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.
Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing
Si, Weijian; Qu, Xinggen; Qu, Zhiyu
2015-01-01
This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods. PMID:26343658
NASA Technical Reports Server (NTRS)
Lopez, Isaac; Follen, Gregory J.; Gutierrez, Richard; Foster, Ian; Ginsburg, Brian; Larsson, Olle; Martin, Stuart; Tuecke, Steven; Woodford, David
2000-01-01
This paper describes a project to evaluate the feasibility of combining Grid and Numerical Propulsion System Simulation (NPSS) technologies, with a view to leveraging the numerous advantages of commodity technologies in a high-performance Grid environment. A team from the NASA Glenn Research Center and Argonne National Laboratory has been studying three problems: a desktop-controlled parameter study using Excel (Microsoft Corporation); a multicomponent application using ADPAC, NPSS, and a controller program-, and an aviation safety application running about 100 jobs in near real time. The team has successfully demonstrated (1) a Common-Object- Request-Broker-Architecture- (CORBA-) to-Globus resource manager gateway that allows CORBA remote procedure calls to be used to control the submission and execution of programs on workstations and massively parallel computers, (2) a gateway from the CORBA Trader service to the Grid information service, and (3) a preliminary integration of CORBA and Grid security mechanisms. We have applied these technologies to two applications related to NPSS, namely a parameter study and a multicomponent simulation.
The cancer cell 'energy grid': TGF-β1 signaling coordinates metabolism for migration.
Jiang, Lei; Deberardinis, Ralph; Boothman, David A
2015-01-01
Cancer cells have an increased reliance on lipogenesis, which is required for uncontrolled cell division. We recently reported transcriptional and functional 'reprogramming' of the cellular energy grid, allowing cancer cells to divert metabolism from biosynthesis to bioenergetic pathways and thus supplying enhanced mobility during epithelial-mesenchymal transition (EMT) induced by transforming growth factor β (TGF-β1) (Fig. 1). PMID:27308459
Coordinating the Global Information Grid Initiative with the NG9-1-1 Initiative
Michael Schmitt
2008-05-01
As the Department of Defense develops the Global Information Grid, the Department of Transportation develops the Next Generation 9-1-1 system. Close examinations of these initiatives show that the two are similar in architectures, applications, and communications interoperability. These similarities are extracted from the lowest user level to the highest commander rank that will be involved in each network. Once the similarities are brought into perspective, efforts should be made to collaborate between the two departments.
CUDA accelerated uniform re-sampling for non-Cartesian MR reconstruction.
Feng, Chaolu; Zhao, Dazhe
2015-01-01
A grid-driven gridding (GDG) method is proposed to uniformly re-sample non-Cartesian raw data acquired in PROPELLER, in which a trajectory window for each Cartesian grid is first computed. The intensity of the reconstructed image at this grid is the weighted average of raw data in this window. Taking consider of the single instruction multiple data (SIMD) property of the proposed GDG, a CUDA accelerated method is then proposed to improve the performance of the proposed GDG. Two groups of raw data sampled by PROPELLER in two resolutions are reconstructed by the proposed method. To balance computation resources of the GPU and obtain the best performance improvement, four thread-block strategies are adopted. Experimental results demonstrate that although the proposed GDG is more time consuming than traditional DDG, the CUDA accelerated GDG is almost 10 times faster than traditional DDG. PMID:26406102
NASA Technical Reports Server (NTRS)
Smith, R. E.
1981-01-01
A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.
Rabow, A. A.; Scheraga, H. A.
1996-01-01
We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints. PMID:8880904
A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID
Feng, Xueshang; Zhang, Man; Zhou, Yufen
2014-09-01
In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.
On automating domain connectivity for overset grids
NASA Technical Reports Server (NTRS)
Chiu, Ing-Tsau
1994-01-01
An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximated body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian Systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems.
A Cartesian cut cell method for rarefied flow simulations around moving obstacles
NASA Astrophysics Data System (ADS)
Dechristé, G.; Mieussens, L.
2016-06-01
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including a 3D unsteady simulation of the Crookes radiometer.
Parameter Studies, time-dependent simulations and design with automated Cartesian methods
NASA Technical Reports Server (NTRS)
Aftosmis, Michael
2005-01-01
Over the past decade, NASA has made a substantial investment in developing adaptive Cartesian grid methods for aerodynamic simulation. Cartesian-based methods played a key role in both the Space Shuttle Accident Investigation and in NASA's return to flight activities. The talk will provide an overview of recent technological developments focusing on the generation of large-scale aerodynamic databases, automated CAD-based design, and time-dependent simulations with of bodies in relative motion. Automation, scalability and robustness underly all of these applications and research in each of these topics will be presented.
Minimization of deviations of gear real tooth surfaces determined by coordinate measurements
NASA Technical Reports Server (NTRS)
Litvin, F. L.; Kuan, C.; Wang, J.-C.; Handschuh, R. F.; Masseth, J.; Maruyama, N.
1992-01-01
The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.
Turing instabilities on Cartesian product networks
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-01-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory. PMID:26245138
Turing instabilities on Cartesian product networks.
Asllani, Malbor; Busiello, Daniel M; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-01-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory. PMID:26245138
Turing instabilities on Cartesian product networks
NASA Astrophysics Data System (ADS)
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-08-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory.
Hassouna, M Sabry; Farag, A A
2007-09-01
A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.
Moment Closures on Two-Dimensional Cartesian Grids
Garrett, Charles K.
2015-07-31
Some moment methods for kinetic equations are complicated and take time to develop. Over the course of a couple years, this software was developed to test different closures on standard test problems in the literature. With this software, researchers in the field of moment closures will be able to rapidly test new methods.
NASA Astrophysics Data System (ADS)
Melaaen, M. C.
1992-02-01
Tensor calculus is presently employed to furnish both necessary coordinate and velocity transformations in the present use of two different finite-volume methods for discretization of conservation equations in 3D curvilinear nonorthogonal coordinates. While one method is based on the nonstaggered grid arrangement and employs Cartesian velocity components as dependent variables in the momentum equations, the other combines a staggered grid arrangement with physical covariant velocity projections in a locally fixed coordinate system. In the second part of this work, a comparative evaluation of the two methods indicates that while results of comparable accuracy are achieved after a similar number of iterations, the staggered method may be recommended for curvilinear nonorthogonal coordinate problems due to its reduced memory and computational requirements.
Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1996-01-01
A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
Near-Body Grid Adaption for Overset Grids
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2016-01-01
A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.
Surface Generation and Cartesian Mesh Support
NASA Technical Reports Server (NTRS)
Haimes, Robert
2004-01-01
This document serves as the final report for the grant titled Surface Generation and Cartesian Mesh Support . This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cart3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.
Grossberg, Stephen; Pilly, Praveen K
2014-02-01
A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC ('neural relativity'). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data. PMID:24366136
Grossberg, Stephen; Pilly, Praveen K
2014-02-01
A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC ('neural relativity'). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.
NASA Astrophysics Data System (ADS)
de Zelicourt, Diane; Ge, Liang; Sotiropoulos, Fotis; Yoganathan, Ajit
2008-11-01
Image-guided computational fluid dynamics has recently gained attention as a tool for predicting the outcome of different surgical scenarios. Cartesian Immersed-Boundary methods constitute an attractive option to tackle the complexity of real-life anatomies. However, when such methods are applied to the branching, multi-vessel configurations typically encountered in cardiovascular anatomies the majority of the grid nodes of the background Cartesian mesh end up lying outside the computational domain, increasing the memory and computational overhead without enhancing the numerical resolution in the region of interest. To remedy this situation, the method presented here superimposes local mesh refinement onto an unstructured Cartesian grid formulation. A baseline unstructured Cartesian mesh is generated by eliminating all nodes that reside in the exterior of the flow domain from the grid structure, and is locally refined in the vicinity of the immersed-boundary. The potential of the method is demonstrated by carrying out systematic mesh refinement studies for internal flow problems ranging in complexity from a 90 deg pipe bend to an actual, patient-specific anatomy reconstructed from magnetic resonance.
A spectral element shallow water model on spherical geodesic grids
NASA Astrophysics Data System (ADS)
Giraldo, Francis X.
2001-04-01
The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained from the generalized icosahedral grid introduced previously (Giraldo FX. Lagrange-Galerkin methods on spherical geodesic grids: the shallow water equations. Journal of Computational Physics 2000; 160: 336-368). The equations are written in Cartesian co-ordinates that introduce an additional momentum equation, but the pole singularities disappear. This paper represents a departure from previously published work on solving the shallow water equations on the sphere in that the equations are all written, discretized, and solved in three-dimensional Cartesian space. Because the equations are written in a three-dimensional Cartesian co-ordinate system, the algorithm simplifies into the integration of surface elements on the sphere from the fully three-dimensional equations. A mapping (Song Ch, Wolf JP. The scaled boundary finite element method - alias consistent infinitesimal finite element cell method - for diffusion. International Journal for Numerical Methods in Engineering 1999; 45: 1403-1431) which simplifies these computations is described and is shown to contain the Eulerian version of the method introduced previously by Giraldo (Journal of Computational Physics 2000; 160: 336-368) for the special case of triangular elements. The significance of this mapping is that although the equations are written in Cartesian co-ordinates, the mapping takes into account the curvature of the high-order spectral elements, thereby allowing the elements to lie entirely on the surface of the sphere. In addition, using this mapping simplifies all of the three-dimensional spectral-type finite element surface integrals because any of the typical two-dimensional planar finite element or spectral element basis functions found in any textbook (for example, Huebner et al
Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.
NASA Technical Reports Server (NTRS)
Rumsey, Christopher Lockwood
1991-01-01
A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.
NASA Astrophysics Data System (ADS)
Chen, Lin; Huang, Jianpan; Zhang, Ting; Li, Jing; Cai, Congbo; Cai, Shuhui
2016-11-01
Spatiotemporally encoded (SPEN) single-shot MRI is an emerging ultrafast technique, which is capable of spatially selective acquisition and reduced field-of-view imaging. Compared to uniform sampling, variable density sampling has great potential in reducing aliasing artifacts and improving sampling efficiency. In this study, variable density spiral trajectory and non-Cartesian super-resolved (SR) reconstruction method are developed for SPEN MRI. The gradient waveforms design of spiral trajectory is mathematically described as an optimization problem subjected to the limitations of hardware. Non-Cartesian SR reconstruction with specific gridding method is developed to retrieve a resolution enhanced image from raw SPEN data. The robustness and efficiency of the proposed methods are demonstrated by numerical simulation and various experiments. The results indicate that variable density SPEN MRI can provide better spatial resolution and fewer aliasing artifacts compared to Cartesian counterpart. The proposed methods will facilitate the development of variable density SPEN MRI.
A Cartesian Adaptive Level Set Method for Two-Phase Flows
NASA Technical Reports Server (NTRS)
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
The Cover Time of Cartesian Product Graphs
NASA Astrophysics Data System (ADS)
Abdullah, Mohammed; Cooper, Colin; Radzik, Tomasz
Let P = G□H be the cartesian product of graphs G,H. We relate the cover time COV[P] of P to the cover times of its factors. When one of the factors is in some sense larger than the other, its cover time dominates, and can become of the same order as the cover time of the product as a whole. Our main theorem effectively gives conditions for when this holds. The probabilistic technique which we introduce, based on the blanket time, is more general and may be of independent interest, as might some of our lemmas.
Pilly, Praveen K; Grossberg, Stephen
2012-05-01
Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and exhibit remarkable regular hexagonal spatial firing patterns. They also exhibit a gradient of spatial scales along the dorsoventral axis of the MEC, with neighboring cells at a given dorsoventral location having different spatial phases. A neural model shows how a hierarchy of self-organizing maps, each obeying the same laws, responds to realistic rat trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with unimodal firing fields that fit neurophysiological data about their development in juvenile rats. The hippocampal place fields represent much larger spaces than the grid cells to support navigational behaviors. Both the entorhinal and hippocampal self-organizing maps amplify and learn to categorize the most energetic and frequent co-occurrences of their inputs. Top-down attentional mechanisms from hippocampus to MEC help to dynamically stabilize these spatial memories in both the model and neurophysiological data. Spatial learning through MEC to hippocampus occurs in parallel with temporal learning through lateral entorhinal cortex to hippocampus. These homologous spatial and temporal representations illustrate a kind of "neural relativity" that may provide a substrate for episodic learning and memory.
NASA Technical Reports Server (NTRS)
Moore, Reagan W.; Jagatheesan, Arun; Rajasekar, Arcot; Wan, Michael; Schroeder, Wayne
2004-01-01
The "Grid" is an emerging infrastructure for coordinating access across autonomous organizations to distributed, heterogeneous computation and data resources. Data grids are being built around the world as the next generation data handling systems for sharing, publishing, and preserving data residing on storage systems located in multiple administrative domains. A data grid provides logical namespaces for users, digital entities and storage resources to create persistent identifiers for controlling access, enabling discovery, and managing wide area latencies. This paper introduces data grids and describes data grid use cases. The relevance of data grids to digital libraries and persistent archives is demonstrated, and research issues in data grids and grid dataflow management systems are discussed.
Schäfer, Bernhard; Greisch, Jean-François; Faus, Isabelle; Bodenstein, Tilmann; Šalitroš, Ivan; Fuhr, Olaf; Fink, Karin; Schünemann, Volker; Kappes, Manfred M; Ruben, Mario
2016-08-26
The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism-driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe(II) 4 L4 ](8+) complexes were determined by X-ray diffraction, and the distinctness of the products was confirmed by ion-mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe(II) spin crossover vs. a blocked Fe(II) high-spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology.
Schäfer, Bernhard; Greisch, Jean-François; Faus, Isabelle; Bodenstein, Tilmann; Šalitroš, Ivan; Fuhr, Olaf; Fink, Karin; Schünemann, Volker; Kappes, Manfred M; Ruben, Mario
2016-08-26
The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism-driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe(II) 4 L4 ](8+) complexes were determined by X-ray diffraction, and the distinctness of the products was confirmed by ion-mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe(II) spin crossover vs. a blocked Fe(II) high-spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology. PMID:27411212
On automating domain connectivity for overset grids
NASA Technical Reports Server (NTRS)
Chiu, Ing-Tsau; Meakin, Robert L.
1995-01-01
An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.
A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction
NASA Technical Reports Server (NTRS)
Hood, Caroline; Frendi, Abdelkader
2006-01-01
This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
Chassin, David P.; Kiesling, Lynne
2008-10-15
The project highlights the idea that technology-enabled decentralized coordination can achieve the same, or better, economic and reliability benefits when compared to utility-focused centralized physical and economic control. Among the design's unique features was a retail double auction with five-minute market-clearing intervals that included residential customers as direct, active market participants. (author)
Electrostatic PIC with adaptive Cartesian mesh
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert
2016-05-01
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.
An adaptive Cartesian control scheme for manipulators
NASA Technical Reports Server (NTRS)
Seraji, H.
1987-01-01
A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.
NASA Technical Reports Server (NTRS)
Swinbank, Richard; Purser, James
2006-01-01
Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.
Tao, Liang; McCurdy, Bill; Rescigno, Tom
2010-06-10
Our previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H$_2$ with fixed-nuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1994-01-01
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Martí, José María; Müller, Ewald
2015-12-01
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates.
Coherence Pathways with Cartesian Product Operators. The C3PO Method
NASA Astrophysics Data System (ADS)
Kingsley, P. B.
The product-operator formalism using the Cartesian operator basis was modified, and the notation of Ix(φ) = Ixcos φ + Iysin φ and Iy(φ) = Iycos φ - Ixsin φ simplified the product-operator description of uncoupled or weakly coupled spins in multipulse sequences with arbitrary pulse phases and chemical-shift precessions. The compact Cartesian coordinate product- operator (C3PO) formalism is more compact than any other proposed basis set, easily provides complete coherence-pathway information, and provides better visualization than the original Cartesian basis set. Formulas for evolution under radiofrequency pulses, chemical-shift precession with spin-spin coupling, and multiple-quantum coherences are provided for weakly coupled IS and I 3S spin systems ( I = S = {1}/{2}) and for a strongly coupled IS (AB) spin system. Formulas are also provided for a spin coupled to an S = 1 spin. The C3PO formalism is compared with the spherical basis set, and examples are provided for STEAM-localized spectroscopy, COSY, and a strongly coupled AB spin system.
Rasche, Volker; Bornstedt, Axel; Hombach, Vinzenz
2008-03-01
The variable-kernel extent technique is applied for providing local high-resolution images from k-space data sampled on a Cartesian sampling grid with gradually decreasing sampling density in the phase-encoding direction. The approach is based on a variable spatial resolution reconstruction technique providing gradually decreasing resolution in the phase-encoding direction with increasing distance to the image center, while preserving full spatial resolution in a narrow slab centered in spatial domain. Reconstruction is performed by a variable convolution kernel gridding technique. The convolution kernel width is chosen proportional to the k-space sampling spacing to utilize the respective apodization in the image for reduction of the aliasing artifacts. Application of this technique to carotid artery wall imaging shows the potential of the technique for a significant reduction of image acquisition time without sacrificing image quality in the region of the carotid arteries.
Lin, Dejun
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
NASA Astrophysics Data System (ADS)
Lin, Dejun
2015-09-01
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
An adaptive phase alignment algorithm for cartesian feedback loops
NASA Astrophysics Data System (ADS)
Gimeno-Martin, A.; Pardo-Martin, J.; Ortega-Gonzalez, F.
2010-01-01
An adaptive algorithm to correct phase misalignments in Cartesian feedback linearization loops for power amplifiers has been presented. It yields an error smaller than 0.035 rad between forward and feedback loop signals once convergence is reached. Because this algorithm enables a feedback system to process forward and feedback samples belonging to almost the same algorithm iteration, it is suitable to improve the performance not only of power amplifiers but also any other digital feedback system for communications systems and circuits such as all digital phase locked loops. Synchronizing forward and feedback paths of Cartesian feedback loops takes a small period of time after the system starts up. The phase alignment algorithm needs to converge before the feedback Cartesian loop can start its ideal behavior. However, once the steady state is reached, both paths can be considered synchronized, and the Cartesian feedback loop will only depend on the loop parameters (open-loop gain, loop bandwidth, etc.). It means that the linearization process will also depend only on these parameters since the misalignment effect disappears. Therefore, this algorithm relieves the power amplifier linearizer circuit design of any task required for solving phase misalignment effects inherent to Cartesian feedback systems. Furthermore, when a feedback Cartesian loop has to be designed, the designer can consider that forward and feedback paths are synchronized, since the phase alignment algorithm will do this task. This will reduce the simulation complexity. Then, all efforts are applied to determining the suitable loop parameters that will make the linearization process more efficient.
Umbrella integration in two or more reaction coordinates.
Kästner, Johannes
2009-07-21
Umbrella integration is a method to analyze umbrella sampling simulations by calculating and integrating the mean force. Here, the method is extended to multidimensional reaction coordinates. Approximation of the probability distribution obtained from sampling by a multivariate normal distribution allows to calculate the mean force from the average and the covariance matrix of the reaction coordinate. Integration schemes of the free-energy gradient field are discussed. Integration on a real-space grid is compared to expansion of the gradient in a series of analytic functions (such as a Fourier analysis), which can be integrated, and the expansion of the gradient only at the window means in a series of analytic functions. The Fourier analysis was found particularly useful for periodic reaction coordinates, such as torsion angles. An expression is provided to calculate the Hessian of the free energy with respect to the reaction coordinates from sampling data. The utility of the method is demonstrated at the example of the free-energy surface of the alanine dipeptide in vacuum calculated with respect to the backbone torsion angles Phi and Psi. Relevance of the Jacobian term for non-Cartesian reaction coordinates is discussed.
On Multigrid for Overlapping Grids
Henshaw, W
2004-01-13
The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other important features include optimizations for Cartesian component grids, the use of over-relaxed Red-Black smoothers and the generation of coarse grid operators through Galerkin averaging. Numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for both Dirichlet and Neumann/mixed boundary conditions. A comparison to Krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory.
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
OVERGRID: A Unified Overset Grid Generation Graphical Interface
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin W. (Technical Monitor)
1999-01-01
This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.
NASA Astrophysics Data System (ADS)
Coelho, Pedro J.
2014-08-01
High order resolution schemes based on the NVD and TVD boundedness criteria are applied to radiative transfer problems using the DOM in two-dimensional unstructured triangular grids. The implementation of these schemes in unstructured grids requires approximations, and two implementations reported in the literature are compared with a new one. Three different methods have been used to calculate the gradient of the radiation intensity at the center of the control volumes. The various schemes are applied to several test problems, the results are compared with those obtained using the step scheme, the mean flux interpolation scheme and another high order scheme based on a truncated Taylor series expansion, and the most accurate implementations are identified. It is concluded that although the high order schemes perform much better than the others, they are not as accurate as in Cartesian coordinates, and their order of convergence is lower than in that case.
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers
Zanchi, Marta G.; Pauly, John M.; Scott, Greig C.
2010-01-01
A modified Cartesian feedback method called “frequency-offset Cartesian feedback” and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems. In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200–1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback. In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450
NASA Astrophysics Data System (ADS)
Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis
2016-11-01
A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.
2003-01-01
The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Murman, S. M.; Berger, M. J.
2003-01-01
This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.
A Cartesian parametrization for the numerical analysis of material instability
Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; Ostien, Jakob T.; Lai, Zhengshou
2016-02-25
We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less
Biangular Coordinates Redux: Discovering a New Kind of Geometry
ERIC Educational Resources Information Center
Winkel, Brian; Naylor, Michael
2010-01-01
Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the…
Branduardi, Davide; Faraldo-Gómez, José D
2013-09-10
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID
Branduardi, Davide; Faraldo-Gómez, José D
2013-09-10
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.
Implicit Approaches for Moving Boundaries in a 3-D Cartesian Method
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan
2003-01-01
This work considers numerical simulation of three-dimensional flows with time-evolving boundaries. Such problems pose a variety of challenges for numerical schemes, and have received a substantial amount of attention in the recent literature. Since such simulations are unsteady, time-accurate solution of the governing equations is required. In special cases, the body motion can be treated by a uniform rigid motion of the computational domain. For the more general situation of relative-body motion, however, this simplification is unavailable and the simulations require a mechanism for ensuring that the mesh evolves with the moving boundaries. This involves a "remeshing" of the computational domain (either localized or global) at each physical timestep, and places a premium on both the speed and robustness of the remeshing algorithms. This work presents a method which includes unsteady flow simulation, rigid domain motion, and relative body motion using a time-evolving Cartesian grid system in three dimensions.
Configuration space representation in parallel coordinates
NASA Technical Reports Server (NTRS)
Fiorini, Paolo; Inselberg, Alfred
1989-01-01
By means of a system of parallel coordinates, a nonprojective mapping from R exp N to R squared is obtained for any positive integer N. In this way multivariate data and relations can be represented in the Euclidean plane (embedded in the projective plane). Basically, R squared with Cartesian coordinates is augmented by N parallel axes, one for each variable. The N joint variables of a robotic device can be represented graphically by using parallel coordinates. It is pointed out that some properties of the relation are better perceived visually from the parallel coordinate representation, and that new algorithms and data structures can be obtained from this representation. The main features of parallel coordinates are described, and an example is presented of their use for configuration space representation of a mechanical arm (where Cartesian coordinates cannot be used).
The Cartesian Diver, Surface Tension and the Cheerios Effect
ERIC Educational Resources Information Center
Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai
2014-01-01
A Cartesian diver can be used to measure the surface tension of a liquid to a certain extent. The surface tension measurement is related to the two critical pressures at which the diver is about to sink and about to emerge. After sinking because of increasing pressure, the diver is repulsed to the centre of the vessel. After the pressure is…
The Cartesian Diver as an Aid for Teaching Respiratory Physiology
ERIC Educational Resources Information Center
Fitch, Greg K.
2004-01-01
The mechanism by which air enters the mammalian lung is difficult for many students of physiology. In particular, some students have trouble seeing how pressure can be transmitted through a fluid such as the intrapleural fluid and how the magnitude of that pressure can change. A Cartesian diver, an old-time child's toy, may be used as a visual aid…
A Lot of Good Physics in the Cartesian Diver
ERIC Educational Resources Information Center
De Luca, Roberto; Ganci, Salvatore
2011-01-01
The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…
Lin, Dejun
2015-01-01
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Lin, Dejun
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method
NASA Astrophysics Data System (ADS)
Zhang, Z.; Zhu, G.; Chen, X.
2011-12-01
We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.
Grid Interaction Technical Team Roadmap
2013-06-01
The mission of the Grid Interaction Technical Team (GITT) is to support a transition scenario to large scale grid-connected vehicle charging with transformational technology, proof of concept and information dissemination. The GITT facilitates technical coordination and collaboration between vehicle-grid connectivity and communication activities among U.S. DRIVE government and industry partners.
A finite volume Fokker-Planck collision operator in constants-of-motion coordinates
NASA Astrophysics Data System (ADS)
Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.
2006-04-01
TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.
Simulations of 6-DOF Motion with a Cartesian Method
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)
2003-01-01
Coupled 6-DOF/CFD trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-32/JDAM store separating from an F-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed, and compared with flight-test telemetry and photographic-derived data. Simulation results obtained with a sequential-static series of flow solutions are contrasted with results using a time-dependent flow solver. Both numerical methods show good agreement with the flight-test data through the first half of the simulations. The sequential-static and time-dependent methods diverge over the last half of the trajectory prediction. after the store produces peak angular rates. A cost comparison for the Cartesian method is included, in terms of absolute cost and relative to computing uncoupled 6-DOF trajectories. A detailed description of the 6-DOF method, as well as a verification of its accuracy, is provided in an appendix.
Analyzing correlation functions with tesseral and Cartesian spherical harmonics
Danielewicz, Pawel; Pratt, Scott
2007-03-15
The dependence of interparticle correlations on the orientation of particle relative momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real Cartesian harmonics. Mathematical properties of the lesser known Cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regard to determining angular features of emission regions is investigated. The considered final-state effects include identity interference, strong interactions, and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of Gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.
Frequency-Offset Cartesian Feedback for MRI Power Amplifier Linearization
Zanchi, Marta Gaia; Stang, Pascal; Kerr, Adam; Pauly, John Mark; Scott, Greig Cameron
2011-01-01
High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and DC offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called “frequency-offset Cartesian feedback” (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than DC, so that quadrature ghosts and DC errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system. PMID:20959264
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.
SU-E-I-41: Non-Cartesian MR Image Reconstruction with Integrated Gradient Non-Linearity Correction
Tao, S; Trzasko, JD; Polley, TW; Shu, Y; Bernstein, MA
2014-06-01
Purpose: Nonlinearities in the spatial encoding gradients of MRI systems cause geometric distortion in images. Typically, this is retrospectively corrected via image-domain interpolation (a.k.a., “gradwarp”) albeit with a loss of spatial resolution. For non-Cartesian MRI, the latter problem is exaggerated by noise and undersampling artifact. In this study, we describe a novel correction strategy that accounts for gradient nonlinearities during — rather than after — non-Cartesian MRI reconstruction, and demonstrate that this approach mitigates the resolution loss that can occur with standard methods. Methods: To test the proposed method, the American College of Radiology (ACR) quality control phantom was scanned on at 1.5 T (General Electric, v16.0, “zoom” gradient) using a 1.6x undersampled 3D non- Cartesian Shells trajectory (GRE, FOV=24 cm3, 120 shells, 16552 shots, 512 readout, matrix=2403). Image reconstruction was first performed via standard k-space density-compensated gridding and retrospectively corrected via cubic spline interpolation. Image reconstruction was then separately performed using a k-space and image-domain densitycompensated type-3 non-uniform fast Fourier transform (NUFFT), which provides a direct mapping between non-Cartesian k-space samples and warped image space voxel locations. Thus, no separate distortion correction procedure is needed for the proposed approach. The gradient distortion field was determined using vendor provided calibration data. Results: Phantom scan results show that both processing approaches successfully correct geometric distortion. However, visual inspection of the ACR phantom spatial resolution inserts shows that the proposed strategy preserves the resolution of the nominal (uncorrected) reconstruction while “gradwarp” imparts marked spatial blurring (especially for the 1.0 and 1.1 mm inserts) and thus resolution loss. Conclusion: We've presented a novel reconstruction strategy for non-Cartesian MRI
Plasticity of Intermediate Mechanics Students' Coordinate System Choice
ERIC Educational Resources Information Center
Sayre, Eleanor C.; Wittman, Michael C.
2008-01-01
We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their…
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
Claes Hellerström and Cartesian diver microrespirometry
Welsh, Michael
2016-01-01
Cartesian diver microrespirometry was introduced by Claes Hellerström at the Department of Histology/Medical Cell Biology at Uppsala University, Sweden, to determine rates of oxygen consumption in islets of Langerhans. The theory behind this method is touched upon and the main findings described. Glucose-stimulated beta cell respiration significantly contributes to increased ATP generation, which is a prerequisite for stimulated insulin secretion and synthesis. This has had major implications for understanding the beta cell stimulus–secretion coupling. PMID:27181825
Baker, Kyri; Jin, Xin; Vaidynathan, Deepthi; Jones, Wesley; Christensen, Dane; Sparn, Bethany; Woods, Jason; Sorensen, Harry; Lunacek, Monte
2016-08-04
Dataset demonstrating the potential benefits that residential buildings can provide for frequency regulation services in the electric power grid. In a hardware-in-the-loop (HIL) implementation, simulated homes along with a physical laboratory home are coordinated via a grid aggregator, and it is shown that their aggregate response has the potential to follow the regulation signal on a timescale of seconds. Connected (communication-enabled), devices in the National Renewable Energy Laboratory's (NREL's) Energy Systems Integration Facility (ESIF) received demand response (DR) requests from a grid aggregator, and the devices responded accordingly to meet the signal while satisfying user comfort bounds and physical hardware limitations.
NASA Astrophysics Data System (ADS)
Pathak, Harshavardhana S.; Shukla, Ratnesh K.
2016-08-01
A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of
[Cartesian misunderstanding as a cause of therapeutic failure].
Isler, H
1986-01-01
Headache patients disassociate themselves from their own automatic responses, relying on the traditional separation of body and mind. On the other hand, patients who obtain voluntary control of automatic functions by biofeedback training modify not only vegetative but also voluntary behaviour patterns, losing "neurotic" traits. The basic misconception of the separation of body and mind, Cartesian dualism, is now ingrained in our culture. In the 17th century Descartes asserted that concepts applied to the soul must be entirely different from those used for the body in order to improve comprehension of the immortality of the soul. This dualism also led to "enlightenment" and to many later social and philosophical developments. But his basic neurophysiology was obsolete when he wrote it down. Other models from mainstream natural philosophy were better compatible with observation and experiments. Gassendi assumed a "body soul" consisting of energy as the functional principle of the nervous system, and Willis accommodated a series of anticipations of 19th century discoveries within this model. No comparable progress resulted from Descartes' own medieval model. Cartesian dualism has become untenable in view of recent neuropsychology but it still obstructs our management of functional patients. Instead of reinforcing the delusion of separation of psyche and soma, we ought to encourage patients to understand that their malfunctioning organs are on-line with their emotions, and with their mind. PMID:2420000
NASA Technical Reports Server (NTRS)
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
Van Gorder, Robert A
2013-04-01
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.
Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle
Li, Tingwen; Dietiker, Jean-Francois; Zhang, Yongmin; Shahnam, Mehrdad
2011-12-01
In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.
The Overgrid Interface for Computational Simulations on Overset Grids
NASA Technical Reports Server (NTRS)
Chan, William M.; Kwak, Dochan (Technical Monitor)
2002-01-01
Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.
Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow
NASA Technical Reports Server (NTRS)
Berger, Marsha; Aftosmis, Michael J.
2011-01-01
The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data
NASA Astrophysics Data System (ADS)
Kalinić, Hrvoje; Mihanović, Hrvoje; Cosoli, Simone; Vilibić, Ivica
2015-11-01
In this paper, the Self-Organizing Map (SOM) method was applied to the surface currents data obtained between February and November 2008 by a network of high-frequency (HF) radars in the northern Adriatic. The sensitivity of the derived SOM solutions was tested in respect to the change of coordinate system of the data introduced to the SOM. In one experiment the original radial data measurements were used, and in the other experiment the Cartesian (total) current vectors derived from original radar data were analyzed. Although the computation of SOM solutions was not a demanding task, comparing both neural lattices yielded the nondeterministic polynomial time (NP) problem for which is difficult to propose a solution that will be globally optimal. Thus, we suggested utilizing the greedy algorithm with underlying assumption of 1-to-1 mapping between lattices. The results suggested that such solution could be local, but not global optimum and that the latter assumption could lower the obtained correlations between the patterns. However, without the assumption of 1-to-1 mapping between lattices, correlation between the derived SOM patterns was quite high, indicating that SOM mapping introduced to the radial current vectors and subsequent transformation into Cartesian coordinate system does not significantly affect obtained patterns in comparison to the SOM mapping done on the derived Cartesian current vectors. The documented similarity corroborates the use of total current vectors in various oceanographic studies, as being representative derivative of original radial measurements.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
Compact-range coordinate system established using a laser tracker.
Gallegos, Floyd H.; Bryce, Edwin Anthony
2006-12-01
Establishing a Cartesian coordinate reference system for an existing Compact Antenna Range using the parabolic reflector is presented. A SMX (Spatial Metrix Corporation) M/N 4000 laser-based coordinate measuring system established absolute coordinates for the facility. Electric field characteristics with positional movement correction are evaluated. Feed Horn relocation for alignment with the reflector axis is also described. Reference points are established for follow-on non-laser alignments utilizing a theodolite.
Saloner, David
2014-01-01
Purpose This study proposes and evaluates a novel method for generating efficient undersampling patterns for 3D Cartesian acquisition with compressed sensing (CS) and parallel imaging (PI). Methods Image quality achieved with schemes that accelerate data acquisition, including CS and PI, are sensitive to the design of the specific undersampling scheme used. Ideally random sampling is required to recover MR images from undersampled data with CS. In practice, pseudo-random sampling schemes are usually applied. Radial or spiral sampling either for Cartesian or non-Cartesian acquisitions has been using because of its favorable features such as interleaving flexibility. In this study, we propose to undersample data on the ky-kz plane of the 3D Cartesian acquisition by circularly selecting sampling points in a way that maintains the features of both random and radial or spiral sampling. Results The proposed sampling scheme is shown to outperform conventional random and radial or spiral samplings for 3D Cartesian acquisition and is found to be comparable to advanced variable-density Poisson-Disk sampling (vPDS) while retaining interleaving flexibility for dynamic imaging, based on the results with retrospective undersampling. Our preliminary results with the prospective implementation of the proposed undersampling strategy demonstrated its favorable features. Conclusions The proposed undersampling patterns for 3D Cartesian acquisition possess the desirable properties of randomization and radial or spiral trajectories. It provides easy implementation, flexible sampling, and high accuracy of image reconstruction with CS and PI. PMID:24649436
Optimal online robot trajectory generation in Cartesian space
NASA Astrophysics Data System (ADS)
Bazaz, Shafat A.; Tondu, Bertrand
1997-12-01
We propose the use of cubic quadratic cubic squared (CQCS) spline for the trajectory generation in Cartesian space. Use of CQCS spline gives simple analytical solution to minimum time trajectory generation with velocity and acceleration constraints. The expressions for wandering time and wandering acceleration are also calculated. A straight line path with constant maximum allowed speed in minimum time can be generated with this method. This property leads to interpolate two position points by constant speed straight line motion with smooth transition. The advantage of this method is that the trajectory thus obtained is traversed in minimum time while passing through the given intermediate points. The simplicity of this method makes its on-line computation possible.
Direct adaptive control of manipulators in Cartesian space
NASA Technical Reports Server (NTRS)
Seraji, H.
1987-01-01
A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.
Multi-fault Tolerance for Cartesian Data Distributions
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
2013-06-01
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale sys- tems. Algorithm-based fault tolerance (ABFT) is a promising approach that involves modications to the algorithm to recover from faults with lower over- heads than replicated storage and a signicant reduction in lost work compared to checkpoint-restart techniques. Fault-tolerant linear algebra (FTLA) algo- rithms employ additional processors that store parities along the dimensions of a matrix to tolerate multiple, simultaneous faults. Existing approaches as- sume regular data distributions (blocked or block-cyclic) with the failures of each data block being independent. To match the characteristics of failures on parallel computers, we extend these approaches to mapping parity blocks in several important ways. First, we handle parity computation for generalized Cartesian data distributions with each processor holding arbitrary subsets of blocks in a Cartesian-distributed array. Second, techniques to handle corre- lated failures, i.e., multiple processors that can be expected to fail together, are presented. Third, we handle the colocation of parity blocks with the data blocks and do not require them to be on additional processors. Several al- ternative approaches, based on graph matching, are presented that attempt to balance the memory overhead on processors while guaranteeing the same fault tolerance properties as existing approaches that assume independent fail- ures on regular blocked data distributions. The evaluation of these algorithms demonstrates that the additional desirable properties are provided by the pro- posed approach with minimal overhead.
Constructing the ASCI computational grid
BEIRIGER,JUDY I.; BIVENS,HUGH P.; HUMPHREYS,STEVEN L.; JOHNSON,WILBUR R.; RHEA,RONALD E.
2000-06-01
The Accelerated Strategic Computing Initiative (ASCI) computational grid is being constructed to interconnect the high performance computing resources of the nuclear weapons complex. The grid will simplify access to the diverse computing, storage, network, and visualization resources, and will enable the coordinated use of shared resources regardless of location. To match existing hardware platforms, required security services, and current simulation practices, the Globus MetaComputing Toolkit was selected to provide core grid services. The ASCI grid extends Globus functionality by operating as an independent grid, incorporating Kerberos-based security, interfacing to Sandia's Cplant{trademark},and extending job monitoring services. To fully meet ASCI's needs, the architecture layers distributed work management and criteria-driven resource selection services on top of Globus. These services simplify the grid interface by allowing users to simply request ''run code X anywhere''. This paper describes the initial design and prototype of the ASCI grid.
An Efficient Means of Adaptive Refinement Within Systems of Overset Grids
NASA Technical Reports Server (NTRS)
Meakin, Robert L.
1996-01-01
An efficient means of adaptive refinement within systems of overset grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend only a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian grids of varying levels of refinement. a novel off-body grid generation and management scheme provides the mechanism for carrying out adaptive refinement of off-body flow dynamics and solid body motion. The scheme allows for very efficient use of memory resources, and flow solvers and domain connectivity routines that can exploit the structure inherent to uniform Cartesian grids.
Internal Coordinate Molecular Dynamics: A Foundation for Multiscale Dynamics
2015-01-01
Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic, which adversely impacts the complexity and the robustness of the simulations. On the other hand, constraints can be easily placed in BAT coordinates by removing the degrees of freedom that need to be constrained. Thus, the internal coordinate MD (ICMD) offers an attractive alternative to Cartesian coordinate MD for developing multiscale MD method. The torsional MD method is a special adaptation of the ICMD method, where all the bond lengths and bond angles are kept rigid. The advantages of ICMD simulation methods are the longer time step size afforded by freezing high frequency degrees of freedom and performing a conformational search in the more important low frequency torsional degrees of freedom. However, the advancements in the ICMD simulations have been slow and stifled by long-standing mathematical bottlenecks. In this review, we summarize the recent mathematical advancements we have made based on spatial operator algebra, in developing a robust long time scale ICMD simulation toolkit useful for various applications. We also present the applications of ICMD simulations to study conformational changes in proteins and protein structure refinement. We review the advantages of the ICMD simulations over the Cartesian simulations when used with enhanced sampling methods and project the future use of ICMD simulations in protein dynamics. PMID:25517406
77 FR 38768 - Smart Grid Advisory Committee
Federal Register 2010, 2011, 2012, 2013, 2014
2012-06-29
... to Office of the National Coordinator for Smart Grid Interoperability, National Institute of... participate are invited to submit written statements to the Office of the National Coordinator for Smart Grid... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF...
76 FR 46279 - Smart Grid Advisory Committee
Federal Register 2010, 2011, 2012, 2013, 2014
2011-08-02
... National Institute of Standards and Technology Smart Grid Advisory Committee AGENCY: Department of Commerce, National Institute of Standards and Technology ACTION: Notice of open meeting. SUMMARY: The Smart Grid... should be sent to Office of the National Coordinator for Smart Grid Interoperability, National...
A HYBRID SOLAR WIND MODEL OF THE CESE+HLL METHOD WITH A YIN-YANG OVERSET GRID AND AN AMR GRID
Feng Xueshang; Zhang Shaohua; Xiang Changqing; Yang Liping; Jiang Chaowei; Wu, S. T.
2011-06-10
A hybrid three-dimensional (3D) MHD model for solar wind study is proposed in the present paper with combined grid systems and solvers. The computational domain from the Sun to Earth space is decomposed into the near-Sun and off-Sun domains, which are respectively constructed with a Yin-Yang overset grid system and a Cartesian adaptive mesh refinement (AMR) grid system and coupled with a domain connection interface in the overlapping region between the near-Sun and off-Sun domains. The space-time conservation element and solution element method is used in the near-Sun domain, while the Harten-Lax-Leer method is employed in the off-Sun domain. The Yin-Yang overset grid can avoid well-known singularity and polar grid convergence problems and its body-fitting property helps achieve high-quality resolution near the solar surface. The block structured AMR Cartesian grid can automatically capture far-field plasma flow features, such as heliospheric current sheets and shock waves, and at the same time, it can save significant computational resources compared to the uniformly structured Cartesian grid. A numerical study of the solar wind structure for Carrington rotation 2069 shows that the newly developed hybrid MHD solar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by comparisons with multiple solar and interplanetary observations.
Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates
Nagaitsev, S.; Kharkov, Y.; Morozov, I.A.; Zolkin, T.V.; /Chicago U.
2012-05-01
Several families of nonlinear accelerator lattices with integrable transverse motion were suggested recently. One of the requirements for the existence of two analytic invariants is a special longitudinal coordinate dependence of fields. This paper presents the particle motion analysis when a problem becomes integrable in the normalized polar coordinates. This case is distinguished from the others: it yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields (since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates). A number of interesting features are revealed: while the frequency of radial oscillations is independent of the amplitude, the spread of angular frequencies in a beam is absolute. A corresponding spread of frequencies of oscillations in the Cartesian coordinates is evaluated via the simulation of transverse Schottky noise.
NASA Astrophysics Data System (ADS)
Ebrahimi, F.; Blackman, E. G.
2016-06-01
For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard `Ω effect' (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations - even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Iterative reconstruction method for three-dimensional non-cartesian parallel MRI
NASA Astrophysics Data System (ADS)
Jiang, Xuguang
Parallel magnetic resonance imaging (MRI) with non-Cartesian sampling pattern is a promising technique that increases the scan speed using multiple receiver coils with reduced samples. However, reconstruction is challenging due to the increased complexity. Three reconstruction methods were evaluated: gridding, blocked uniform resampling (BURS) and non-uniform FFT (NUFFT). Computer simulations of parallel reconstruction were performed. Root mean square error (RMSE) of the reconstructed images to the simulated phantom were used as image quality criterion. Gridding method showed best RMSE performance. Two type of a priori constraints to reduce noise and artifacts were evaluated: edge preserving penalty, which suppresses noise and aliasing artifact in image while preventing over-smoothness, and object support penalty, which reduces background noise amplification. A trust region based step-ratio method that iteratively calculates the penalty coefficient was proposed for the penalty functions. Two methods to alleviate computation burden were evaluated: smaller over sampling ratio, and interpolation coefficient matrix compression. The performance were individually tested using computer simulations. Edge preserving penalty and object support penalty were shown to have consistent improvement on RMSE. The performance of calculated penalty coefficients on the two penalties were close to the best RMSE. Oversampling ratio as low as 1.125 was shown to have impact of less than one percent on RMSE for the radial sampling pattern reconstruction. The value reduced the three dimensional data requirement to less than 1/5 of what the conventional 2x grid needed. Interpolation matrix compression with compression ratio up to 50 percent showed small impact on RMSE. The proposed method was validated on 25MR data set from a GEMR scanner. Six image quality metrics were used to evaluate the performance. RMSE, normalized mutual information (NMI) and joint entropy (JE) relative to a reference
NASA Astrophysics Data System (ADS)
Pogson, E. M.; Bell, L.; Batumalai, V.; Koh, E. S.; Delaney, G.; Metcalfe, P.; Holloway, L.
2014-03-01
Cartesian co-ordinates, traditionally used for radiotherapy margins, calculated at 6 points, may not adequately represent changes in inter-observer contour variation as necessary to define a delineation margin. As a first step, this study compared the standard deviation (SD) in contour delineation using Polar and Cartesian co-ordinates for whole breast. Whole breast Clinical Target Volumes (CTV) were delineated by eight observers for 9 patients. The SD of contour position was determined for Polar co-ordinates at 1° increments for 5 slices and averaged across all patients. The mean centre of mass (COM) was used as the origin for the right breast, for the left the COM was shifted 1cm superiorly to avoid clipping. The SD was determined for Cartesian co-ordinates for medial-lateral and anterior-posterior positions. At slice Z=0cm considering Polar co-ordinates, the SD peaked medially reaching 3.55cm at 15° for the right breast, and 1.44cm at 171° for the left. The SD of the remaining slices maintained a similar distribution, with variation in the peak occurring within 10° of the Z=0cm positions. By comparison, for Cartesian co-ordinates at slice Z=0cm, the largest SD in the medial-lateral and anterior-posterior directions was 0.54/0.57cm and 1.03/0.67cm respectively for right/left breasts. The SD for inter-observer variation for whole breast varies with anatomical position. The maximum SD determined with Polar co-ordinates was greater than with Cartesian coordinates. A delineation margin may thus need to vary with angle over the entire structure and Cartesian co-ordinates may not be the best approach for margin determination for whole breast.
Finite element method formulation in polar coordinates for transient heat conduction problems
NASA Astrophysics Data System (ADS)
Duda, Piotr
2016-04-01
The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.
Al-Rizzo, Hussain M; Tranquilla, Jim M; Feng, Ma
2005-01-01
In this paper, we present a versatile mathematical formulation of a newly developed 3-D locally conformal Finite Difference (FD) thermal algorithm developed specificallyfor coupled electromagnetic (EM) and heat diffusion simulations utilizing Overlapping Grids (OGFD) in the Cartesian and cylindrical coordinate systems. The motivation for this research arises from an attempt to characterize the dominant thermal transport phenomena typically encountered during the process cycle of a high-power, microwave-assisted material processing system employing a geometrically composite cylindrical multimode heating furnace. The cylindrical FD scheme is only applied to the outer shell of the housing cavity whereas the Cartesian FD scheme is used to advance the temperature elsewhere including top and bottom walls, and most of the inner region of the cavity volume. The temperature dependency of the EM constitutive and thermo-physical parameters of the material being processed is readily accommodated into the OGFD update equations. The time increment, which satisfies the stability constraint of the explicit OGFD time-marching scheme, is derived. In a departure from prior work, the salient features of the proposed algorithm are first, the locally conformal discretization scheme accurately describes the diffusion of heat and second, significant heat-loss mechanisms usually encountered in microwave heating problems at the interfacial boundary temperature nodes have been considered. These include convection and radiation between the surface of the workload and air inside the cavity, heat convection and radiation between the inner cavity walls and interior cavity volume, and free cooling of the outermost cavity walls.
Sidler, Rolf; Carcione, José M.; Holliger, Klaus
2013-02-15
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
2014-07-15
Matlab Toolbox for simulating the impact of solar energy on the distribution grid. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving GridPV Toolbox information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feedermore » on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions.« less
Broderick, Robert; Quiroz, Jimmy; Grijalva, Santiago; Reno, Matthew; Coogan, Kyle
2014-07-15
Matlab Toolbox for simulating the impact of solar energy on the distribution grid. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving GridPV Toolbox information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feeder on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions.
Post, R.F.
1960-08-01
An electronic grid is designed employing magnetic forces for controlling the passage of charged particles. The grid is particularly applicable to use in gas-filled tubes such as ignitrons. thyratrons, etc., since the magnetic grid action is impartial to the polarity of the charged particles and, accordingly. the sheath effects encountered with electrostatic grids are not present. The grid comprises a conductor having sections spaced apart and extending in substantially opposite directions in the same plane, the ends of the conductor being adapted for connection to a current source.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
NASA Technical Reports Server (NTRS)
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
NASA Technical Reports Server (NTRS)
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary Cartesian-mesh flow solver is coupled with a three degree-offreedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves the complete system of aero-structural equations using a modular, loosely-coupled strategy which allows the lower-fidelity structural model to deform the highfidelity CFD model. The approach uses an open-source, 3-D discrete-geometry engine to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. This extended abstract includes a brief description of the architecture, along with some preliminary validation of underlying assumptions and early results on a generic 3D transport model. The final paper will present more concrete cases and validation of the approach. Preliminary results demonstrate convergence of the complete aero-structural system and investigate the accuracy of the approximations used in the formulation of the structural model.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
NASA Astrophysics Data System (ADS)
Paganoni, Marco
The EUAsiaGrid proposal contributes to the aims of the Research Infrastructures part of the EU Seventh Framework Programme (FP7) by promoting interoperation between the European and the Asian-Pacific Grids. The project, with a total number of 15 partners coordinated by INFN, started on April 1st 2008. It will disseminate the knowledge about the EGEE Grid infrastructure, organize specific training events and support applications both within the scientific communities with an already long experience in the Computing Grids (High Energy Physics, Computational Chemistry, Bioinformatics and Biomedics) and in the most recent ones (Social Sciences, Disaster Mitigation, Cultural Heritage). Ultimately the EUAsiaGrid project will pave the way towards a common e-Infrastructure with the European and the Asian Grids.
NASA Astrophysics Data System (ADS)
Hoeft, B.; Epting, U.; Koenig, T.
2008-07-01
While many fields relevant to Grid security are already covered by existing working groups, their remit rarely goes beyond the scope of the Grid infrastructure itself. However, security issues pertaining to the internal set-up of compute centres have at least as much impact on Grid security. Thus, this talk will present briefly the EU ISSeG project (Integrated Site Security for Grids). In contrast to groups such as OSCT (Operational Security Coordination Team) and JSPG (Joint Security Policy Group), the purpose of ISSeG is to provide a holistic approach to security for Grid computer centres, from strategic considerations to an implementation plan and its deployment. The generalised methodology of Integrated Site Security (ISS) is based on the knowledge gained during its implementation at several sites as well as through security audits, and this will be briefly discussed. Several examples of ISS implementation tasks at the Forschungszentrum Karlsruhe will be presented, including segregation of the network for administration and maintenance and the implementation of Application Gateways. Furthermore, the web-based ISSeG training material will be introduced. This aims to offer ISS implementation guidance to other Grid installations in order to help avoid common pitfalls.
General formulation of vibronic spectroscopy in internal coordinates.
Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo
2016-02-28
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.
General formulation of vibronic spectroscopy in internal coordinates
NASA Astrophysics Data System (ADS)
Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo
2016-02-01
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.
Sinusoidal error perturbation reveals multiple coordinate systems for sensorymotor adaptation.
Hudson, Todd E; Landy, Michael S
2016-02-01
A coordinate system is composed of an encoding, defining the dimensions of the space, and an origin. We examine the coordinate encoding used to update motor plans during sensory-motor adaptation to center-out reaches. Adaptation is induced using a novel paradigm in which feedback of reach endpoints is perturbed following a sinewave pattern over trials; the perturbed dimensions of the feedback were the axes of a Cartesian coordinate system in one session and a polar coordinate system in another session. For center-out reaches to randomly chosen target locations, reach errors observed at one target will require different corrections at other targets within Cartesian- and polar-coded systems. The sinewave adaptation technique allowed us to simultaneously adapt both dimensions of each coordinate system (x-y, or reach gain and angle), and identify the contributions of each perturbed dimension by adapting each at a distinct temporal frequency. The efficiency of this technique further allowed us to employ perturbations that were a fraction the size normally used, which avoids confounding automatic adaptive processes with deliberate adjustments made in response to obvious experimental manipulations. Subjects independently corrected errors in each coordinate in both sessions, suggesting that the nervous system encodes both a Cartesian- and polar-coordinate-based internal representation for motor adaptation. The gains and phase lags of the adaptive responses are not readily explained by current theories of sensory-motor adaptation.
Stromyer, Michael L.; Lilly, Cassandra P.; Dillner, Adam J.; Knaust, Jacqueline M.
2016-01-01
Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4′-bipyridine N,N′-dioxide (bpydo) are reported, namely poly[[tris(nitrato-κ2 O,O′)cerium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′)], [Ce(NO3)3(C10H8N2O2)2], poly[[tris(nitrato-κ2 O,O′)praeseodymium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′)], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ2 O,O′)neodymium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln III cations, forming interdigitating 44 grid-like layers extending parallel to (-101), where interdigitation of layers is promoted by C—H⋯O interactions between nitrate anions and bpydo ligands. The interdigitated layers are linked to sets of neighboring layers via further C—H⋯O and π–π interactions. PMID:26870578
Stromyer, Michael L; Lilly, Cassandra P; Dillner, Adam J; Knaust, Jacqueline M
2016-01-01
Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4'-bi-pyridine N,N'-dioxide (bpydo) are reported, namely poly[[tris-(nitrato-κ(2) O,O')cerium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Ce(NO3)3(C10H8N2O2)2], poly[[tris-(nitrato-κ(2) O,O')praeseodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ(2) O,O')neodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N'], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln (III) cations, forming inter-digitating 4(4) grid-like layers extending parallel to (-101), where inter-digitation of layers is promoted by C-H⋯O inter-actions between nitrate anions and bpydo ligands. The inter-digitated layers are linked to sets of neighboring layers via further C-H⋯O and π-π inter-actions. PMID:26870578
Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids
Burton, D.E.
1994-10-17
We consider the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH). Hydrodynamics algorithms are often formulated in a relatively ad hoc manner in which independent discretizations are proposed for mass, momentum, energy, and so forth. We show that, once discretizations for mass and momentum are stated, the remaining discretizations are very nearly uniquely determined, so there is very little latitude for variation. As has been known for some time, the kinetic energy discretization must follow directly from the momentum equation; and the internal energy must follow directly from the energy currents affecting the kinetic energy. A fundamental requirement (termed isentropicity) for numerical hydrodynamics algorithms is the ability to remain on an isentrope in the absence of heating or viscous forces and in the limit of small timesteps. We show that the requirements of energy conservation and isentropicity lead to the replacement of the usual volume calculation with a conservation integral. They further forbid the use of higher order functional representations for either velocity or stress within zones or control volumes, forcing the use of a constant stress element and a constant velocity control volume. This, in turn, causes the point and zone coordinates to formally disappear from the Cartesian formulation. The form of the work equations and the requirement for dissipation by viscous forces strongly limits the possible algebraic forms for artificial viscosity. The momentum equation and a center-of-mass definition lead directly to an angular momentum conservation law that is satisfied by the system. With a few straightforward substitutions, the Cartesian formulation can be converted to a multidimensional curvilinear one. The formulation in 2D symmetric geometry preserves rotational symmetry.
Simulation of disk-disk encounters with co-moving polar grids
NASA Technical Reports Server (NTRS)
Salo, Heikki
1990-01-01
The two-grid simulation method combining advantages of both polar and Cartesian mesh-codes is described. In addition to the stellar component reacting solely to gravitational forces, the gas component is included with dissipatively colliding particles. This allows fairly realistic simulation of planar encounters where both systems contain star plus gas disks.
On the Crossing Numbers of Cartesian Products of Stars and Graphs on Five Vertices
NASA Astrophysics Data System (ADS)
Klešč, Marián
There are known crossing numbers of Cartesian products of stars with all graphs of order at most four. In this paper we are dealing with the Cartesian products of stars with graphs on five vertices. We give the exact values of crossing numbers for some of these graphs and we summarise all known results concerning crossing numbers of these graphs. In addition, we give the crossing number of the join product of star and the cycle C 5 with one additional edge.
Towards Hybrid Overset Grid Simulations of the Launch Environment
NASA Astrophysics Data System (ADS)
Moini-Yekta, Shayan
A hybrid overset grid approach has been developed for the design and analysis of launch vehicles and facilities in the launch environment. The motivation for the hybrid grid methodology is to reduce the turn-around time of computational fluid dynamic simulations and improve the ability to handle complex geometry and flow physics. The LAVA (Launch Ascent and Vehicle Aerodynamics) hybrid overset grid scheme consists of two components: an off-body immersed-boundary Cartesian solver with block-structured adaptive mesh refinement and a near-body unstructured body-fitted solver. Two-way coupling is achieved through overset connectivity between the off-body and near-body grids. This work highlights verification using code-to-code comparisons and validation using experimental data for the individual and hybrid solver. The hybrid overset grid methodology is applied to representative unsteady 2D trench and 3D generic rocket test cases.
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei
2013-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-15
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
NASA Astrophysics Data System (ADS)
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
NASA Astrophysics Data System (ADS)
Mignone, A.
2014-08-01
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.
Tracking algorithms using log-polar mapped image coordinates
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.; Juday, Richard D.
1990-01-01
The use of log-polar image sampling coordinates rather than conventional Cartesian coordinates offers a number of advantages for visual tracking and docking of space vehicles. Pixel count is reduced without decreasing the field of view, with commensurate reduction in peripheral resolution. Smaller memory requirements and reduced processing loads are the benefits in working environments where bulk and energy are at a premium. Rotational and zoom symmetries of log-polar coordinates accommodate range and orientation extremes without computational penalties. Separation of radial and rotational coordinates reduces the complexity of several target centering algorithms, described below.
Continuous parallel coordinates.
Heinrich, Julian; Weiskopf, Daniel
2009-01-01
Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data.
Resolution enhancement in tilted coordinates
NASA Astrophysics Data System (ADS)
Hariri Naghadeh, Diako; Keith Morley, Christopher
2016-11-01
Deconvolution is applied to remove source wavelet effects from seismograms. The results are resolution enhancement that enables detection of thin layers. Following enhancement of resolution, low frequency and high angle reflectors, particularly at great depth, appear as low amplitude and semi-invisible reflectors that are difficult to track and pick. A new approach to enhance resolution is introduced that estimates a derivative using continuous wavelet transform in tilted coordinates. The results are compared with sparse spike deconvolution, curvelet deconvolution and inverse quality filtering in wavelet domain. The positive consequence of the new method is to increase sampling of high dip features by changing the coordinate system from Cartesian to tilted. To compare those methods a complex data set was chosen that includes high angle faults and chaotic mass transport complex. Image enhancement using curvelet deconvolution shows a chaotic system as a non-chaotic one. The results show that sparse spike deconvolution and inverse quality filtering in wavelet domain are able to enhance resolution more than curvelet deconvolution especially at great depth but it is impossible to follow steep dip reflectors after resolution enhancement using these methods, especially when their apparent dips are more than 45°. By estimating derivatives in a continuous wavelet transform from tilted data sets similar resolution enhancement as the other deconvolution methods is achieved but additionally steep dipping reflectors are imaged much better than others. Subtracted results of the enhanced resolution data set using new method and the other introduced methods show that steeply dipping reflectors are highlighted as a particular ability of the new method. The results show that high frequency recovery in Cartesian co-ordinate is accompanied by inability to image steeply dipping reflectors especially at great depths. Conversely recovery of high frequency data and imaging of the data
The National Grid Project: A system overview
NASA Technical Reports Server (NTRS)
Gaither, Adam; Gaither, Kelly; Jean, Brian; Remotigue, Michael; Whitmire, John; Soni, Bharat; Thompson, Joe; Dannenhoffer,, John; Weatherill, Nigel
1995-01-01
The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.
Freitas, Andreia C.; Wylezinska, Marzena; Birch, Malcolm J.; Petersen, Steffen E.; Miquel, Marc E.
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal
Numerical solution of the full potential equation using a chimera grid approach
NASA Technical Reports Server (NTRS)
Holst, Terry L.
1995-01-01
A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.
A three-dimensional hybrid grid generation technique with application to bodies in relative motion
Noack, R.W.; Steinbrenner, J.P.; Bishop, D.G.
1996-12-31
A three-dimensional hybrid grid generation technique is described. The method combines structured grids with unstructured triangular or tetrahedral meshes and Cartesian quadtree/octree grids to provide great flexibility in discretizing a domain. The method utilizes as input a set of structured quadrilateral or hexahedral cell grids that may overlap each other and may not completely cover the domain of interest. An advancing front grid generation algorithm is used to trim the structured grids and remove any overlap. The voids in the domain of interest are filled with unstructured triangular or tetrahedral cells. The method is applied to bodies in relative motion such as occurs in the separation of a store from an aircraft. Local grid restructuring is used to accommodate the motion of the bodies.
Advances in Distance-Based Hole Cuts on Overset Grids
NASA Technical Reports Server (NTRS)
Chan, William M.; Pandya, Shishir A.
2015-01-01
An automatic and efficient method to determine appropriate hole cuts based on distances to the wall and donor stencil maps for overset grids is presented. A new robust procedure is developed to create a closed surface triangulation representation of each geometric component for accurate determination of the minimum hole. Hole boundaries are then displaced away from the tight grid-spacing regions near solid walls to allow grid overlap to occur away from the walls where cell sizes from neighboring grids are more comparable. The placement of hole boundaries is efficiently determined using a mid-distance rule and Cartesian maps of potential valid donor stencils with minimal user input. Application of this procedure typically results in a spatially-variable offset of the hole boundaries from the minimum hole with only a small number of orphan points remaining. Test cases on complex configurations are presented to demonstrate the new scheme.
An assessment of unstructured grid technology for timely CFD analysis
NASA Technical Reports Server (NTRS)
Kinard, Tom A.; Schabowski, Deanne M.
1995-01-01
An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.
An assessment of unstructured grid technology for timely CFD analysis
NASA Astrophysics Data System (ADS)
Kinard, Tom A.; Schabowski, Deanne M.
1995-03-01
An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.
NASA Astrophysics Data System (ADS)
Foster, Ian
2001-08-01
The term "Grid Computing" refers to the use, for computational purposes, of emerging distributed Grid infrastructures: that is, network and middleware services designed to provide on-demand and high-performance access to all important computational resources within an organization or community. Grid computing promises to enable both evolutionary and revolutionary changes in the practice of computational science and engineering based on new application modalities such as high-speed distributed analysis of large datasets, collaborative engineering and visualization, desktop access to computation via "science portals," rapid parameter studies and Monte Carlo simulations that use all available resources within an organization, and online analysis of data from scientific instruments. In this article, I examine the status of Grid computing circa 2000, briefly reviewing some relevant history, outlining major current Grid research and development activities, and pointing out likely directions for future work. I also present a number of case studies, selected to illustrate the potential of Grid computing in various areas of science.
The Wigner-Eckart Theorem for Reducible Symmetric Cartesian Tensor Operators
NASA Astrophysics Data System (ADS)
Bouzas, Antonio O.
2016-08-01
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and Cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that constitute simultaneously a basis of the spaces of Cartesian and spherical irreducible tensors. As a consequence, we extend the Wigner-Eckart theorem to Cartesian irreducible tensor operators of any rank, and to totally symmetric reducible ones. We also discuss the tensorial structure of several standard spherical irreducible tensors such as ordinary, bipolar and tensor spherical harmonics, spin-polarization operators and multipole operators. As an application, we obtain an explicit expression for the derivatives of any order of spherical harmonics in terms of tensor spherical harmonics.
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.
Unstructured Grid Generation Techniques and Software
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K. (Editor)
1993-01-01
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.
MESH2D GRID GENERATOR DESIGN AND USE
Flach, G.; Smith, F.
2012-01-20
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
NASA Astrophysics Data System (ADS)
Muralidharan, Balaji; Menon, Suresh
2016-09-01
A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.
Solving Partial Differential Equations on Overlapping Grids
Henshaw, W D
2008-09-22
We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solution of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data.
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches. PMID:20236843
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data
NASA Astrophysics Data System (ADS)
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches.
NASA Astrophysics Data System (ADS)
Saiz, P.; Andreeva, J.; Cirstoiu, C.; Gaidioz, B.; Herrala, J.; Maguire, E. J.; Maier, G.; Rocha, R.
2008-07-01
Thanks to the Grid, users have access to computing resources distributed all over the world. The Grid hides the complexity and the differences of its heterogeneous components. In such a distributed system, it is clearly very important that errors are detected as soon as possible, and that the procedure to solve them is well established. We focused on two of its main elements: the workload and the data management systems. We developed an application to investigate the efficiency of the different centres. Furthermore, our system can be used to categorize the most common error messages, and control their time evolution.
[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].
Gysel, C
1979-01-01
In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
ERIC Educational Resources Information Center
Lelwica, Michelle Mary
2009-01-01
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…
ERIC Educational Resources Information Center
Earnest, Darrell Steven
2012-01-01
This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…
Real-time cartesian force feedback control of a teleoperated robot
NASA Technical Reports Server (NTRS)
Campbell, Perry
1989-01-01
Active cartesian force control of a teleoperated robot is investigated. An economical microcomputer based control method was tested. Limitations are discussed and methods of performance improvement suggested. To demonstrate the performance of this technique, a preliminary test was performed with success. A general purpose bilateral force reflecting hand controller is currently being constructed based on this control method.
Dynamic coordination of a self-reconfigurable manipulator system
NASA Technical Reports Server (NTRS)
Kim, Sungbok; Lee, Sukhan
1991-01-01
The authors present the dynamic coordination of a self-reconfigurable manipulator system capable of changing its mechanical structure according to given task requirements. The self-reconfiguration is achieved by reconfiguring the topology of a dual-arm system through serial, parallel, and bracing structures. Particular emphasis is placed on the dynamic coordination of two arms having three different dual-arm topologies. The authors develop the Cartesian space dynamic models of a dual-arm system of three dual-arm topologies and derive the kinematic and dynamic constraints imposed on two arms in cooperation. Dual-arm dynamic manipulabilities are defined to quantify the dynamic performance of three dual-arm topologies in terms of the efficiency of generating Cartesian accelerations. A methodology of selecting serial, parallel, and bracing structures based on dual-arm dynamic manipulabilities is provided.
An improved method for calculating self-motion coordinates for redundant manipulators
Reister, D.B.
1997-04-01
For a redundant manipulator, the objective of redundancy resolution is to follow a specified path in Cartesian space and simultaneously perform another task (for example, maximize an objective function or avoid obstacles) at every point along the path. The conventional methods have several drawbacks: a new function must be defined for each task, the extended Jacobian can be singular, closed cycles in Cartesian space may not yield closed cycles in joint space, and the objective is point-wise redundancy resolution (to determine a single point in joint space for each point in Cartesian space). The author divides the redundancy resolution problem into two parts: (1) calculate self-motion coordinates for all possible positions of a manipulator at each point along a Cartesian path and (2) determination of optimal self-motion coordinates that maximize an objective function along the path. This paper will discuss the first part of the problem. The path-wise approach overcomes all of the drawbacks of conventional redundancy resolution methods: no need to define a new function for each task, extended Jacobian cannot be singular, and closed cycles in extended Cartesian space will yield closed cycles in joint space.
Structure sensitive normal coordinate analysis of metal-diethyldithiocarbamate - complexes
NASA Astrophysics Data System (ADS)
Mikosch, H.; Bauer, G.; Kellner, R.; Trendafilova, N. S.; St. Nikolov, G.
1986-03-01
Symmetry changes in the course of dissolution are assumed to produce frequency shifts in molecular spectra of N, N-Disubstituted Dithiocarbamates. Using (mass-weighted) cartesian coordinates it is possible to calculate eigenvalues both for the site- and the molecular symmetry. Calculated shifts for Cu- and Zn- complexes are of the same order of magnitude as experimental results and calculation of frequencies even for assumed structures is possible.
Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo
2008-06-28
Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.
TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION
NASA Technical Reports Server (NTRS)
Smith, R. E.
1994-01-01
TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.
MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS
Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.
2013-04-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.
Technology for a NASA Space-Based Science Operations Grid
NASA Technical Reports Server (NTRS)
Bradford, Robert N.; Redman, Sandra H.
2003-01-01
This viewgraph representation presents an overview of a proposal to develop a space-based operations grid in support of space-based science experiments. The development of such a grid would provide a dynamic, secure and scalable architecture based on standards and next-generation reusable software and would enable greater science collaboration and productivity through the use of shared resources and distributed computing. The authors propose developing this concept for use on payload experiments carried aboard the International Space Station. Topics covered include: grid definitions, portals, grid development and coordination, grid technology and potential uses of such a grid.
NASA Astrophysics Data System (ADS)
O'Kuinghttons, Ryan; Koziol, Benjamin; Oehmke, Robert; DeLuca, Cecelia; Theurich, Gerhard; Li, Peggy; Jacob, Joseph
2016-04-01
The Earth System Modeling Framework (ESMF) Python interface (ESMPy) supports analysis and visualization in Earth system modeling codes by providing access to a variety of tools for data manipulation. ESMPy started as a Python interface to the ESMF grid remapping package, which provides mature and robust high-performance and scalable grid remapping between 2D and 3D logically rectangular and unstructured grids and sets of unconnected data. ESMPy now also interfaces with OpenClimateGIS (OCGIS), a package that performs subsetting, reformatting, and computational operations on climate datasets. ESMPy exposes a subset of ESMF grid remapping utilities. This includes bilinear, finite element patch recovery, first-order conservative, and nearest neighbor grid remapping methods. There are also options to ignore unmapped destination points, mask points on source and destination grids, and provide grid structure in the polar regions. Grid remapping on the sphere takes place in 3D Cartesian space, so the pole problem is not an issue as it can be with other grid remapping software. Remapping can be done between any combination of 2D and 3D logically rectangular and unstructured grids with overlapping domains. Grid pairs where one side of the regridding is represented by an appropriate set of unconnected data points, as is commonly found with observational data streams, is also supported. There is a developing interoperability layer between ESMPy and OpenClimateGIS (OCGIS). OCGIS is a pure Python, open source package designed for geospatial manipulation, subsetting, and computation on climate datasets stored in local NetCDF files or accessible remotely via the OPeNDAP protocol. Interfacing with OCGIS has brought GIS-like functionality to ESMPy (i.e. subsetting, coordinate transformations) as well as additional file output formats (i.e. CSV, ESRI Shapefile). ESMPy is distinguished by its strong emphasis on open source, community governance, and distributed development. The user
NASA Technical Reports Server (NTRS)
Chow, Edward T.; Stewart, Helen; Korsmeyer, David (Technical Monitor)
2003-01-01
The biggest users of GRID technologies came from the science and technology communities. These consist of government, industry and academia (national and international). The NASA GRID is moving into a higher technology readiness level (TRL) today; and as a joint effort among these leaders within government, academia, and industry, the NASA GRID plans to extend availability to enable scientists and engineers across these geographical boundaries collaborate to solve important problems facing the world in the 21 st century. In order to enable NASA programs and missions to use IPG resources for program and mission design, the IPG capabilities needs to be accessible from inside the NASA center networks. However, because different NASA centers maintain different security domains, the GRID penetration across different firewalls is a concern for center security people. This is the reason why some IPG resources are been separated from the NASA center network. Also, because of the center network security and ITAR concerns, the NASA IPG resource owner may not have full control over who can access remotely from outside the NASA center. In order to obtain organizational approval for secured remote access, the IPG infrastructure needs to be adapted to work with the NASA business process. Improvements need to be made before the IPG can be used for NASA program and mission development. The Secured Advanced Federated Environment (SAFE) technology is designed to provide federated security across NASA center and NASA partner's security domains. Instead of one giant center firewall which can be difficult to modify for different GRID applications, the SAFE "micro security domain" provide large number of professionally managed "micro firewalls" that can allow NASA centers to accept remote IPG access without the worry of damaging other center resources. The SAFE policy-driven capability-based federated security mechanism can enable joint organizational and resource owner approved remote
Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2003-01-01
The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.
Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction
Yang, Zhili; Jacob, Mathews
2014-01-01
The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when multi-dimensional datasets are involved. The main focus of this work is to design an NUFFT algorithm with minimal memory demands. Specifically, we introduce an analytical expression for the expected mean square error in the NUFFT approximation based on our earlier work. We then introduce an iterative algorithm to design the interpolator and scale factors.Experimental comparisons show that the proposed optimized NUFFT scheme provides considerably lower approximation errors than our previous scheme that rely on worst case error metrics. The improved approximations are also seen to considerably reduce the errors and artifacts in non-Cartesian MRI reconstruction. PMID:24637054
On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2004-01-01
Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.
The Cartesian clock metaphor for pineal gland operation pervades the origin of modern chronobiology.
Barrera-Mera, B; Barrera-Calva, E
1998-01-01
In theoretical descriptions formulated during the 1600s, R. Descartes attributed a clock-like role to the pineal gland. He established the belief that pineal function underlies the laws of the universe that determine the cyclic sleep-awake states in man. Recent reports about pineal circadian pacemakers now validate the brilliant accuracy of Cartesian thought, in relation to the relevant role of the pineal gland.
A parallel performance study of the Cartesian method for partial differential equations on a sphere
Drake, J.B.; Coddington, M.P.
1997-04-01
A 3-D Cartesian method for integration of partial differential equations on a spherical surface is developed for parallel computation. The target computer architectures are distributed memory, message passing computers such as the Intel Paragon. The parallel algorithms are described along with mesh partitioning strategies. Performance of the algorithms is considered for a standard test case of the shallow water equations on the sphere. The authors find the computation time scale well with increasing numbers of processors.
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
NASA Astrophysics Data System (ADS)
Schmitz, Phillip G.; Ying, Lexing
2014-02-01
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining the nested dissection matrix factorization method with hierarchical matrices in two dimensions and extend it to the three dimensional case. A theoretical linear time complexity is derived and a more practical variant with slightly worse scaling is demonstrated.
Cartesian path control of a two-degree-of-freedom robot manipulator
NASA Technical Reports Server (NTRS)
Nguyen, Charles C.; Pooran, Farhad J.
1988-01-01
The problem of cartesian trajectory control of a closed-kinematic chain mechanism robot manipulator with possible space station applications is considered. The study was performed by both computer simulation and experimentation for tracking of three different paths: a straight line, a sinusoid and a circle. Linearization and pole placement methods are employed to design controller gains. Results show that the controllers are robust and there are good agreements between simulation and experimentation. Excellent tracking quality and small overshoots are also evident.
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20
Michael, J. Robert; Volkov, Anatoliy
2015-03-01
The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20
Michael, J. Robert; Volkov, Anatoliy
2015-03-01
The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily for
Moriguchi, H; Wendt, M; Duerk, J L
2000-11-01
Various kinds of nonrectilinear Cartesian k-space trajectories have been studied, such as spiral, circular, and rosette trajectories. Although the nonrectilinear Cartesian sampling techniques generally have the advantage of fast data acquisition, the gridding process prior to 2D-FFT image reconstruction usually requires a number of additional calculations, thus necessitating an increase in the computation time. Further, the reconstructed image often exhibits artifacts resulting from both the k-space sampling pattern and the gridding procedure. To date, it has been demonstrated in only a few studies that the special geometric sampling patterns of certain specific trajectories facilitate fast image reconstruction. In other words, the inherent link among the trajectory, the sampling scheme, and the associated complexity of the regridding/reconstruction process has been investigated to only a limited extent. In this study, it is demonstrated that a Lissajous trajectory has the special geometric characteristics necessary for rapid reconstruction of nonrectilinear Cartesian k-space trajectories with constant sampling time intervals. Because of the applicability of a uniform resampling (URS) algorithm, a high-quality reconstructed image is obtained in a short reconstruction time when compared to other gridding algorithms. PMID:11064412
Easing The Calculation Of Bolt-Circle Coordinates
NASA Technical Reports Server (NTRS)
Burley, Richard K.
1995-01-01
Bolt Circle Calculation (BOLT-CALC) computer program used to reduce significant time consumed in manually computing trigonometry of rectangular Cartesian coordinates of holes in bolt circle as shown on blueprint or drawing. Eliminates risk of computational errors, particularly in cases involving many holes or in cases in which coordinates expressed to many significant digits. Program assists in many practical situations arising in machine shops. Written in BASIC. Also successfully compiled and implemented by use of Microsoft's QuickBasic v4.0.
A Vertical Grid Module for Baroclinic Models of the Atmosphere
Drake, John B
2008-04-01
The vertical grid of an atmospheric model assigns dynamic and thermo- dynamic variables to grid locations. The vertical coordinate is typically not height but one of a class of meteorological variables that vary with atmo- spheric conditions. The grid system is chosen to further numerical approx- imations of the boundary conditions so that the system is terrain following at the surface. Lagrangian vertical coordinates are useful in reducing the numerical errors from advection processes. That the choices will effect the numercial properties and accuracy is explored in this report. A MATLAB class for Lorentz vertical grids is described and applied to the vertical struc- ture equation and baroclinic atmospheric circulation. A generalized meteo- rolgoical coordinate system is developed which can support σ, isentropic θ vertical coordinate, or Lagrangian vertical coordinates. The vertical atmo- spheric column is a MATLAB class that includes the kinematic and ther- modynamic variables along with methods for computing geopoentials and terms relevant to a 3D baroclinc atmospheric model.
Determination of Ship Approach Parameters in the Polar Coordinates System
NASA Astrophysics Data System (ADS)
Banachowicz, Andrzej; Wolski, Adam
2014-06-01
An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision avoiding problems in rectangular planar coordinates, and the results are transformed to the polar coordinate system. This article presents a method for an analysis of a collision situation at sea performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation
Intelligent geospatial data retrieval based on the geospatial grid portal
NASA Astrophysics Data System (ADS)
Yuan, Jie; Yue, Peng; Gong, Jianya
2008-12-01
The Open Geospatial Consortium (OGC) standard-compliant services define a set of standard interfaces for geospatial Web services to achieve the interoperability in an open distributed computing environment. Grid technology is a distributed computing infrastructure to allow distributed resources sharing and coordinated problem solving. Based on the OGC standards for geospatial services and grid technology, we propose the geospatial grid portal to integrate and interoperate grid-enabled geospatial services. The implementation of the geospatial grid portal is based on a three-tier architecture which consists of grid-enabled geospatial services tier, grid service portal tier and application tier. The OGC standard-compliant services are deployed in a grid environment, the so-called grid-enabled geospatial services. Grid service portals for each type of geospatial services, including WFS, WMS, WCS and CSW, provide a single point of Web entry to discover and access different types of geospatial information. A resource optimization mechanism is incorporated into these service portals to optimize the selection of grid nodes. At the top tier, i.e. the application tier, the client interacts with a semantic middleware for the grid CSW portal, thus allows the semantics-enabled search. The proposed approach can not only optimize the grid resource selection among multiple grid nodes, but also incorporate the power of Semantic Web technology into geospatial grid portal to allow the precise discovery of geospatial data.
GridMan: A grid manipulation system
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Wang, Zhu
1992-01-01
GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.
Grid evolution in time asymptotic problems
NASA Technical Reports Server (NTRS)
Rai, M. M.; Anderson, D. A.
1980-01-01
A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.
NASA Technical Reports Server (NTRS)
Hartman, Steven
1992-01-01
Viewgraphs on technology coordination are provided. Topics covered include: technology coordination process to date; goals; how the Office of Aeronautics and Space Technology (OAST) can support the Office of Space Science and Applications (OSSA); how OSSA can support OAST; steps to technology transfer; and recommendations.
A computer program for converting rectangular coordinates to latitude-longitude coordinates
Rutledge, A.T.
1989-01-01
A computer program was developed for converting the coordinates of any rectangular grid on a map to coordinates on a grid that is parallel to lines of equal latitude and longitude. Using this program in conjunction with groundwater flow models, the user can extract data and results from models with varying grid orientations and place these data into grid structure that is oriented parallel to lines of equal latitude and longitude. All cells in the rectangular grid must have equal dimensions, and all cells in the latitude-longitude grid measure one minute by one minute. This program is applicable if the map used shows lines of equal latitude as arcs and lines of equal longitude as straight lines and assumes that the Earth 's surface can be approximated as a sphere. The program user enters the row number , column number, and latitude and longitude of the midpoint of the cell for three test cells on the rectangular grid. The latitude and longitude of boundaries of the rectangular grid also are entered. By solving sets of simultaneous linear equations, the program calculates coefficients that are used for making the conversion. As an option in the program, the user may build a groundwater model file based on a grid that is parallel to lines of equal latitude and longitude. The program reads a data file based on the rectangular coordinates and automatically forms the new data file. (USGS)
Minor, B.M.
1993-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport with rectangular cells is developed. Numerical problems arising in the derivation required the development of exponential moment functions. These functions are used to remove indeterminant forms which can cause catastrophic cancellations. The EC method is positive and nonlinear. It conserves particles and satisfies first moment balance. Comparisons of the EC method's performance to other methods in optically thin and thick spatial cells were performed. For optically thin cells, the EC method was shown to converge to the correct answer, with third order truncation error in the thin cell limit. In deep penetration problems, the EC method attained its highest computational efficiencies compared to the other methods. For all the deep penetration problems examined, the number of spatial cells required by the EC method to attain a desired accuracy was less than the other methods.... Mathematics functions, Nuclear radiation, Nuclear engineering, Radiation attenuation, Radiation shielding, Transport theory, Radiation transport.
Plasticity of intermediate mechanics students' coordinate system choice
NASA Astrophysics Data System (ADS)
Sayre, Eleanor C.; Wittmann, Michael C.
2008-12-01
We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.
A Moving Grid Capability for NPARC
NASA Technical Reports Server (NTRS)
Slater, John W.
1998-01-01
Version 3.1 of the NPARC computational fluid dynamics flow solver introduces a capability to solve unsteady flow on moving multi-block, structured grids with nominally second-order time accuracy. The grid motion is due to segments of the boundary grid that translate and rotate in a rigid-body manner or deform. The grid is regenerated at each time step to accommodate the boundary grid motion. The flow equations and computational models sense the moving grid through the grid velocities, which are computed from a time-difference of the grids at two consecutive time levels. For three-dimensional flow domains, it is assumed that the grid retains a planar character with respect to one coordinate. The application and accuracy of NPARC v3.1 is demonstrated for flow about a flying wedge, rotating flap, a collapsing bump in a duct, and the upstart / restart flow in a variable-geometry inlet. The results compare well with analytic and experimental results.
Streamwise Upwind, Moving-Grid Flow Algorithm
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Guruswamy, Guru P.; Obayashi, Shigeru
1992-01-01
Extension to moving grids enables computation of transonic flows about moving bodies. Algorithm computes unsteady transonic flow on basis of nondimensionalized thin-layer Navier-Stokes equations in conservation-law form. Solves equations by use of computational grid based on curvilinear coordinates conforming to, and moving with, surface(s) of solid body or bodies in flow field. Simulates such complicated phenomena as transonic flow (including shock waves) about oscillating wing. Algorithm developed by extending prior streamwise upwind algorithm solving equations on fixed curvilinear grid described in "Streamwise Algorithm for Simulation of Flow" (ARC-12718).
Li, Xian-Ying; Hu, Shi-Min
2013-02-01
Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.
NASA Astrophysics Data System (ADS)
Kemp, Martin
1998-08-01
If matter fills the Universe, making everything happen by its interactions, what does it all look like? René Descartes may have been over-mechanistic in his view, but his efforts to visualize the invisible created striking images.
Fara, Patricia
2008-12-01
Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.
NASA Astrophysics Data System (ADS)
Abad Lopez, Carlos Adrian
Current electricity infrastructure is being stressed from several directions -- high demand, unreliable supply, extreme weather conditions, accidents, among others. Infrastructure planners have, traditionally, focused on only the cost of the system; today, resilience and sustainability are increasingly becoming more important. In this dissertation, we develop computational tools for efficiently managing electricity resources to help create a more reliable and sustainable electrical grid. The tools we present in this work will help electric utilities coordinate demand to allow the smooth and large scale integration of renewable sources of energy into traditional grids, as well as provide infrastructure planners and operators in developing countries a framework for making informed planning and control decisions in the presence of uncertainty. Demand-side management is considered as the most viable solution for maintaining grid stability as generation from intermittent renewable sources increases. Demand-side management, particularly demand response (DR) programs that attempt to alter the energy consumption of customers either by using price-based incentives or up-front power interruption contracts, is more cost-effective and sustainable in addressing short-term supply-demand imbalances when compared with the alternative that involves increasing fossil fuel-based fast spinning reserves. An essential step in compensating participating customers and benchmarking the effectiveness of DR programs is to be able to independently detect the load reduction from observed meter data. Electric utilities implementing automated DR programs through direct load control switches are also interested in detecting the reduction in demand to efficiently pinpoint non-functioning devices to reduce maintenance costs. We develop sparse optimization methods for detecting a small change in the demand for electricity of a customer in response to a price change or signal from the utility
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis,Michael J.
2006-01-01
Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach
CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
2003-01-01
A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.
System Wide Joint Position Sensor Fault Tolerance in Robot Systems Using Cartesian Accelerometers
NASA Technical Reports Server (NTRS)
Aldridge, Hal A.; Juang, Jer-Nan
1997-01-01
Joint position sensors are necessary for most robot control systems. A single position sensor failure in a normal robot system can greatly degrade performance. This paper presents a method to obtain position information from Cartesian accelerometers without integration. Depending on the number and location of the accelerometers. the proposed system can tolerate the loss of multiple position sensors. A solution technique suitable for real-time implementation is presented. Simulations were conducted using 5 triaxial accelerometers to recover from the loss of up to 4 joint position sensors on a 7 degree of freedom robot moving in general three dimensional space. The simulations show good estimation performance using non-ideal accelerometer measurements.
Alj, Domenico; Caputo, Roberto; Umeton, Cesare
2014-11-01
We report on the realization of a liquid crystal (LC)-based optical diffraction grating showing a polar symmetry of the director alignment. This has been obtained as a natural evolution of the POLICRYPS technique, which enables the realization of highly efficient, switchable, planar diffraction gratings. Performances exhibited in the Cartesian geometry are extended to the polar one by exploiting the spherical aberration produced by simple optical elements. This enables producing the required highly stable polar pattern that allows fabricating a circular optical diffraction grating. Results are promising for their possible application in fields in which a rotational structure of the optical beam is needed.
Parallel adaptive Cartesian upwind methods for shock-driven multiphysics simulation
Deiterding, Ralf
2011-01-01
The multiphysics fluid-structure interaction simulation of shock-loaded thin-walled structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. By combining a Cartesian embedded boundary approach with dynamic mesh adaptation a generic software framework for such flow solvers has been constructed that allows easy exchange of the specific hydrodynamic finite volume upwind scheme and coupling to various explicit finite element solid dynamics solvers. The paper gives an overview of the computational approach and presents first simulations that couple the software to the general purpose solid dynamics code DYNA3D.
Alj, Domenico; Caputo, Roberto; Umeton, Cesare
2014-11-01
We report on the realization of a liquid crystal (LC)-based optical diffraction grating showing a polar symmetry of the director alignment. This has been obtained as a natural evolution of the POLICRYPS technique, which enables the realization of highly efficient, switchable, planar diffraction gratings. Performances exhibited in the Cartesian geometry are extended to the polar one by exploiting the spherical aberration produced by simple optical elements. This enables producing the required highly stable polar pattern that allows fabricating a circular optical diffraction grating. Results are promising for their possible application in fields in which a rotational structure of the optical beam is needed. PMID:25361314
NASA Astrophysics Data System (ADS)
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
Elking, Dennis M
2016-08-15
New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Cao, Jian; Li, Qi; Cheng, Jicheng
2005-10-01
This paper discusses the concept, key technologies and main application of Spatial Services Grid. The technologies of Grid computing and Webservice is playing a revolutionary role in studying the spatial information services. The concept of the SSG (Spatial Services Grid) is put forward based on the SIG (Spatial Information Grid) and OGSA (open grid service architecture). Firstly, the grid computing is reviewed and the key technologies of SIG and their main applications are reviewed. Secondly, the grid computing and three kinds of SIG (in broad sense)--SDG (spatial data grid), SIG (spatial information grid) and SSG (spatial services grid) and their relationships are proposed. Thirdly, the key technologies of the SSG (spatial services grid) is put forward. Finally, three representative applications of SSG (spatial services grid) are discussed. The first application is urban location based services gird, which is a typical spatial services grid and can be constructed on OGSA (Open Grid Services Architecture) and digital city platform. The second application is region sustainable development grid which is the key to the urban development. The third application is Region disaster and emergency management services grid.
Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".
Başar, Erol; Güntekin, Bahar
2009-01-01
Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered. PMID:18805445
Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".
Başar, Erol; Güntekin, Bahar
2009-01-01
Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered.
Overcoming high-field RF problems with non-magnetic Cartesian feedback transceivers.
Hoult, D I; Foreman, D; Kolansky, G; Kripiakevich, D
2008-03-01
In extending human MR to field strengths approaching 10 T, the wavelength of electromagnetic radiation at the proton Larmor frequency becomes less than human body size and conventional radio-frequency coil circumference. Consequently, radio-frequency magnetic fields are better generated by an array of small coils than by one large coil. In this article, the primary problem of array coil interactions during transmission is examined, and a standard proposed whereby secondary induced currents should be less than 1% of the primary coil current. The use of cancellation methods and of power amplifiers with high output impedance to reduce interactions is examined in the light of this standard and found wanting. Non-magnetic Cartesian feedback transceivers functioning at the magnet entrance are then proposed as a solution that both reduces instrumentation cost and increases the bandwidth over which the standard may be met. The compromises inherent in instrument design are detailed and examples given of the innovative circuitry used. It is shown experimentally that when connected to interacting coils, two Cartesian feedback instruments function stably in accord with theory and such that the proposed standard is typically attained over a bandwidth of 22 kHz during transmission (much greater during signal reception)-enough for all current MR protocols.
Systematic and Deterministic Graph-Minor Embedding of Cartesian Products of Complete Graphs
NASA Astrophysics Data System (ADS)
Zaribafiyan, Arman; Marchand, Dominic J. J.; Changiz Rezaei, Seyed Saeed
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. The overhead of the widely used heuristic techniques is quickly proving to be a significant bottleneck for real-world applications. To alleviate this obstacle, we propose a systematic deterministic embedding method that exploits the structures of both the input graph of the specific combinatorial optimization problem and the quantum annealer. We focus on the specific case of the Cartesian product of two complete graphs, a regular structure that occurs in many problems. We first divide the problem by embedding one of the factors of the Cartesian product in a repeatable unit. The resulting simplified problem consists of placing copies of this unit and connecting them together appropriately. Aside from the obvious speed and efficiency advantages of a systematic deterministic approach, the embeddings produced can be easily scaled for larger processors and show desirable properties with respect to the number of qubits used and the chain length distribution.
Rybkin, Vladimir V; Ekström, Ulf
2014-08-14
In this paper, we modify quasiclassical harmonic sampling of microcanonical ensembles of trajectories by using the curvilinear internal coordinates. The harmonic approximation in the curvilinear normal coordinates provides a more realistic description of the PES than in the conventional rectilinear ones at finite displacements. Therefore, the sampling of vibrations in the internal coordinates significantly improves the quality of the sampling in a block-box fashion, providing more realistic displacements and reducing the errors in the potential energy. In particular, the sampling of large-amplitude torsion vibrations, which is non-realistic in the Cartesian modes, becomes accurate or acceptable in the curvilinear modes.
ERIC Educational Resources Information Center
CLEAVES, PAUL C.; AND OTHERS
THE INSTRUCTIONAL MATERIALS CENTER IS LOCATED IN THE LOCAL HIGH SCHOOL AND SUPPLIES ALL SCHOOLS IN THE AREA. AUDIOVISUAL EQUIPMENT ORDERS, AFTER SELECTIONS ARE MADE BY THE CLASSROOM TEACHER, ARE PROCESSED BY THE CENTER, CONFIRMED AND DELIVERED BY TRUCK THREE TIMES EACH WEEK. EACH SCHOOL HAS A BUILDING COORDINATOR WHO CHECKS THE ORDERS INTO THE…
Parallel Grid Manipulations in Earth Science Calculations
NASA Technical Reports Server (NTRS)
Sawyer, W.; Lucchesi, R.; daSilva, A.; Takacs, L. L.
1999-01-01
The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a
Comprehensive Smart Grid Planning in a Regulated Utility Environment
NASA Astrophysics Data System (ADS)
Turner, Matthew; Liao, Yuan; Du, Yan
2015-06-01
This paper presents the tools and exercises used during the Kentucky Smart Grid Roadmap Initiative in a collaborative electric grid planning process involving state regulators, public utilities, academic institutions, and private interest groups. The mandate of the initiative was to assess the existing condition of smart grid deployments in Kentucky, to enhance understanding of smart grid concepts by stakeholders, and to develop a roadmap for the deployment of smart grid technologies by the jurisdictional utilities of Kentucky. Through involvement of many important stakeholder groups, the resultant Smart Grid Deployment Roadmap proposes an aggressive yet achievable strategy and timetable designed to promote enhanced availability, security, efficiency, reliability, affordability, sustainability and safety of the electricity supply throughout the state while maintaining Kentucky's nationally competitive electricity rates. The models and methods developed for this exercise can be utilized as a systematic process for the planning of coordinated smart grid deployments.
Wald, Ingo; Ize, Santiago
2015-07-28
Parallel population of a grid with a plurality of objects using a plurality of processors. One example embodiment is a method for parallel population of a grid with a plurality of objects using a plurality of processors. The method includes a first act of dividing a grid into n distinct grid portions, where n is the number of processors available for populating the grid. The method also includes acts of dividing a plurality of objects into n distinct sets of objects, assigning a distinct set of objects to each processor such that each processor determines by which distinct grid portion(s) each object in its distinct set of objects is at least partially bounded, and assigning a distinct grid portion to each processor such that each processor populates its distinct grid portion with any objects that were previously determined to be at least partially bounded by its distinct grid portion.
Computer coordination of limb motion for a three-legged walking robot
NASA Technical Reports Server (NTRS)
Klein, C. A.; Patterson, M. R.
1980-01-01
Coordination of the limb motion of a vehicle which could perform assembly and maintenance operations on large structures in space is described. Manipulator kinematics and walking robots are described. The basic control scheme of the robot is described. The control of the individual arms are described. Arm velocities are generally described in Cartesian coordinates. Cartesian velocities are converted to joint velocities using the Jacobian matrix. The calculation of a trajectory for an arm given a sequence of points through which it is to pass is described. The free gait algorithm which controls the lifting and placing of legs for the robot is described. The generation of commanded velocities for the robot, and the implementation of those velocities by the algorithm are discussed. Suggestions for further work in the area of robot legged locomotion are presented.
NASA Astrophysics Data System (ADS)
Mazur, Alexey K.
1999-07-01
Internal coordinate molecular dynamics (ICMD) is a recent efficient method for modeling polymer molecules which treats them as chains of rigid bodies rather than ensembles of point particles as in Cartesian MD. Unfortunately, it is readily applicable only to linear or tree topologies without closed flexible loops. Important examples violating this condition are sugar rings of nucleic acids, proline residues in proteins, and also disulfide bridges. This paper presents the first complete numerical solution of the chain closure problem within the context of ICMD. The method combines natural implicit fixation of bond lengths and bond angles by the choice of internal coordinates with explicit constraints similar to Cartesian dynamics used to maintain the chain closure. It is affordable for large molecules and makes possible 3-5 times faster dynamics simulations of molecular systems with flexible rings, including important biological objects like nucleic acids and disulfide-bonded proteins.
Coveney, Peter V
2005-08-15
We introduce a definition of Grid computing which is adhered to throughout this Theme Issue. We compare the evolution of the World Wide Web with current aspirations for Grid computing and indicate areas that need further research and development before a generally usable Grid infrastructure becomes available. We discuss work that has been done in order to make scientific Grid computing a viable proposition, including the building of Grids, middleware developments, computational steering and visualization. We review science that has been enabled by contemporary computational Grids, and associated progress made through the widening availability of high performance computing.
Visual SLAM Using Variance Grid Maps
NASA Technical Reports Server (NTRS)
Howard, Andrew B.; Marks, Tim K.
2011-01-01
An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance
Faster tomographic fan-beam back-projection using Cartesian axes pre-projection
NASA Astrophysics Data System (ADS)
Davis, G. R.
1998-02-01
The convolution back-projection algorithm is the most common method for reconstructing images from complete sets of fan-beam projections. For each pixel and for every projection, the interception point on the detector array must be determined and a weighted value from the appropriate point on the filtered back projection added. Thus the number of operations required is of order n2p, where n is the number of points per projection, and p the number of projections. This can mean a considerable computation time, even with modern, fast computer workstations. The complexity of each pixel operation (weighting and geometric computations) is reduced if the projection is first pre-projected onto one or other of the Cartesian axes. This has been demonstrated to reduce the computational time by a factor of 2, with no loss of accuracy, when compared with a highly optimised implementation of the conventional fan-beam back-projection algorithm.
Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam
2012-03-22
Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν^{2}) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.
Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method
NASA Technical Reports Server (NTRS)
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted in aerodynamic simulations of aircraft due to the complexities involved in the modeling of engine details and flow physics. However, the omission is often improper since inlet or plume flows may have a substantial effect on vehicle aerodynamics. A method for modeling the effect of inlets and exhaust plumes using boundary conditions within an inviscid Cartesian flow solver is presented. This approach couples with both CAD systems and legacy geometry to provide an automated tool suitable for parameter studies. The method is validated using two and three-dimensional test problems which are compared with both theoretical and experimental results. The numerical results demonstrate excellent agreement with theory and available data, even for extremely strong jets and very sensitive inlets.
Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems
Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam
2012-07-03
We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.
Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems
Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam
2012-07-03
We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within themore » context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.« less
Investigation of Radar Propagation in Buildings: A 10 Billion Element Cartesian-Mesh FETD Simulation
Stowell, M L; Fasenfest, B J; White, D A
2008-01-14
In this paper large scale full-wave simulations are performed to investigate radar wave propagation inside buildings. In principle, a radar system combined with sophisticated numerical methods for inverse problems can be used to determine the internal structure of a building. The composition of the walls (cinder block, re-bar) may effect the propagation of the radar waves in a complicated manner. In order to provide a benchmark solution of radar propagation in buildings, including the effects of typical cinder block and re-bar, we performed large scale full wave simulations using a Finite Element Time Domain (FETD) method. This particular FETD implementation is tuned for the special case of an orthogonal Cartesian mesh and hence resembles FDTD in accuracy and efficiency. The method was implemented on a general-purpose massively parallel computer. In this paper we briefly describe the radar propagation problem, the FETD implementation, and we present results of simulations that used over 10 billion elements.
Overton, Willis F
2013-01-01
This chapter argues that the Cartesian-split-mechanistic scientific paradigm that until recently functioned as the standard conceptual framework for subfields of developmental science (including inheritance, evolution, and organismic--prenatal, cognitive, emotional, motivational, sociocultural--development) has been progressively failing as a scientific research program. An alternative scientific paradigm composed of nested metatheories with relationism at the broadest level and relational developmental systems as a midrange metatheory is offered as a more progressive conceptual framework for developmental science. Termed broadly the relational developmental systems paradigm, this framework accounts for the findings that are anomalies for the old paradigm; accounts for the emergence of new findings; and points the way to future scientific productivity.
Numerical Simulation of Rolling-Airframes Using a Multi-Level Cartesian Method
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)
2002-01-01
A supersonic rolling missile with two synchronous canard control surfaces is analyzed using an automated, inviscid, Cartesian method. Sequential-static and time-dependent dynamic simulations of the complete motion are computed for canard dither schedules for level flight, pitch, and yaw maneuver. The dynamic simulations are compared directly against both high-resolution viscous simulations and relevant experimental data, and are also utilized to compute dynamic stability derivatives. The results show that both the body roll rate and canard dither motion influence the roll-averaged forces and moments on the body. At the relatively, low roll rates analyzed in the current work these dynamic effects are modest, however the dynamic computations are effective in predicting the dynamic stability derivatives which can be significant for highly-maneuverable missiles.
A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2001-01-01
This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.
Cross-sectional optoacoustic tomographic reconstructions in a polar grid
NASA Astrophysics Data System (ADS)
Deán-Ben, X. Luís.; Lutzweiler, Christian; Razansky, Daniel
2014-03-01
Some commonly employed optoacoustic (photoacoustic) tomographic configurations make use of an array of cylindrically-focused transducers located around the imaging sample to selectively acquire the optoacoustic signals generated in the imaging plane. Thereby, the feasibility of simultaneous acquisition of signals leads to important advantages such as high-throughput performance or real-time imaging capacity. For this particular geometry, two-dimensional model-based reconstruction has showcased good performance in terms of imaging accuracy and flexibility to account for various transducer-related effects and acoustic propagation phenomena. The forward model is expressed as a linear operator (model-matrix) that maps the optical absorption in a grid containing the sample to the resulting wavefield at the sensor positions. The standard approach, however, may lead to excessive memory requirements for the storage of the model-matrix. Herein, an optoacoustic model based on a discretization of the time-domain equation in a polar grid is introduced. Due to the rotational symmetry of the acquisition geometry and the discretization grid, only the part of the model-matrix directly corresponding to one transducer position (projection) needs to be stored. As a result, inversion of the model-matrix can be done in a memory efficient manner. Performance of the method was tested in numerical simulations and experimental measurements, attaining results equivalent to Cartesian-based grids but using a much more computationally efficient implementation.
An overset grid method for the study of reflex tearing.
Maki, K L; Braun, R J; Driscoll, T A; King-Smith, P E
2008-09-01
We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as 'black lines' and a Cartesian grid covers the remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film model show qualitative agreement with in vivo tear film thickness measurements. Furthermore, the role of the black lines in the presence of tear supply from the lid margins, reflex tearing, was found to be more subtle than a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. During reflex tearing, tears may flow through the region normally containing the black line and drift down over the cornea under the influence of gravity.
Advancing Smart Grid Interoperability and Implementing NIST's Interoperability Roadmap
Basso,T.; DeBlasio, R.
2010-04-01
The IEEE American National Standards project P2030TM addressing smart grid interoperability and the IEEE 1547 series of standards addressing distributed resources interconnection with the grid have been identified in priority action plans in the Report to NIST on the Smart Grid Interoperability Standards Roadmap. This paper presents the status of the IEEE P2030 development, the IEEE 1547 series of standards publications and drafts, and provides insight on systems integration and grid infrastructure. The P2030 and 1547 series of standards are sponsored by IEEE Standards Coordinating Committee 21.
ERIC Educational Resources Information Center
Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao
2012-01-01
This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…
Barnette, Daniel W.
2002-01-01
The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.
2015-09-14
GridDyn is a part of power grid simulation toolkit. The code is designed using modern object oriented C++ methods utilizing C++11 and recent Boost libraries to ensure compatibility with multiple operating systems and environments.
NASA Technical Reports Server (NTRS)
Hinke, Thomas
2003-01-01
This presentation will describe what is meant by grids and then cover the current state of the IPG. This will include an overview of the middleware that is key to the operation of the grid. The presentation will then describe some of the future directions that are planned for the IPG. Finally the presentation will conclude with a brief overview of the Global Grid Forum, which is a key activity that will contribute to the successful availability of grid components.
NASA Technical Reports Server (NTRS)
Kumar, D.
1980-01-01
The computer program AFTBDY generates a body fitted curvilinear coordinate system for a wedge curved after body. This wedge curved after body is being used in an experimental program. The coordinate system generated by AFTBDY is used to solve 3D compressible N.S. equations. The coordinate system in the physical plane is a cartesian x,y,z system, whereas, in the transformed plane a rectangular xi, eta, zeta system is used. The coordinate system generated is such that in the transformed plane coordinate spacing in the xi, eta, zeta direction is constant and equal to unity. The physical plane coordinate lines in the different regions are clustered heavily or sparsely depending on the regions where physical quantities to be solved for by the N.S. equations have high or low gradients. The coordinate distribution in the physical plane is such that x stays constant in eta and zeta direction, whereas, z stays constant in xi and eta direction. The desired distribution in x and z is input to the program. Consequently, only the y-coordinate is solved for by the program AFTBDY.
NASA Technical Reports Server (NTRS)
Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert
2005-01-01
Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
DSMC Grid Methodologies for Computing Low-Density, Hypersonic Flows About Reusable Launch Vehicles
NASA Technical Reports Server (NTRS)
Wilmoth, Richard G.; LeBeau, Gerald J.; Carlson, Ann B.
1996-01-01
Two different grid methodologies are studied for application to DSMC simulations about reusable launch vehicles. One method uses an unstructured, tetrahedral grid while the other uses a structured, variable-resolution Cartesian grid. The relative merits of each method are discussed in terms of accuracy, computational efficiency, and overall ease of use. Both methods are applied to the computation of a low-density, hypersonic flow about a winged single-stage-to-orbit reusable launch vehicle concept at conditions corresponding to an altitude of 120 km. Both methods are shown to give comparable results for both surface and flowfield quantities as well as for the overall aerodynamic behavior. For the conditions simulated, the flowfield about the vehicle is very rarefied but the DSMC simulations show significant departure from free-molecular predictions for the surface friction and heat transfer as well as certain aerodynamic quantities.
An adaptive grid method for computing the high speed 3D viscous flow about a re-entry vehicle
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Smith, Robert E.
1992-01-01
An algebraic solution adaptive grid generation method that allows adapting the grid in all three coordinate directions is presented. Techniques are described that maintain the integrity of the original vehicle definition for grid point movement on the vehicle surface and that avoid grid cross over in the boundary layer portion of the grid lying next to the vehicle surface. The adaptive method is tested by computing the Mach 6 hypersonic three dimensional viscous flow about a proposed Martian entry vehicle.
Yocum, D.R.; Berman, E.; Canal, P.; Chadwick, K.; Hesselroth, T.; Garzoglio, G.; Levshina, T.; Sergeev, V.; Sfiligoi, I.; Sharma, N.; Timm, S.; /Fermilab
2007-05-01
As one of the founding members of the Open Science Grid Consortium (OSG), Fermilab enables coherent access to its production resources through the Grid infrastructure system called FermiGrid. This system successfully provides for centrally managed grid services, opportunistic resource access, development of OSG Interfaces for Fermilab, and an interface to the Fermilab dCache system. FermiGrid supports virtual organizations (VOs) including high energy physics experiments (USCMS, MINOS, D0, CDF, ILC), astrophysics experiments (SDSS, Auger, DES), biology experiments (GADU, Nanohub) and educational activities.
Taft, Jeffrey D.
2016-01-01
The report describes work done on Grid Architecture under the auspices of the Department of Electricity Office of Electricity Delivery and Reliability in 2015. As described in the first Grid Architecture report, the primary purpose of this work is to provide stakeholder insight about grid issues so as to enable superior decision making on their part. Doing this requires the creation of various work products, including oft-times complex diagrams, analyses, and explanations. This report provides architectural insights into several important grid topics and also describes work done to advance the science of Grid Architecture as well.
Noniterative three-dimensional grid generation using parabolic partial differential equations
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1985-01-01
A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.
Spectral Topography Generation for Arbitrary Grids
NASA Astrophysics Data System (ADS)
Oh, T. J.
2015-12-01
A new topography generation tool utilizing spectral transformation technique for both structured and unstructured grids is presented. For the source global digital elevation data, the NASA Shuttle Radar Topography Mission (SRTM) 15 arc-second dataset (gap-filling by Jonathan de Ferranti) is used and for land/water mask source, the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) 30 arc-second land water mask dataset v5 is used. The original source data is coarsened to a intermediate global 2 minute lat-lon mesh. Then, spectral transformation to the wave space and inverse transformation with wavenumber truncation is performed for isotropic topography smoothness control. Target grid topography mapping is done by bivariate cubic spline interpolation from the truncated 2 minute lat-lon topography. Gibbs phenomenon in the water region can be removed by overwriting ocean masked target coordinate grids with interpolated values from the intermediate 2 minute grid. Finally, a weak smoothing operator is applied on the target grid to minimize the land/water surface height discontinuity that might have been introduced by the Gibbs oscillation removal procedure. Overall, the new topography generation approach provides spectrally-derived, smooth topography with isotropic resolution and minimum damping, enabling realistic topography forcing in the numerical model. Topography is generated for the cubed-sphere grid and tested on the KIAPS Integrated Model (KIM).
Time-Accurate Computation of Viscous Flow Around Deforming Bodies Using Overset Grids
Fast, P; Henshaw, W D
2001-04-02
Dynamically evolving boundaries and deforming bodies interacting with a flow are commonly encountered in fluid dynamics. However, the numerical simulation of flows with dynamic boundaries is difficult with current methods. We propose a new method for studying such problems. The key idea is to use the overset grid method with a thin, body-fitted grid near the deforming boundary, while using fixed Cartesian grids to cover most of the computational domain. Our approach combines the strengths of earlier moving overset grid methods for rigid body motion, and unstructured grid methods for Aow-structure interactions. Large scale deformation of the flow boundaries can be handled without a global regridding, and in a computationally efficient way. In terms of computational cost, even a full overset grid regridding is significantly cheaper than a full regridding of an unstructured grid for the same domain, especially in three dimensions. Numerical studies are used to verify accuracy and convergence of our flow solver. As a computational example, we consider two-dimensional incompressible flow past a flexible filament with prescribed dynamics.
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2006-01-01
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
2007-11-15
The report provides an overview of what the Smart Grid is and what is being done to define and implement it. The electric industry is preparing to undergo a transition from a centralized, producer-controlled network to a decentralized, user-interactive one. Not only will the technology involved in the electric grid change, but the entire business model of the industry will change too. A major objective of the report is to identify the changes that the Smart Grid will bring about so that industry participants can be prepared to face them. A concise overview of the development of the Smart Grid is provided. It presents an understanding of what the Smart Grid is, what new business opportunities or risks might come about due to its introduction, and what activities are already taking place regarding defining or implementing the Smart Grid. This report will be of interest to the utility industry, energy service providers, aggregators, and regulators. It will also be of interest to home/building automation vendors, information technology vendors, academics, consultants, and analysts. The scope of the report includes an overview of the Smart Grid which identifies the main components of the Smart Grid, describes its characteristics, and describes how the Smart Grid differs from the current electric grid. The overview also identifies the key concepts involved in the transition to the Smart Grid and explains why a Smart Grid is needed by identifying the deficiencies of the current grid and the need for new investment. The report also looks at the impact of the Smart Grid, identifying other industries which have gone through a similar transition, identifying the overall benefits of the Smart Grid, and discussing the impact of the Smart Grid on industry participants. Furthermore, the report looks at current activities to implement the Smart Grid including utility projects, industry collaborations, and government initiatives. Finally, the report takes a look at key technology
Kamarchik, Eugene; Jasper, Ahren W
2013-05-21
An algorithm is presented for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules using Monte Carlo integration of classical phase space. The algorithm includes numerical evaluations of the elements of the Jacobian and is general enough to allow for sampling in arbitrary curvilinear or rectilinear coordinate systems. Invariance to the choice of coordinate system is demonstrated for vibrational state densities of methane, where we find comparable sampling efficiency when using curvilinear z-matrix and rectilinear Cartesian normal mode coordinates. In agreement with past work, we find that anharmonicity increases the vibrational state density of methane by a factor of ∼2 at its dissociation threshold. For the vinyl radical, we find a significant (∼10×) improvement in sampling efficiency when using curvilinear z-matrix coordinates relative to Cartesian normal mode coordinates. We attribute this improved efficiency, in part, to a more natural curvilinear coordinate description of the double well associated with the H2C-C-H wagging motion. The anharmonicity correction for the vinyl radical state density is ∼1.4 at its dissociation threshold. Finally, we demonstrate that with trivial parallelizations of the Monte Carlo step, tractable calculations can be made for the vinyl radical using direct ab initio potential energy surface evaluations and a composite QCISD(T)/MP2 method.
Navigation in Grid Space with the NAS Grid Benchmarks
NASA Technical Reports Server (NTRS)
Frumkin, Michael; Hood, Robert; Biegel, Bryan A. (Technical Monitor)
2002-01-01
We present a navigational tool for computational grids. The navigational process is based on measuring the grid characteristics with the NAS Grid Benchmarks (NGB) and using the measurements to assign tasks of a grid application to the grid machines. The tool allows the user to explore the grid space and to navigate the execution at a grid application to minimize its turnaround time. We introduce the notion of gridscape as a user view of the grid and show how it can be me assured by NGB, Then we demonstrate how the gridscape can be used with two different schedulers to navigate a grid application through a rudimentary grid.
Grid enabled Service Support Environment - SSE Grid
NASA Astrophysics Data System (ADS)
Goor, Erwin; Paepen, Martine
2010-05-01
The SSEGrid project is an ESA/ESRIN project which started in 2009 and is executed by two Belgian companies, Spacebel and VITO, and one Dutch company, Dutch Space. The main project objectives are the introduction of a Grid-based processing on demand infrastructure at the Image Processing Centre for earth observation products at VITO and the inclusion of Grid processing services in the Service Support Environment (SSE) at ESRIN. The Grid-based processing on demand infrastructure is meant to support a Grid processing on demand model for Principal Investigators (PI) and allow the design and execution of multi-sensor applications with geographically spread data while minimising the transfer of huge volumes of data. In the first scenario, 'support a Grid processing on demand model for Principal Investigators', we aim to provide processing power close to the EO-data at the processing and archiving centres. We will allow a PI (non-Grid expert user) to upload his own algorithm, as a process, and his own auxiliary data from the SSE Portal and use them in an earth observation workflow on the SSEGrid Infrastructure. The PI can design and submit workflows using his own processes, processes made available by VITO/ESRIN and possibly processes from other users that are available on the Grid. These activities must be user-friendly and not requiring detailed knowledge about the underlying Grid middleware. In the second scenario we aim to design, implement and demonstrate a methodology to set up an earth observation processing facility, which uses large volumes of data from various geographically spread sensors. The aim is to provide solutions for problems that we face today, like wasting bandwidth by copying large volumes of data to one location. We will avoid this by processing the data where they are. The multi-mission Grid-based processing on demand infrastructure will allow developing and executing complex and massive multi-sensor data (re-)processing applications more
Mathews, K.A.; Brennan, C.R.
1995-12-31
The exponential characteristic method is one of a family of nonlinear spatial quadratures which are positive and at least second order accurate. The authors initially developed the method in slab geometry, where it gave accurate results for deep penetration problems using coarse meshes. Characteristic methods are restricted to Cartesian geometries, so they next tested it with rectangular cells, where it was again a strong performer. Here the authors extend the method to unstructured grids of arbitrarily shaped and oriented triangles and report on its performance.
NASA Technical Reports Server (NTRS)
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1991-01-01
The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.
Securing smart grid technology
NASA Astrophysics Data System (ADS)
Chaitanya Krishna, E.; Kosaleswara Reddy, T.; Reddy, M. YogaTeja; Reddy G. M., Sreerama; Madhusudhan, E.; AlMuhteb, Sulaiman
2013-03-01
In the developing countries electrical energy is very important for its all-round improvement by saving thousands of dollars and investing them in other sector for development. For Growing needs of power existing hierarchical, centrally controlled grid of the 20th Century is not sufficient. To produce and utilize effective power supply for industries or people we should have Smarter Electrical grids that address the challenges of the existing power grid. The Smart grid can be considered as a modern electric power grid infrastructure for enhanced efficiency and reliability through automated control, high-power converters, modern communications infrastructure along with modern IT services, sensing and metering technologies, and modern energy management techniques based on the optimization of demand, energy and network availability and so on. The main objective of this paper is to provide a contemporary look at the current state of the art in smart grid communications as well as critical issues on smart grid technologies primarily in terms of information and communication technology (ICT) issues like security, efficiency to communications layer field. In this paper we propose new model for security in Smart Grid Technology that contains Security Module(SM) along with DEM which will enhance security in Grid. It is expected that this paper will provide a better understanding of the technologies, potential advantages and research challenges of the smart grid and provoke interest among the research community to further explore this promising research area.
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer.
Dennis, Sarah Grace; Trusk, Thomas; Richards, Dylan; Jia, Jia; Tan, Yu; Mei, Ying; Fann, Stephen; Markwald, Roger; Yost, Michael
2015-09-22
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters.
Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam
2012-03-22
Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectricmore » structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.« less
On the Use of CAD and Cartesian Methods for Aerodynamic Optimization
NASA Technical Reports Server (NTRS)
Nemec, M.; Aftosmis, M. J.; Pulliam, T. H.
2004-01-01
The objective for this paper is to present the development of an optimization capability for Curt3D, a Cartesian inviscid-flow analysis package. We present the construction of a new optimization framework and we focus on the following issues: 1) Component-based geometry parameterization approach using parametric-CAD models and CAPRI. A novel geometry server is introduced that addresses the issue of parallel efficiency while only sparingly consuming CAD resources; 2) The use of genetic and gradient-based algorithms for three-dimensional aerodynamic design problems. The influence of noise on the optimization methods is studied. Our goal is to create a responsive and automated framework that efficiently identifies design modifications that result in substantial performance improvements. In addition, we examine the architectural issues associated with the deployment of a CAD-based approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute engines. We demonstrate the effectiveness of the framework for a design problem that features topology changes and complex geometry.
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer.
Dennis, Sarah Grace; Trusk, Thomas; Richards, Dylan; Jia, Jia; Tan, Yu; Mei, Ying; Fann, Stephen; Markwald, Roger; Yost, Michael
2015-01-01
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters. PMID:26436877
Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow
NASA Technical Reports Server (NTRS)
Berger, Marsha; Aftosmis, Michael J.
2012-01-01
We present preliminary development of an approach for simulating high Reynolds number steady compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider both laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells, and uses a wall model to address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features a forward evaluation for flow velocity and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as approx.0.1% chord. With the current analytic wall model, one or two additional refinements near the wall are required to obtain mesh converged values of skin friction.
López-Muñoz, Francisco; Rubio, Gabriel; Molina, Juan D; Alamo, Cecilio
2011-04-25
The relationship between the "passions" (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. In this context, melancholy was considered a perversion of the soul (corruption of the passions). One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that "passions" were sensitive movements that the soul experienced due to its union with the body (res extensa). According to this theory, the soul was located in the pineal gland, where it was actively involved in overseeing the functions of the "human machine" and kept its dysfunctions under control, by circulating animal spirits. Descartes described sadness as one of "the six primitive passions of the soul", which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century (Spinoza, Willis, Pitcairn) and during much of the 18th century (Le Cat, Tissot). From the 19th century onwards, emotional symptomatology finally began to be used in diagnostic criteria for mood disorders.
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer
Dennis, SG.; Trusk, T.; Richards, D.; Jia, J.; Tan, Y.; Mei, Y.; Fann, S.; Markwald, R.; Yost, M.
2016-01-01
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters. PMID:26436877
A novel 3D Cartesian random sampling strategy for Compressive Sensing Magnetic Resonance Imaging.
Valvano, Giuseppe; Martini, Nicola; Santarelli, Maria Filomena; Chiappino, Dante; Landini, Luigi
2015-01-01
In this work we propose a novel acquisition strategy for accelerated 3D Compressive Sensing Magnetic Resonance Imaging (CS-MRI). This strategy is based on a 3D cartesian sampling with random switching of the frequency encoding direction with other K-space directions. Two 3D sampling strategies are presented. In the first strategy, the frequency encoding direction is randomly switched with one of the two phase encoding directions. In the second strategy, the frequency encoding direction is randomly chosen between all the directions of the K-Space. These strategies can lower the coherence of the acquisition, in order to produce reduced aliasing artifacts and to achieve a better image quality after Compressive Sensing (CS) reconstruction. Furthermore, the proposed strategies can reduce the typical smoothing of CS due to the limited sampling of high frequency locations. We demonstrated by means of simulations that the proposed acquisition strategies outperformed the standard Compressive Sensing acquisition. This results in a better quality of the reconstructed images and in a greater achievable acceleration.
NASA Technical Reports Server (NTRS)
Yasui, R. K.; Berman, P. A. (Inventor)
1976-01-01
A grid pattern is described for a solar cell of the type which includes a semiconductive layer doped to a first polarity and a top counter-doped layer. The grid pattern comprises a plurality of concentric conductive grids of selected geometric shapes which are centered about the center of the exposed active surface of the counter-doped layer. Connected to the grids is one or more conductors which extend to the cell's periphery. For the pattern area, the grids and conductors are arranged in the pattern to minimize the maximum distance which any injected majority carriers have to travel to reach any of the grids or conductors. The pattern has a multiaxes symmetry with respect to the cell center to minimize the maximum temperature differentials between points on the cell surface and to provide a more uniform temperature distribution across the cell face.
Başar, Erol; Güntekin, Bahar
2007-04-01
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the
New iterative gridding algorithm using conjugate gradient method
NASA Astrophysics Data System (ADS)
Jiang, Xuguang; Thedens, Daniel
2004-05-01
Non-uniformly sampled data in MRI applications must be interpolated onto a regular Cartesian grid to perform fast image reconstruction using FFT. The conventional method for this is gridding, which requires a density compensation function (DCF). The calculation of DCF may be time-consuming, ambiguously defined, and may not be always reusable due to changes in k-space trajectories. A recently proposed reconstruction method that eliminates the requirement of DCF is block uniform resampling (BURS) which uses singular value decomposition (SVD). However, the SVD is still computationally intensive. In this work, we present a modified BURS algorithm using conjugate gradient method (CGM) in place of direct SVD calculation. Calculation of a block of grid point values in each iteration further reduces the computational load. The new method reduces the calculation complexity while maintaining a high-quality reconstruction result. For an n-by-n matrix, the time complexity per iteration is reduced from O(n*n*n) in SVD to O(n*n) in CGM. The time can be further reduced when we stop the iteration in CGM earlier according to the norm of the residual vector. Using this method, the quality of the reconstructed image improves compared to regularized BURS. The reduced time complexity and improved reconstruction result make the new algorithm promising in dealing with large-sized images and 3D images.
On Efficient Parallel Implementation of Moving Body Overset Grid Methods
NASA Technical Reports Server (NTRS)
Wissink, Andrew M.; Meakin, Robert L.; Warmbrodt, William (Technical Monitor)
1997-01-01
An investigation into the parallel performance of moving-body overset grid methods will be presented. Parallel versions of the OVERFLOW flow solver, DCF3D domain connectivity software, and SIXDO six-degree-of-freedom routine are coupled with an automatic load balance routine and tested for 3D Navier-Stokes calculations on the IBM SP2. The primary source of parallel inefficiency in moving and problems are the domain connectivity costs with DCF 3D. Although this algorithm constitutes a relatively low fraction of the total solution cost (e.g. 10-20%) in calculations on serial machines, the consequently cause a significant degradation in the overall parallel performance. The paper will highlight some approaches for improving the scalability of DCF3D. The paper will present results of a proposed new load balancing scheme that seeks more equal distribution of the inter-grid boundary points in order to more evenly load balance the donor search costs associated with DCF3D. Some preliminary results will also be given from a new solution-adaption algorithm coupled with OVERFLOW which incorporates overset cartesian grids with various levels of refinement. The measured parallel performance from a descending delta-wing configuration and a generic store-separation from a wing/pylon case will be presented.
Challenges facing production grids
Pordes, Ruth; /Fermilab
2007-06-01
Today's global communities of users expect quality of service from distributed Grid systems equivalent to that their local data centers. This must be coupled to ubiquitous access to the ensemble of processing and storage resources across multiple Grid infrastructures. We are still facing significant challenges in meeting these expectations, especially in the underlying security, a sustainable and successful economic model, and smoothing the boundaries between administrative and technical domains. Using the Open Science Grid as an example, I examine the status and challenges of Grids operating in production today.
NASA Technical Reports Server (NTRS)
Kim, Moonil; Weikle, Robert M., II; Hacker, Jonathan B.; Delisio, Michael P.; Rutledge, David B.; Rosenberg, James J.; Smith, R. P.
1991-01-01
A 50-MESFET grid amplifier is reported that has a gain of 11 dB at 3.3 GHz. The grid isolates the input from the output by using vertical polarization for the input beam and horizontal polarization for the transmitted output beam. The grid unit cell is a two-MESFET differential amplifier. A simple calibration procedure allows the gain to be calculated from a relative power measurement. This grid is a hybrid circuit, but the structure is suitable for fabrication as a monolithic wafer-scale integrated circuit, particularly at millimeter wavelengths.
Mukherjee, Sudipto; Rizzo, Robert C.
2014-01-01
Scoring functions are a critically important component of computer-aided screening methods for the identification of lead compounds during early stages of drug discovery. Here, we present a new multi-grid implementation of the footprint similarity (FPS) scoring function that was recently developed in our laboratory which has proven useful for identification of compounds which bind to a protein on a per-residue basis in a way that resembles a known reference. The grid-based FPS method is much faster than its Cartesian-space counterpart which makes it computationally tractable for on-the-fly docking, virtual screening, or de novo design. In this work, we establish that: (i) relatively few grids can be used to accurately approximate Cartesian space footprint similarity, (ii) the method yields improved success over the standard DOCK energy function for pose identification across a large test set of experimental co-crystal structures, for crossdocking, and for database enrichment, and (iii) grid-based FPS scoring can be used to tailor construction of new molecules to have specific properties, as demonstrated in a series of test cases targeting the viral protein HIVgp41. The method will be made available in the program DOCK6. PMID:23436713
Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates
NASA Astrophysics Data System (ADS)
Bleck, Rainer; Boudra, Douglas
1986-06-01
Wind-driven spin-up of the four-layer, quasi-isopycnic, eddy-resolving primitive equation model of Bleck and Boudra (1981) is compared with that obtained with a (numerically dissimilar) "pure" isopycnic coordinate model and an isobaric (i.e., quasi-Cartesian) coordinate model. In particular, the onset of hydrodynamic instabilities in the flow forced by a double-gyre wind stress pattern is studied. The spin-up processes associated with the isopycnic and quasi-isopycnic model are found to be similar, whereas the flow pattern produced by the quasi-Cartesian model deviates in the direction of Holland's (1978) and Holland and Lin's (1975a, b) two-layer solutions.
Liu, Yangfan; Bolton, J Stuart
2016-08-01
The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.
Calculation of Water Entry Problem for Free-falling Bodies Using a Developed Cartesian Cut Cell Mesh
NASA Astrophysics Data System (ADS)
Wenhua, Wang; Yanying, Wang
2010-05-01
This paper describes the development of free surface capturing method on Cartesian cut cell mesh to water entry problem for free-falling bodies with body-fluid interaction. The incompressible Euler equations for a variable density fluid system are presented as governing equations and the free surface is treated as a contact discontinuity by using free surface capturing method. In order to be convenient for dealing with the problem with moving body boundary, the Cartesian cut cell technique is adopted for generating the boundary-fitted mesh around body edge by cutting solid regions out of a background Cartesian mesh. Based on this mesh system, governing equations are discretized by finite volume method, and at each cell edge inviscid flux is evaluated by means of Roe's approximate Riemann solver. Furthermore, for unsteady calculation in time domain, a time accurate solution is achieved by a dual time-stepping technique with artificial compressibility method. For the body-fluid interaction, the projection method of momentum equations and exact Riemann solution are applied in the calculation of fluid pressure on the solid boundary. Finally, the method is validated by test case of water entry for free-falling bodies.
Shooshtary, S; Solbach, K
2015-08-01
A 7 Tesla Magnetic Resonance Imaging (MRI) system with parallel transmission (pTx) for 32 near-magnet Cartesian feedback loop power amplifiers (PA) with output power of 1kW is under construction at Erwin L. Hahn Institute for Magnetic Resonance Imaging. Variation of load impedance due to mutual coupling of neighborhood coils in the array may lead to instability of the Cartesian feedback loop amplifier. MRI safety requires unconditional stability of the PAs at any load. In order to avoid instability in the pTx system, conditions and limits of stability have to be investigated for every possible excitation mode for the coil array. In this work, an efficient method of stability check for an array of two transmit channels (Tx) with Cartesian feedback loop amplifier and a selective excitation mode for the coil array is proposed which allows extension of stability investigations to a large pTx array with any arbitrary excitation mode for the coil array. PMID:26736573
Liu, Yangfan; Bolton, J Stuart
2016-08-01
The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis. PMID:27586772
ICFF: a new method to incorporate implicit flexibility into an internal coordinate force field.
Katritch, Vsevolod; Totrov, Maxim; Abagyan, Ruben
2003-01-30
We introduce a new method to accurately "project" a Cartesian force field onto an internal coordinate molecular model with fixed-bond geometry. The algorithm automatically generates the Internal Coordinate Force Field (ICFF), which is a close approximation of the "source" Cartesian force field. The ICFF method reduces the number of free variables in a model by at least 10-fold and facilitates the fast convergence of geometry optimizations, an advantage that is critical for many applications such as the docking of flexible ligands or conformational modeling of macromolecules. Although covalent geometry is fixed in an ICFF model, implicit flexibility is incorporated into the force field parameters in the following two ways. First, we formulate an empirical torsion energy term in ICFF as a sixfold Fourier series and develop a procedure to calculate the Fourier coefficients from the conformational energy profiles of the fully flexible Cartesian model. The ICFF torsion parameters thus represent not only torsion component of the source force field, but also bond bending, bond stretching, and "1-4" van der Waals interactions. Second, we use a soft polynomial repulsion function for "1-5" and "1-6" interactions to mimic the flexibility of bonds, connecting these atoms. Also, we suggest a way to use a local part of the Cartesian force field to automatically generate fixed covalent geometries, compatible with the ICFF energy function. Here, we present an implementation of the ICFF algorithm, which employs the MMFF94s Cartesian force field as a "source." Extensive benchmarking of ICFF with a representative set of organic molecules demonstrates that the implicit flexibility model accurately reproduces MMFF94s equilibrium conformational energy differences (RMSD approximately 0.64 kcal) and, most importantly, detailed torsion energy profiles (RMSD approximately 0.37 kcal). This accuracy is characteristic of the method, because all the ICFF parameters (except one scaling factor in
Miliordos, Evangelos; Xantheas, Sotiris S.
2013-08-15
We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson’s GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C_{1} symmetry the computational savings in the energy calculations amount to 36N – 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. Finally, in all cases the frequencies based on internal coordinates differ on average by <1 cm^{–1} from those obtained from Cartesian coordinates.
Miliordos, Evangelos; Xantheas, Sotiris S
2013-08-15
We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson's GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N - 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. In all cases the frequencies based on internal coordinates differ on average by <1 cm(-1) from those obtained from Cartesian coordinates.
Zimmerman, Paul M
2013-05-14
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.
Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo
2015-07-14
The interpretation and analysis of experimental resonance-Raman (RR) spectra can be significantly facilitated by vibronic computations based on reliable quantum-mechanical (QM) methods. With the aim of improving the description of large and flexible molecules, our recent time-dependent formulation to compute vibrationally resolved electronic spectra, based on Cartesian coordinates, has been extended to support internal coordinates. A set of nonredundant delocalized coordinates is automatically generated from the molecular connectivity thanks to a new general and robust procedure. In order to validate our implementation, a series of molecules has been used as test cases. Among them, rigid systems show that normal modes based on Cartesian and delocalized internal coordinates provide equivalent results, but the latter set is much more convenient and reliable for systems characterized by strong geometric deformations associated with the electronic transition. The so-called Z-matrix internal coordinates, which perform well for chain molecules, are also shown to be poorly suited in the presence of cycles or nonstandard structures.
Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator
Omar, Mohamed A.
2014-01-01
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732
NASA Astrophysics Data System (ADS)
Zimmerman, Paul M.
2013-05-01
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.
Omar, Mohamed A
2014-01-01
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.
Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain
Hagmeijer, R.
1994-11-01
A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of the computational coordinates.
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
ERIC Educational Resources Information Center
Simco, Greg
2002-01-01
Discussion of the Internet 2 Initiative, which is based on collaboration among universities, businesses, and government, focuses on the Access Grid, a Computational Grid that includes interactive multimedia within high-speed networks to provide resources to enable remote collaboration among the research community. (Author/LRW)
Humphrey, Marty; Thompson, Mary R.; Jackson, Keith R.
2005-08-14
Securing a Grid environment presents a distinctive set of challenges. This paper groups the activities that need to be secured into four categories: naming and authentication; secure communication; trust, policy, and authorization; and enforcement of access control. It examines the current state of the art in securing these processes and introduces new technologies that promise to meet the security requirements of Grids more completely.
Hollman, David S; Schaefer, Henry F
2012-10-28
In recent years, internal coordinates have become the preferred means of expressing potential energy surfaces. The ability to transform quantities from chemically significant internal coordinates to primitive Cartesian coordinates and spectroscopically relevant normal coordinates is thus critical to the further development of computational chemistry. In the present work, general nth order formulas are presented for the Cartesian derivatives of the five most commonly used internal coordinates--bond stretching, bond angle, torsion, out-of-plane angle, and linear bending. To compose such formulas in a reasonably understandable fashion, a new notation is developed that is a generalization of that which has been used previously for similar purposes. The notation developed leads to easily programmable and reasonably understandable arbitrary order formulas, yet it is powerful enough to express the arbitrary order B tensor of a general, N-point internal coordinate, as is done herein. The techniques employed in the derivation of such formulas are relatively straightforward, and could presumably be applied to a number of other internal coordinates as needed.
NASA Astrophysics Data System (ADS)
Slowik, Edward Steven
What properties must space, or the modern notion of space-time, possess to allow the development of a coherent description of the natural world? My dissertation explores various aspects of this problem, both as they developed historically in a famous dispute between Descartes and Newton, and as they appear in more modern approaches to mechanics. In an early paper, De gravitatione, Newton presented an argument against Descartes' theory of space and time that has generated much controversy. Descartes had postulated a theory that regards space and time as formed merely from the relations among material bodies; yet, on the other hand, he had appealed to a particle's velocity in his theory of motion. Newton objected, claiming that, in order to define velocity or motion coherently, the natural world must possess a means of identifying the same spatial locations over time (i.e., the places passed by an object must remain fixed in time if the notion of a "change in distance" is to be rendered coherent). However, if space is viewed as a special form of entity with an independent existence, as Newton believed, then the enduring spatial locations required for determining "velocity" make sense. Although philosophers for many years were receptive to Descartes' "relationalist" philosophy, modern research has tended to favor Newton's side of the dispute, for most physical theories rely upon notions of "velocity" or "acceleration" that require an independent space-time backdrop. Nevertheless, not all coherent theories meet Newton's demands--the modern theory of machines (i.e., connected gears) does not; thus, I explore the possibility that Newton's argument could be answered in this vein. My thesis traces through these concerns in great detail, concluding that, despite the appeal of Descartes' rejection of space as an independent entity, Cartesian science is unable to completely resolve the dilemma posed by Newton's argument.
Pseudo‐projection–driven, self‐gated cardiac cine imaging using cartesian golden step phase encoding
Guo, Liheng; Derbyshire, J. Andrew
2015-01-01
Purpose To develop and evaluate a novel two‐dimensional self‐gated imaging technique for free‐breathing cardiac cine MRI that is free of motion‐detection overhead and requires minimal planning for motion tracking. Methods Motion along the readout direction was extracted solely from normal Cartesian imaging readouts near ky = 0. During imaging, the readouts below a certain |ky| threshold were scaled in magnitude and filtered in time to form “pseudo‐projections,” enabling projection‐based motion tracking along readout without frequently acquiring the central phase encode. A discrete golden step phase encode scheme allowed the |ky| threshold to be freely set after the scan while maintaining uniform motion sampling. Results The pseudo‐projections stream displayed sufficient spatiotemporal resolution for both cardiac and respiratory tracking, allowing retrospective reconstruction of free‐breathing non‐electrocardiogram (ECG) cines. The technique was tested on healthy subjects, and the resultant image quality, measured by blood‐myocardium boundary sharpness, myocardial mass, and single‐slice ejection fraction was found to be comparable to standard breath‐hold ECG‐gated cines. Conclusion The use of pseudo‐projections for motion tracking was found feasible for cardiorespiratory self‐gated imaging. Despite some sensitivity to flow and eddy currents, the simplicity of acquisition makes the proposed technique a valuable tool for self‐gated cardiac imaging. Magn Reson Med 76:417–429, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. PMID
Moore, Reagan W.; Studham, Ronald S.; Rajasekar, Arcot; Watson, Chip; Stockinger, Heinz; Kunszt, Peter; Charlie Catlett and Ian Foster
2002-02-27
Data grids link distributed, heterogeneous storage resources into a coherent data management system. From a user perspective, the data grid provides a uniform name space across the underlying storage systems, while supporting retrieval and storage of files. In the high energy physics community, at least six data grids have been implemented for the storage and distribution of experimental data. Data grids are also being used to support projects as diverse as digital libraries (National Library of Medicine Visible Embryo project), federation of multiple astronomy sky surveys (NSF National Virtual Observatory project), and integration of distributed data sets (Long Term Ecological Reserve). Data grids also form the core interoperability mechanisms for creating persistent archives, in which data collections are migrated to new technologies over time. The ability to provide a uniform name space across multiple administration domains is becoming a critical component of national-scale, collaborative projects.
A conservative approach for flow field calculations on multiple grids
NASA Technical Reports Server (NTRS)
Kathong, Monchai; Tiwari, Surendra N.
1988-01-01
In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.
The MammoGrid Virtual Organisation - Federating Distributed Mammograms.
Estrella, Florida; McClatchey, Richard; Rogulin, Dmitry
2005-01-01
The MammoGrid project aims to deliver a prototype which enables the effective collaboration between radiologists using grid, service-orientation and database solutions. The grid technologies and service-based database management solution provide the platform for integrating diverse and distributed resources, creating what is called a 'virtual organisation'. The MammoGrid Virtual Organisation facilitates the sharing and coordinated access to mammography data, medical imaging software and computing resources of participating hospitals. Hospitals manage their local database of mammograms, but in addition, radiologists who are part of this organisation can share mammograms, reports, results and image analysis software. The MammoGrid Virtual Organisation is a federation of autonomous multi-centres sites which transcends national boundaries. This paper outlines the service-based approach in the creation and management of the federated distributed mammography database and discusses the role of virtual organisations in distributed image analysis.
Transforming Power Grid Operations
Huang, Zhenyu; Guttromson, Ross T.; Nieplocha, Jarek; Pratt, Robert G.
2007-04-15
While computation is used to plan, monitor, and control power grids, some of the computational technologies now used are more than a hundred years old, and the complex interactions of power grid components impede real-time operations. Thus it is hard to speed up “state estimation,” the procedure used to estimate the status of the power grid from measured input. State estimation is the core of grid operations, including contingency analysis, automatic generation control, and optimal power flow. How fast state estimation and contingency analysis are conducted (currently about every 5 minutes) needs to be increased radically so the analysis of contingencies is comprehensive and is conducted in real time. Further, traditional state estimation is based on a power flow model and only provides a static snapshot—a tiny piece of the state of a large-scale dynamic machine. Bringing dynamic aspects into real-time grid operations poses an even bigger challenge. Working with the latest, most advanced computing techniques and hardware, researchers at Pacific Northwest National Laboratory (PNNL) intend to transform grid operations by increasing computational speed and improving accuracy. Traditional power grid computation is conducted on single PC hardware platforms. This article shows how traditional power grid computation can be reformulated to take advantage of advanced computing techniques and be converted to high-performance computing platforms (e.g., PC clusters, reconfigurable hardware, scalable multicore shared memory computers, or multithreaded architectures). The improved performance is expected to have a huge impact on how power grids are operated and managed and ultimately will lead to more reliability and better asset utilization to the power industry. New computational capabilities will be tested and demonstrated on the comprehensive grid operations platform in the Electricity Infrastructure Operations Center, which is a newly commissioned PNNL facility for
Flexible Residential Smart Grid Simulation Framework
NASA Astrophysics Data System (ADS)
Xiang, Wang
Different scheduling and coordination algorithms controlling household appliances' operations can potentially lead to energy consumption reduction and/or load balancing in conjunction with different electricity pricing methods used in smart grid programs. In order to easily implement different algorithms and evaluate their efficiency against other ideas, a flexible simulation framework is desirable in both research and business fields. However, such a platform is currently lacking or underdeveloped. In this thesis, we provide a simulation framework to focus on demand side residential energy consumption coordination in response to different pricing methods. This simulation framework, equipped with an appliance consumption library using realistic values, aims to closely represent the average usage of different types of appliances. The simulation results of traditional usage yield close matching values compared to surveyed real life consumption records. Several sample coordination algorithms, pricing schemes, and communication scenarios are also implemented to illustrate the use of the simulation framework.
NASA Astrophysics Data System (ADS)
Schäfer, Benjamin; Matthiae, Moritz; Timme, Marc; Witthaut, Dirk
2015-01-01
Stable operation of complex flow and transportation networks requires balanced supply and demand. For the operation of electric power grids—due to their increasing fraction of renewable energy sources—a pressing challenge is to fit the fluctuations in decentralized supply to the distributed and temporally varying demands. To achieve this goal, common smart grid concepts suggest to collect consumer demand data, centrally evaluate them given current supply and send price information back to customers for them to decide about usage. Besides restrictions regarding cyber security, privacy protection and large required investments, it remains unclear how such central smart grid options guarantee overall stability. Here we propose a Decentral Smart Grid Control, where the price is directly linked to the local grid frequency at each customer. The grid frequency provides all necessary information about the current power balance such that it is sufficient to match supply and demand without the need for a centralized IT infrastructure. We analyze the performance and the dynamical stability of the power grid with such a control system. Our results suggest that the proposed Decentral Smart Grid Control is feasible independent of effective measurement delays, if frequencies are averaged over sufficiently large time intervals.
Absolute flatness testing of skip-flat interferometry by matrix analysis in polar coordinates.
Han, Zhi-Gang; Yin, Lu; Chen, Lei; Zhu, Ri-Hong
2016-03-20
A new method utilizing matrix analysis in polar coordinates has been presented for absolute testing of skip-flat interferometry. The retrieval of the absolute profile mainly includes three steps: (1) transform the wavefront maps of the two cavity measurements into data in polar coordinates; (2) retrieve the profile of the reflective flat in polar coordinates by matrix analysis; and (3) transform the profile of the reflective flat back into data in Cartesian coordinates and retrieve the profile of the sample. Simulation of synthetic surface data has been provided, showing the capability of the approach to achieve an accuracy of the order of 0.01 nm RMS. The absolute profile can be retrieved by a set of closed mathematical formulas without polynomial fitting of wavefront maps or the iterative evaluation of an error function, making the new method more efficient for absolute testing.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
NASA Astrophysics Data System (ADS)
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2016-07-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Pordes, R.; /Fermilab
2004-12-01
The U.S. LHC Tier-1 and Tier-2 laboratories and universities are developing production Grids to support LHC applications running across a worldwide Grid computing system. Together with partners in computer science, physics grid projects and active experiments, we will build a common national production grid infrastructure which is open in its architecture, implementation and use. The Open Science Grid (OSG) model builds upon the successful approach of last year's joint Grid2003 project. The Grid3 shared infrastructure has for over eight months provided significant computational resources and throughput to a range of applications, including ATLAS and CMS data challenges, SDSS, LIGO, and biology analyses, and computer science demonstrators and experiments. To move towards LHC-scale data management, access and analysis capabilities, we must increase the scale, services, and sustainability of the current infrastructure by an order of magnitude or more. Thus, we must achieve a significant upgrade in its functionalities and technologies. The initial OSG partners will build upon a fully usable, sustainable and robust grid. Initial partners include the US LHC collaborations, DOE & NSF Laboratories and Universities & Trillium Grid projects. The approach is to federate with other application communities in the U.S. to build a shared infrastructure open to other sciences and capable of being modified and improved to respond to needs of other applications, including CDF, D0, BaBar, and RHIC experiments. We describe the application-driven, engineered services of the OSG, short term plans and status, and the roadmap for a consortium, its partnerships and national focus.
Trends in life science grid: from computing grid to knowledge grid
Konagaya, Akihiko
2006-01-01
Background Grid computing has great potential to become a standard cyberinfrastructure for life sciences which often require high-performance computing and large data handling which exceeds the computing capacity of a single institution. Results This survey reviews the latest grid technologies from the viewpoints of computing grid, data grid and knowledge grid. Computing grid technologies have been matured enough to solve high-throughput real-world life scientific problems. Data grid technologies are strong candidates for realizing "resourceome" for bioinformatics. Knowledge grids should be designed not only from sharing explicit knowledge on computers but also from community formulation for sharing tacit knowledge among a community. Conclusion Extending the concept of grid from computing grid to knowledge grid, it is possible to make use of a grid as not only sharable computing resources, but also as time and place in which people work together, create knowledge, and share knowledge and experiences in a community. PMID:17254294
Parallel grid library for rapid and flexible simulation development
NASA Astrophysics Data System (ADS)
Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.
2013-04-01
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as cell data. The amount of data in grid cells can vary both in space and time allowing dccrg to be used in very different types of simulations, for example in fluid and particle codes. Dccrg transfers the data between neighboring cells on different processes transparently and asynchronously allowing one to overlap computation and communication. This enables excellent scalability at least up to 32 k cores in magnetohydrodynamic tests depending on the problem and hardware. In the version of dccrg presented here part of the mesh metadata is replicated between MPI processes reducing the scalability of adaptive mesh refinement (AMR) to between 200 and 600 processes. Dccrg is free software that anyone can use, study and modify and is available at https://gitorious.org/dccrg. Users are also kindly requested to cite this work when publishing results obtained with dccrg. Catalogue identifier: AEOM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 54975 No. of bytes in distributed program, including test data, etc.: 974015 Distribution format: tar.gz Programming language: C++. Computer: PC, cluster, supercomputer. Operating system: POSIX. The code has been parallelized using MPI and tested with 1-32768 processes RAM: 10 MB-10 GB per process Classification: 4.12, 4.14, 6.5, 19.3, 19.10, 20. External routines: MPI-2 [1], boost [2], Zoltan [3], sfc++ [4] Nature of problem: Grid library supporting arbitrary data in grid cells, parallel adaptive mesh refinement, transparent remote neighbor data updates and
Grid Computing Education Support
Steven Crumb
2008-01-15
The GGF Student Scholar program enabled GGF the opportunity to bring over sixty qualified graduate and under-graduate students with interests in grid technologies to its three annual events over the three-year program.
NASA Technical Reports Server (NTRS)
Vaziri, Arsi
2004-01-01
This viewgraph presentation provides information on the development of a portal to provide secure and distributed grid computing for Payload Operations Integrated Center and Mission Control Center ground services.
NASA Technical Reports Server (NTRS)
Johnston, William E.; Ziobarth, John (Technical Monitor)
2002-01-01
We have presented the essence of experience gained in building two production Grids, and provided some of the global context for this work. As the reader might imagine, there were a lot of false starts, refinements to the approaches and to the software, and several substantial integration projects (SRB and Condor integrated with Globus) to get where we are today. However, the point of this paper is to try and make it substantially easier for others to get to the point where Information Power Grids (IPG) and the DOE Science Grids are today. This is what is needed in order to move us toward the vision of a common cyber infrastructure for science. The author would also like to remind the readers that this paper primarily represents the actual experiences that resulted from specific architectural and software choices during the design and implementation of these two Grids. The choices made were dictated by the criteria laid out in section 1. There is a lot more Grid software available today that there was four years ago, and various of these packages are being integrated into IPG and the DOE Grids. However, the foundation choices of Globus, SRB, and Condor would not be significantly different today than they were four years ago. Nonetheless, if the GGF is successful in its work - and we have every reason to believe that it will be - then in a few years we will see that the 28 functions provided by these packages will be defined in terms of protocols and MIS, and there will be several robust implementations available for each of the basic components, especially the Grid Common Services. The impact of the emerging Web Grid Services work is not yet clear. It will likely have a substantial impact on building higher level services, however it is the opinion of the author that this will in no way obviate the need for the Grid Common Services. These are the foundation of Grids, and the focus of almost all of the operational and persistent infrastructure aspects of Grids.
NASA Astrophysics Data System (ADS)
Petitdidier, Monique; Schwichtenberg, Horst
2010-05-01
The worldwide Earth science community covers a mosaic of disciplines and players such as academia, industry, national surveys, international organizations, and so forth. It provides a scientific basis for addressing societal issues, which require that the Earth science community utilize massive amounts of data, both in real and remote time. This data is usually distributed among many different organizations and data centers. These facts, the utilization of massive, distributed data amounts, explain the interest of the Earth science community for Grid technology, also noticeable by the variety of applications ported and tools developed. In parallel to the participation in EGEE, other projects involving ES disciplines were or have been carried out as related projects to EGEE (Enabling Grids for E-sciencE) such as CYCLOPS, SEEGrid, EELA2, EUASIA or outside e.g., in the framework of WGISS/CEOS. Numerous applications in atmospheric chemistry, meteorology, seismology, hydrology, pollution, climate and biodiversity were deployed successfully on Grid. In order to fulfill requirements of risk management, several prototype applications have been deployed using OGC (Open geospatial Consortium) components with Grid middleware. Examples are in hydrology for flood or Black Sea Catchment monitoring, and in fire monitoring. Meteorological, pollution and climate applications are based on meteorological models ported on Grid such as MM5 (Mesoscale Model), WRF (Weather Research and Forecasting), RAMS (Regional Atmospheric Modeling System) or CAM (Community Atmosphere Model). Seismological applications on Grid are numerous in locations where their occurrence is important and computer resources too small; then interfaces and gateways have been developed to facilitate the access to data and specific software and avoid work duplication. A portal has been deployed for commercial seismological software, Geocluster, for academic users. In this presentation examples of such applications will
Exploring Hypersonic, Unstructured-Grid Issues through Structured Grids
NASA Technical Reports Server (NTRS)
Mazaheri, Ali R.; Kleb, Bill
2007-01-01
Pure-tetrahedral unstructured grids have been shown to produce asymmetric heat transfer rates for symmetric problems. Meanwhile, two-dimensional structured grids produce symmetric solutions and as documented here, introducing a spanwise degree of freedom to these structured grids also yields symmetric solutions. The effects of grid skewness and other perturbations of structured-grids are investigated to uncover possible mechanisms behind the unstructured-grid solution asymmetries. By using controlled experiments around a known, good solution, the effects of particular grid pathologies are uncovered. These structured-grid experiments reveal that similar solution degradation occurs as for unstructured grids, especially for heat transfer rates. Non-smooth grids within the boundary layer is also shown to produce large local errors in heat flux but do not affect surface pressures.
Using Grid Benchmarks for Dynamic Scheduling of Grid Applications
NASA Technical Reports Server (NTRS)
Frumkin, Michael; Hood, Robert
2003-01-01
Navigation or dynamic scheduling of applications on computational grids can be improved through the use of an application-specific characterization of grid resources. Current grid information systems provide a description of the resources, but do not contain any application-specific information. We define a GridScape as dynamic state of the grid resources. We measure the dynamic performance of these resources using the grid benchmarks. Then we use the GridScape for automatic assignment of the tasks of a grid application to grid resources. The scalability of the system is achieved by limiting the navigation overhead to a few percent of the application resource requirements. Our task submission and assignment protocol guarantees that the navigation system does not cause grid congestion. On a synthetic data mining application we demonstrate that Gridscape-based task assignment reduces the application tunaround time.
NASA Technical Reports Server (NTRS)
Constantinescu, George S.; Lele, S. K.
2001-01-01
Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius
GRIDS: Grid-Scale Rampable Intermittent Dispatchable Storage
2010-09-01
GRIDS Project: The 12 projects that comprise ARPA-E’s GRIDS Project, short for “Grid-Scale Rampable Intermittent Dispatchable Storage,” are developing storage technologies that can store renewable energy for use at any location on the grid at an investment cost less than $100 per kilowatt hour. Flexible, large-scale storage would create a stronger and more robust electric grid by enabling renewables to contribute to reliable power generation.
ERIC Educational Resources Information Center
Tennant, Roy
2005-01-01
In the article, the author talks about the benefits of grid networks. In speaking of grid networks the author is referring to both networks of computers and networks of humans connected together in a grid topology. Examples are provided of how grid networks are beneficial today and the ways in which they have been used.
Computer Code Generates Homotopic Grids
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1992-01-01
HOMAR is computer code using homotopic procedure to produce two-dimensional grids in cross-sectional planes, which grids then stacked to produce quasi-three-dimensional grid systems for aerospace configurations. Program produces grids for use in both Euler and Navier-Stokes computation of flows. Written in FORTRAN 77.
NASA Astrophysics Data System (ADS)
Geannakakes, G. N.
1995-05-01
A Rayleigh-Ritz method mapping arbitrarily shaped plates on to a natural co-ordinate plane using serendipity functions is presented. The displacement function uses normalized beam characteristic orthogonal polynomials. The kinetic and strain energy equations are mapped from Cartesian co-ordinates to natural co-ordinates and the Rayleigh coefficient is minimized. Flexural free vibration analyses of various shaped plates is performed. Results are in excellent agreement with those found in the literature. This paper corrects the theory previously presented on this topic.
Smart Grid Integration Laboratory
Troxell, Wade
2011-12-22
The initial federal funding for the Colorado State University Smart Grid Integration Laboratory is through a Congressionally Directed Project (CDP), DE-OE0000070 Smart Grid Integration Laboratory. The original program requested in three one-year increments for staff acquisition, curriculum development, and instrumentation all which will benefit the Laboratory. This report focuses on the initial phase of staff acquisition which was directed and administered by DOE NETL/ West Virginia under Project Officer Tom George. Using this CDP funding, we have developed the leadership and intellectual capacity for the SGIC. This was accomplished by investing (hiring) a core team of Smart Grid Systems engineering faculty focused on education, research, and innovation of a secure and smart grid infrastructure. The Smart Grid Integration Laboratory will be housed with the separately funded Integrid Laboratory as part of CSU's overall Smart Grid Integration Center (SGIC). The period of performance of this grant was 10/1/2009 to 9/30/2011 which included one no cost extension due to time delays in faculty hiring. The Smart Grid Integration Laboratory's focus is to build foundations to help graduate and undergraduates acquire systems engineering knowledge; conduct innovative research; and team externally with grid smart organizations. Using the results of the separately funded Smart Grid Workforce Education Workshop (May 2009) sponsored by the City of Fort Collins, Northern Colorado Clean Energy Cluster, Colorado State University Continuing Education, Spirae, and Siemens has been used to guide the hiring of faculty, program curriculum and education plan. This project develops faculty leaders with the intellectual capacity to inspire its students to become leaders that substantially contribute to the development and maintenance of Smart Grid infrastructure through topics such as: (1) Distributed energy systems modeling and control; (2) Energy and power conversion; (3) Simulation of
Can Clouds replace Grids? Will Clouds replace Grids?
NASA Astrophysics Data System (ADS)
Shiers, J. D.
2010-04-01
The world's largest scientific machine - comprising dual 27km circular proton accelerators cooled to 1.9oK and located some 100m underground - currently relies on major production Grid infrastructures for the offline computing needs of the 4 main experiments that will take data at this facility. After many years of sometimes difficult preparation the computing service has been declared "open" and ready to meet the challenges that will come shortly when the machine restarts in 2009. But the service is not without its problems: reliability - as seen by the experiments, as opposed to that measured by the official tools - still needs to be significantly improved. Prolonged downtimes or degradations of major services or even complete sites are still too common and the operational and coordination effort to keep the overall service running is probably not sustainable at this level. Recently "Cloud Computing" - in terms of pay-per-use fabric provisioning - has emerged as a potentially viable alternative but with rather different strengths and no doubt weaknesses too. Based on the concrete needs of the LHC experiments - where the total data volume that will be acquired over the full lifetime of the project, including the additional data copies that are required by the Computing Models of the experiments, approaches 1 Exabyte - we analyze the pros and cons of Grids versus Clouds. This analysis covers not only technical issues - such as those related to demanding database and data management needs - but also sociological aspects, which cannot be ignored, neither in terms of funding nor in the wider context of the essential but often overlooked role of science in society, education and economy.
2011-08-30
GridLAB-D is a new power system simulation tool that provides valuable information to users who design and operate electric power transmission and distribution systems, and to utilities that wish to take advantage of the latest smart grid technology. This special release of GridLAB-D was developed to study the proposed Smart Grid technology that is used by Battelle Memorial Institute in the AEP gridSMART demonstration project in Northeast Columbus, Ohio.
A nonhydrostatic model with a generalized vertical coordinate
NASA Astrophysics Data System (ADS)
He, Zuwen
The advantages of a hybrid coordinate representation which is isentropic in the free atmosphere are that it dynamically provides high resolution near the tropopause and fronts, and that truncation error of vertical advection terms virtually vanishes in the adiabatic limit. A complete set of compressible and nonhydrostatic equations framed in generalized vertical coordinates are introduced. The hybrid coordinate is implemented by prescribing the vertical velocity in the coordinate space subject to the conditions that its associated grid locations generally follow isentropic surfaces, and that the grid locations always vary monotonically in z. In this respect, the current set of equations represents a nonhydrostatic generalization of the hybrid isentropic system used with success in hydrostatic models. The numerical system has been tested using a series of two-dimensional mountain wave simulations. In the case of steep and tall mountains; it is found that the system is flexible and robust enough to simulate nonlinear flow phenomena, such as rotors, which represent serious obstacles to traditional entropy-related coordinate models. In addition, a three-dimensional dry baroclinic simulation has been used to compare the hybrid coordinate model with a traditional z coordinate model. It is found that the hybrid coordinate model has slight advantages over the z coordinate model in prediction of upper-level PV gradient near the tropopause and fronts.
Complex Volume Grid Generation Through the Use of Grid Reusability
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
This paper presents a set of surface and volume grid generation techniques which reuse existing surface and volume grids. These methods use combinations of data manipulations to reduce grid generation time, improve grid characteristics, and increase the capabilities of existing domain discretization software. The manipulation techniques utilize physical and computational domains to produce basis function on which to operate and modify grid character and smooth grids using Trans-Finite Interpolation, a vector interpolation method and parametric re-mapping technique. With these new techniques, inviscid grids can be converted to viscous grids, multiple zone grid adaption can be performed to improve CFD solver efficiency, and topological changes to improve modeling of flow fields can be done simply and quickly. Examples of these capabilities are illustrated as applied to various configurations.
An Adaptive Unstructured Grid Method by Grid Subdivision, Local Remeshing, and Grid Movement
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
1999-01-01
An unstructured grid adaptation technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The approach is based on a combination of grid subdivision, local remeshing, and grid movement. For solution adaptive grids, the surface triangulation is locally refined by grid subdivision, and the tetrahedral grid in the field is partially remeshed at locations of dominant flow features. A grid redistribution strategy is employed for geometric adaptation of volume grids to moving or deforming surfaces. The method is automatic and fast and is designed for modular coupling with different solvers. Several steady state test cases with different inviscid flow features were tested for grid/solution adaptation. In all cases, the dominant flow features, such as shocks and vortices, were accurately and efficiently predicted with the present approach. A new and robust method of moving tetrahedral "viscous" grids is also presented and demonstrated on a three-dimensional example.
Hambrick, J.
2012-01-01
Although implementing Smart Grid projects at the distribution level provides many advantages and opportunities for advanced operation and control, a number of significant challenges must be overcome to maintain the high level of safety and reliability that the modern grid must provide. For example, while distributed generation (DG) promises to provide opportunities to increase reliability and efficiency and may provide grid support services such as volt/var control, the presence of DG can impact distribution operation and protection schemes. Additionally, the intermittent nature of many DG energy sources such as photovoltaics (PV) can present a number of challenges to voltage regulation, etc. This presentation provides an overview a number of Smart Grid projects being performed by the National Renewable Energy Laboratory (NREL) along with utility, industry, and academic partners. These projects include modeling and analysis of high penetration PV scenarios (with and without energy storage), development and testing of interconnection and microgrid equipment, as well as the development and implementation of advanced instrumentation and data acquisition used to analyze the impacts of intermittent renewable resources. Additionally, standards development associated with DG interconnection and analysis as well as Smart Grid interoperability will be discussed.
Grid Data Management and Customer Demands at MeteoSwiss
NASA Astrophysics Data System (ADS)
Rigo, G.; Lukasczyk, Ch.
2010-09-01
near-real-time datasets to build up trust in the product in different applications. The implementation of a new method called RSOI for the daily production allowed to bring the daily precipitation field up to the expectations of customers. The main use of the grids were near-realtime and past event analysis in areas scarcely covered with stations, and inputs for forecast tools and models. Critical success factors of the product were speed of delivery and at the same time accuracy, temporal and spatial resolution, and configuration (coordinate system, projection). To date, grids of archived precipitation data since 1961 and daily/monthly precipitation gridsets with 4h-delivery lag of Switzerland or subareas are available.
NASA Astrophysics Data System (ADS)
Kernkamp, Herman W. J.; Petit, Henri A. H.; Gerritsen, Herman; de Goede, Erik D.
2005-12-01
In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a β-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50-100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains
Grid generation about a fin-cylinder combination
NASA Astrophysics Data System (ADS)
Hoffman, G. H.
1983-03-01
An algebraic grid generation procedure is presented which produces a three dimensional, body fitted coordinate system about a right circular cylinder with four symmetric fins attached. Special features of the grid are an initial value plane normal to the cylinder axis and the ability to cluster lines near the fin and cylinder surfaces for viscous/turbulent flow calculations. The method used is a modification of the Jameson-Caughey procedure developed originally for inviscid transonic flow calculations about wing-fuselage combinations. In this procedure, a sequence of conformal transformations followed by a shearing transformation is used to map the irregular flow domain in physical space into a rectangular shaped computational domain. A three dimensional grid is produced by stacking two dimensional mappings. The method is therefore extremely fast. The main features of the procedure are discussed and two numerical examples of grids are presented for a fin composed of a symmetric Joukowsky airfoil.
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
Henshaw, W D; Schwendeman, D W
2005-08-30
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach.
NASA Astrophysics Data System (ADS)
Shasharina, Svetlana; Wang, Nanbor
2004-11-01
Simulations and experiments in the fusion and plasma physics community generate large datasets at remote sites. Visualization and analysis of these datasets are difficult because of the incompatibility among the various data formats adopted by simulation, experiments, and analysis tools, and the large sizes of analyzed data. Grids and Web Services technologies are capable of providing solutions for such heterogeneous settings, but need to be customized to the field-specific needs and merged with distributed technologies currently used by the community. This paper describes how we are addressing these issues in the Fusion Grid Service under development. We also present performance results of relevant data transfer mechanisms including binary SOAP, DIME, GridFTP and MDSplus and CORBA. We will describe the status of data converters (between HDF5 and MDSplus data types), developed in collaboration with MIT (J. Stillerman). Finally, we will analyze bottlenecks of MDSplus data transfer mechanism (work performed in collaboration with General Atomics (D. Schissel and M. Qian).
Information Power Grid Posters
NASA Technical Reports Server (NTRS)
Vaziri, Arsi
2003-01-01
This document is a summary of the accomplishments of the Information Power Grid (IPG). Grids are an emerging technology that provide seamless and uniform access to the geographically dispersed, computational, data storage, networking, instruments, and software resources needed for solving large-scale scientific and engineering problems. The goal of the NASA IPG is to use NASA's remotely located computing and data system resources to build distributed systems that can address problems that are too large or complex for a single site. The accomplishments outlined in this poster presentation are: access to distributed data, IPG heterogeneous computing, integration of large-scale computing node into distributed environment, remote access to high data rate instruments,and exploratory grid environment.
Integrating Renewable Electricity on the Grid
NASA Astrophysics Data System (ADS)
Crabtree, George; Misewich, Jim; Ambrosio, Ron; Clay, Kathryn; DeMartini, Paul; James, Revis; Lauby, Mark; Mohta, Vivek; Moura, John; Sauer, Peter; Slakey, Francis; Lieberman, Jodi; Tai, Humayun
2011-11-01
patchwork of conventional transmission lines would create an interstate highway system for electricity that moves large amounts of renewable electric power efficiently over long distances from source to load. Research and development is needed to identify the technical challenges associated with DC superconducting transmission and how it can be most effectively deployed. The challenge of variability can be met (i) by switching conventional generation capacity in or out in response to sophisticated forecasts of weather and power generation, (ii) by large scale energy storage in heat, pumped hydroelectric, compressed air or stationary batteries designed for the grid, or (iii) by national balancing of regional generation deficits and excesses using long distance transmission. Each of these solutions to variability has merit and each requires significant research and development to understand its capacity, performance, cost and effectiveness. The challenge of variability is likely to be met by a combination of these three solutions; the interactions among them and the appropriate mix needs to be explored. The long distances from renewable sources to demand centers span many of the grid's physical, ownership and regulatory boundaries. This introduces a new feature to grid structure and operation: national and regional coordination. The grid is historically a patchwork of local generation resources and load centers that has been built, operated and regulated to meet local needs. Although it is capable of sharing power across moderate distances, the arrangements for doing so are cumbersome and inefficient. The advent of renewable electricity with its enormous potential and inherent regional and national character presents an opportunity to examine the local structure of the grid and establish coordinating principles that will not only enable effective renewable integration but also simplify and codify the grid's increasingly regional and national character.
A priori grid quality estimation for high-order finite differencing
NASA Astrophysics Data System (ADS)
Fattah, Ryu; Angland, David; Zhang, Xin
2016-06-01
Structured grids using the finite differencing method contain two sources of grid-induced truncation errors. The first is dependent on the solution field. The second is related only to the metrics of the grid transformation. The accuracy of the grid transformation metrics is affected by the inverse metrics, which are spatial derivatives of the grid in the generalised coordinates. The truncation errors contained in the inverse metrics are generated by the spatial schemes. Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters. This similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid-induced errors. An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching. A strong correlation is obtained, provided that the grid transformation errors are the most significant sources of error.
Global structure search for molecules on surfaces: Efficient sampling with curvilinear coordinates.
Krautgasser, Konstantin; Panosetti, Chiara; Palagin, Dennis; Reuter, Karsten; Maurer, Reinhard J
2016-08-28
Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves. This approach has recently been shown to be efficient in structure determination of clusters [C. Panosetti et al., Nano Lett. 15, 8044-8048 (2015)] and is here extended for its application to covalent, complex molecules and large adsorbates on surfaces. The employed automatically constructed delocalized internal coordinates are similar to molecular vibrations, which enhances the generation of chemically meaningful trial structures. By introducing flexible constraints and local translation and rotation of independent geometrical subunits, we enable the use of this method for molecules adsorbed on surfaces and interfaces. For two test systems, trans-β-ionylideneacetic acid adsorbed on a Au(111) surface and methane adsorbed on a Ag(111) surface, we obtain superior performance of the method compared to standard optimization moves based on Cartesian coordinates.
Global structure search for molecules on surfaces: Efficient sampling with curvilinear coordinates
NASA Astrophysics Data System (ADS)
Krautgasser, Konstantin; Panosetti, Chiara; Palagin, Dennis; Reuter, Karsten; Maurer, Reinhard J.
2016-08-01
Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves. This approach has recently been shown to be efficient in structure determination of clusters [C. Panosetti et al., Nano Lett. 15, 8044-8048 (2015)] and is here extended for its application to covalent, complex molecules and large adsorbates on surfaces. The employed automatically constructed delocalized internal coordinates are similar to molecular vibrations, which enhances the generation of chemically meaningful trial structures. By introducing flexible constraints and local translation and rotation of independent geometrical subunits, we enable the use of this method for molecules adsorbed on surfaces and interfaces. For two test systems, trans-β-ionylideneacetic acid adsorbed on a Au(111) surface and methane adsorbed on a Ag(111) surface, we obtain superior performance of the method compared to standard optimization moves based on Cartesian coordinates.
Essential Grid Workflow Monitoring Elements
Gunter, Daniel K.; Jackson, Keith R.; Konerding, David E.; Lee,Jason R.; Tierney, Brian L.
2005-07-01
Troubleshooting Grid workflows is difficult. A typicalworkflow involves a large number of components networks, middleware,hosts, etc. that can fail. Even when monitoring data from all thesecomponents is accessible, it is hard to tell whether failures andanomalies in these components are related toa given workflow. For theGrid to be truly usable, much of this uncertainty must be elim- inated.We propose two new Grid monitoring elements, Grid workflow identifiersand consistent component lifecycle events, that will make Gridtroubleshooting easier, and thus make Grids more usable, by simplifyingthe correlation of Grid monitoring data with a particular Gridworkflow.
Distributed Accounting on the Grid
NASA Technical Reports Server (NTRS)
Thigpen, William; Hacker, Thomas J.; McGinnis, Laura F.; Athey, Brian D.
2001-01-01
By the late 1990s, the Internet was adequately equipped to move vast amounts of data between HPC (High Performance Computing) systems, and efforts were initiated to link together the national infrastructure of high performance computational and data storage resources together into a general computational utility 'grid', analogous to the national electrical power grid infrastructure. The purpose of the Computational grid is to provide dependable, consistent, pervasive, and inexpensive access to computational resources for the computing community in the form of a computing utility. This paper presents a fully distributed view of Grid usage accounting and a methodology for allocating Grid computational resources for use on a Grid computing system.
Marshall Space Flight Center surface modeling and grid generation applications
NASA Technical Reports Server (NTRS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-01-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
Architecture and grid application of cluster computing system
NASA Astrophysics Data System (ADS)
Lv, Yi; Yu, Shuiqin; Mao, Youju
2004-11-01
Recently, people pay more attention to the grid technology. It can not only connect all kinds of resources in the network, but also put them into a super transparent computing environment for customers to realize mete-computing which can share computing resources. Traditional parallel computing system, such as SMP(Symmetrical multiprocessor) and MPP(massively parallel processor), use multi-processors to raise computing speed in a close coupling way, so the flexible and scalable performance of the system are limited, as a result of it, the system can't meet the requirement of the grid technology. In this paper, the architecture of cluster computing system applied in grid nodes is introduced. It mainly includes the following aspects. First, the network architecture of cluster computing system in grid nodes is analyzed and designed. Second, how to realize distributing computing (including coordinating computing and sharing computing) of cluster computing system in grid nodes to construct virtual node computers is discussed. Last, communication among grid nodes is analyzed. In other words, it discusses how to realize single reflection to let all the service requirements from customers be met through sending to the grid nodes.
Marshall Space Flight Center surface modeling and grid generation applications
NASA Astrophysics Data System (ADS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-03-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
The BioGRID interaction database: 2015 update.
Chatr-Aryamontri, Andrew; Breitkreutz, Bobby-Joe; Oughtred, Rose; Boucher, Lorrie; Heinicke, Sven; Chen, Daici; Stark, Chris; Breitkreutz, Ashton; Kolas, Nadine; O'Donnell, Lara; Reguly, Teresa; Nixon, Julie; Ramage, Lindsay; Winter, Andrew; Sellam, Adnane; Chang, Christie; Hirschman, Jodi; Theesfeld, Chandra; Rust, Jennifer; Livstone, Michael S; Dolinski, Kara; Tyers, Mike
2015-01-01
The Biological General Repository for Interaction Datasets (BioGRID: http://thebiogrid.org) is an open access database that houses genetic and protein interactions curated from the primary biomedical literature for all major model organism species and humans. As of September 2014, the BioGRID contains 749,912 interactions as drawn from 43,149 publications that represent 30 model organisms. This interaction count represents a 50% increase compared to our previous 2013 BioGRID update. BioGRID data are freely distributed through partner model organism databases and meta-databases and are directly downloadable in a variety of formats. In addition to general curation of the published literature for the major model species, BioGRID undertakes themed curation projects in areas of particular relevance for biomedical sciences, such as the ubiquitin-proteasome system and various human disease-associated interaction networks. BioGRID curation is coordinated through an Interaction Management System (IMS) that facilitates the compilation interaction records through structured evidence codes, phenotype ontologies, and gene annotation. The BioGRID architecture has been improved in order to support a broader range of interaction and post-translational modification types, to allow the representation of more complex multi-gene/protein interactions, to account for cellular phenotypes through structured ontologies, to expedite curation through semi-automated text-mining approaches, and to enhance curation quality control.
The BioGRID interaction database: 2015 update
Chatr-aryamontri, Andrew; Breitkreutz, Bobby-Joe; Oughtred, Rose; Boucher, Lorrie; Heinicke, Sven; Chen, Daici; Stark, Chris; Breitkreutz, Ashton; Kolas, Nadine; O'Donnell, Lara; Reguly, Teresa; Nixon, Julie; Ramage, Lindsay; Winter, Andrew; Sellam, Adnane; Chang, Christie; Hirschman, Jodi; Theesfeld, Chandra; Rust, Jennifer; Livstone, Michael S.; Dolinski, Kara; Tyers, Mike
2015-01-01
The Biological General Repository for Interaction Datasets (BioGRID: http://thebiogrid.org) is an open access database that houses genetic and protein interactions curated from the primary biomedical literature for all major model organism species and humans. As of September 2014, the BioGRID contains 749 912 interactions as drawn from 43 149 publications that represent 30 model organisms. This interaction count represents a 50% increase compared to our previous 2013 BioGRID update. BioGRID data are freely distributed through partner model organism databases and meta-databases and are directly downloadable in a variety of formats. In addition to general curation of the published literature for the major model species, BioGRID undertakes themed curation projects in areas of particular relevance for biomedical sciences, such as the ubiquitin-proteasome system and various human disease-associated interaction networks. BioGRID curation is coordinated through an Interaction Management System (IMS) that facilitates the compilation interaction records through structured evidence codes, phenotype ontologies, and gene annotation. The BioGRID architecture has been improved in order to support a broader range of interaction and post-translational modification types, to allow the representation of more complex multi-gene/protein interactions, to account for cellular phenotypes through structured ontologies, to expedite curation through semi-automated text-mining approaches, and to enhance curation quality control. PMID:25428363
An overset grid method for global geomagnetic induction
NASA Astrophysics Data System (ADS)
Weiss, Chester J.
2014-07-01
A new finite difference solution to the global geomagnetic induction problem is developed and tested, based on a modified Lorenz gauge of the magnetic vector and electric scalar potentials and implementing a novel, overset `Yin-Yang' grid that avoids unnecessary mesh refinement at the geographic poles. Previously used in whole-earth mantle convection models, the overset grid is built from a pair of partially overlapping mid-latitude latitude-longitude (lat/lon) grids, one of which is rotated with respect to the other for complete coverage of the sphere. Because of this symmetry, only one set of finite difference templates is required for global discretization of the governing Maxwell equations, a redundancy that is exploited for computational efficiency and multithreaded parallelization. Comparisons between solutions obtained by the proposed method show excellent agreement with those obtained by independent integral equation methods for 1-D, 2-D and 3-D problem geometries. The computational footprint of the method is minimized through a (non-symmetric) matrix-free BiCG-STAB iterative solver which computes finite difference matrix coefficients `on the fly' as needed, rather than pulling stored values from memory. Scaling of the matrix-free BiCG-STAB algorithm with problem size shows behaviour similar to that seen with the (symmetric) QMR algorithm used in the Cartesian case from which the present algorithm is based. The proposed method may therefore provide a competitive addition to the existing body of global-scale geomagnetic induction modelling algorithms, allowing for resource-efficient forward modelling as the kernel for large-scale computing such as inversion of geomagnetic response functions, computational hypothesis testing and parametric studies of mantle geodynamics and physiochemical state.
NASA Technical Reports Server (NTRS)
Ziebarth, John P.; Meyer, Doug
1992-01-01
The coordination is examined of necessary resources, facilities, and special personnel to provide technical integration activities in the area of computational fluid dynamics applied to propulsion technology. Involved is the coordination of CFD activities between government, industry, and universities. Current geometry modeling, grid generation, and graphical methods are established to use in the analysis of CFD design methodologies.
Enabling Campus Grids with Open Science Grid Technology
NASA Astrophysics Data System (ADS)
Weitzel, Derek; Bockelman, Brian; Fraser, Dan; Pordes, Ruth; Swanson, David
2011-12-01
The Open Science Grid is a recognized key component of the US national cyber-infrastructure enabling scientific discovery through advanced high throughput computing. The principles and techniques that underlie the Open Science Grid can also be applied to Campus Grids since many of the requirements are the same, even if the implementation technologies differ. We find five requirements for a campus grid: trust relationships, job submission, resource independence, accounting, and data management. The Holland Computing Center's campus grid at the University of Nebraska-Lincoln was designed to fulfill the requirements of a campus grid. A bridging daemon was designed to bring non-Condor clusters into a grid managed by Condor. Condor features which make it possible to bridge Condor sites into a multi-campus grid have been exploited at the Holland Computing Center as well.
Finite-surface method for the Maxwell equations in generalized coordinates
NASA Technical Reports Server (NTRS)
Vinokur, Marcel; Yarrow, Maurice
1993-01-01
A finite-surface technique for the Maxwell equations in generalized nonorthogonal coordinates is developed. It directly applies the integral Faraday's and Ampere's laws to faces of primary and secondary grid cells, respectively. The technique features an accurate treatment of matching conditions at a material interface, grid singularities, and radiation conditions at outer boundaries.
... will seem to be continually on the go—running, kicking, climbing, jumping. His attention span, which was ... his coordination. In the months ahead, your child’s running will become smoother and more coordinated. He’ll ...
Rokach, Joshua Z.
2010-10-15
The country has progressed in a relatively short time from rotary dial phones to computers, cell phones, and iPads. With proper planning and orderly policy implementation, the same will happen with the Smart Grid. Here are some suggestions on how to proceed. (author)
Bloyd, Cary N.
2012-03-01
This brief paper describes the activities of the Asia Pacific Economic Cooperation (APEC) Smart Grid Initiative (ASGI) which is being led by the U.S. and developed by the APEC Energy Working Group. In the paper, I describe the origin of the initiative and briefly mention the four major elements of the initiative along with existing APEC projects which support it.
Rabari, Anil; Fadipe, Oloruntomi
2014-03-31
NSTAR Electric & Gas Corporation (“the Company”, or “NSTAR”) developed and implemented a Smart Grid pilot program beginning in 2010 to demonstrate the viability of leveraging existing automated meter reading (“AMR”) deployments to provide much of the Smart Grid functionality of advanced metering infrastructure (“AMI”), but without the large capital investment that AMI rollouts typically entail. In particular, a central objective of the Smart Energy Pilot was to enable residential dynamic pricing (time-of-use “TOU” and critical peak rates and rebates) and two-way direct load control (“DLC”) by continually capturing AMR meter data transmissions and communicating through customer-sited broadband connections in conjunction with a standardsbased home area network (“HAN”). The pilot was supported by the U.S. Department of Energy’s (“DOE”) through the Smart Grid Demonstration program. NSTAR was very pleased to not only receive the funding support from DOE, but the guidance and support of the DOE throughout the pilot. NSTAR is also pleased to report to the DOE that it was able to execute and deliver a successful pilot on time and on budget. NSTAR looks for future opportunities to work with the DOE and others in future smart grid projects.
High resolution finite volume methods on arbitrary grids via wave propagation
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1987-01-01
A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.
An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement.
Edgel, Jared; Benzley, Steven E.; Owen, Steven James
2010-08-01
Most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is often too coarse in some areas and over refined in other areas. Because this method generates 27 new hexes in place of a single hex, there is little control on mesh density. This paper presents an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement method. 2-refinement is based on dividing the hex to be refined into eight new hexes. This method allows a greater control on mesh density when compared to a 3-refinement procedure. This adaptive all-hexahedral meshing algorithm provides a mesh that is efficient for analysis by providing a high element density in specific locations and a reduced mesh density in other areas. In addition, this tool can be effectively used for inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, which have shown great promise in accommodating automatic all-hexahedral algorithms. This adaptive all-hexahedral grid-based meshing algorithm employs a 2-refinement insertion method. This allows greater control on mesh density when compared to 3-refinement methods. This algorithm uses a two layer transition zone to increase element quality and keeps transitions from lower to higher mesh densities smooth. Templates were introduced to allow both convex and concave refinement.
Well-balanced shallow water flow simulation on quadtree cut cell grids
NASA Astrophysics Data System (ADS)
An, Hyunuk; Yu, Soonyoung
2012-04-01
A well-balanced shallow water flow model on quadtree cut cell grids is presented. The Cartesian cut cell method is applied due to its flexibility in treating curvilinear boundaries. In order to preserve a lake-at-rest and the positivity of water depths in drying/wetting zones, the hydrostatic reconstruction proposed by Audusse et al. [1] is implemented on cut cell grids. In addition, the gradient construction method on cut cells proposed by Causon et al. [8] is modified due to the spurious calculation when a solid boundary is nearly parallel to grids. The numerical schemes mentioned above are employed in Gerris which is open source free software and provides a shallow water solver on adaptive quadtree grids. The applied numerical schemes are validated using four test simulations: still water in an inclined domain; oscillation in a parabolic container; shock reflection by a circular cylinder; flash flood experiment in a model city. The simulation results are compared with analytical solutions, experiment data and the results simulated by other researchers.
A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids
Henshaw, W D
2005-09-23
A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.
Klonoff, David C; Lias, Courtney; Vigersky, Robert; Clarke, William; Parkes, Joan Lee; Sacks, David B; Kirkman, M Sue; Kovatchev, Boris
2014-07-01
Currently used error grids for assessing clinical accuracy of blood glucose monitors are based on out-of-date medical practices. Error grids have not been widely embraced by regulatory agencies for clearance of monitors, but this type of tool could be useful for surveillance of the performance of cleared products. Diabetes Technology Society together with representatives from the Food and Drug Administration, the American Diabetes Association, the Endocrine Society, and the Association for the Advancement of Medical Instrumentation, and representatives of academia, industry, and government, have developed a new error grid, called the surveillance error grid (SEG) as a tool to assess the degree of clinical risk from inaccurate blood glucose (BG) monitors. A total of 206 diabetes clinicians were surveyed about the clinical risk of errors of measured BG levels by a monitor. The impact of such errors on 4 patient scenarios was surveyed. Each monitor/reference data pair was scored and color-coded on a graph per its average risk rating. Using modeled data representative of the accuracy of contemporary meters, the relationships between clinical risk and monitor error were calculated for the Clarke error grid (CEG), Parkes error grid (PEG), and SEG. SEG action boundaries were consistent across scenarios, regardless of whether the patient was type 1 or type 2 or using insulin or not. No significant differences were noted between responses of adult/pediatric or 4 types of clinicians. Although small specific differences in risk boundaries between US and non-US clinicians were noted, the panel felt they did not justify separate grids for these 2 types of clinicians. The data points of the SEG were classified in 15 zones according to their assigned level of risk, which allowed for comparisons with the classic CEG and PEG. Modeled glucose monitor data with realistic self-monitoring of blood glucose errors derived from meter testing experiments plotted on the SEG when compared to
NASA Technical Reports Server (NTRS)
Nothnagel, A.
2013-01-01
We present the IVS analysis coordination issues of 2012. The IVS Analysis Coordinator is responsible for generating and disseminating the official IVS products. This requires consistency of the input data by strict adherence to models and conventions. The term of the current IVS Analysis Coordinator will end on February 28, 2013.
Processing Coordination Ambiguity
ERIC Educational Resources Information Center
Engelhardt, Paul E.; Ferreira, Fernanda
2010-01-01
We examined temporarily ambiguous coordination structures such as "put the butter in the bowl and the pan on the towel." Minimal Attachment predicts that the ambiguous noun phrase "the pan" will be interpreted as a noun-phrase coordination structure because it is syntactically simpler than clausal coordination. Constraint-based theories assume…
Literacy Coordinators' Handbook.
ERIC Educational Resources Information Center
Department for Education and Skills, London (England).
This handbook is designed to provide support for England's National Literacy Strategy's Literacy Coordinators leading and coordinating literacy across the school. The handbook is designed as a working document and will contain additional materials, LEA (local education authorities) guidance, and additional papers which Coordinators may choose to…
Basso, T.; DeBlasio, R.
2012-04-01
The IEEE American National Standards smart grid publications and standards development projects IEEE 2030, which addresses smart grid interoperability, and IEEE 1547TM, which addresses distributed resources interconnection with the grid, have made substantial progress since 2009. The IEEE 2030TM and 1547 standards series focus on systems-level aspects and cover many of the technical integration issues involved in a mature smart grid. The status and highlights of these two IEEE series of standards, which are sponsored by IEEE Standards Coordinating Committee 21 (SCC21), are provided in this paper.
Current Grid operation and future role of the Grid
NASA Astrophysics Data System (ADS)
Smirnova, O.
2012-12-01
Grid-like technologies and approaches became an integral part of HEP experiments. Some other scientific communities also use similar technologies for data-intensive computations. The distinct feature of Grid computing is the ability to federate heterogeneous resources of different ownership into a seamless infrastructure, accessible via a single log-on. Like other infrastructures of similar nature, Grid functioning requires not only technologically sound basis, but also reliable operation procedures, monitoring and accounting. The two aspects, technological and operational, are closely related: weaker is the technology, more burden is on operations, and other way around. As of today, Grid technologies are still evolving: at CERN alone, every LHC experiment uses an own Grid-like system. This inevitably creates a heavy load on operations. Infrastructure maintenance, monitoring and incident response are done on several levels, from local system administrators to large international organisations, involving massive human effort worldwide. The necessity to commit substantial resources is one of the obstacles faced by smaller research communities when moving computing to the Grid. Moreover, most current Grid solutions were developed under significant influence of HEP use cases, and thus need additional effort to adapt them to other applications. Reluctance of many non-HEP researchers to use Grid negatively affects the outlook for national Grid organisations, which strive to provide multi-science services. We started from the situation where Grid organisations were fused with HEP laboratories and national HEP research programmes; we hope to move towards the world where Grid will ultimately reach the status of generic public computing and storage service provider and permanent national and international Grid infrastructures will be established. How far will we be able to advance along this path, depends on us. If no standardisation and convergence efforts will take place
Hamilton, Scott; Hamilton, Trevor J
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes's "radical" or "mind-body" dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes's famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student's understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student's understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur. PMID:26321981
Hamilton, Scott; Hamilton, Trevor J
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes's "radical" or "mind-body" dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes's famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student's understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student's understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur.
Hamilton, Scott; Hamilton, Trevor J.
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes’s “radical” or “mind-body” dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes’s famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student’s understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student’s understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur. PMID:26321981
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.
Ion Engine Grid Gap Measurements
NASA Technical Reports Server (NTRS)
Soulas, Gerge C.; Frandina, Michael M.
2004-01-01
A simple technique for measuring the grid gap of an ion engine s ion optics during startup and steady-state operation was demonstrated with beam extraction. The grid gap at the center of the ion optics assembly was measured with a long distance microscope that was focused onto an alumina pin that protruded through the center accelerator grid aperture and was mechanically attached to the screen grid. This measurement technique was successfully applied to a 30 cm titanium ion optics assembly mounted onto an NSTAR engineering model ion engine. The grid gap and each grid s movement during startup from room temperature to both full and low power were measured. The grid gaps with and without beam extraction were found to be significantly different. The grid gaps at the ion optics center were both significantly smaller than the cold grid gap and different at the two power levels examined. To avoid issues associated with a small grid gap during thruster startup with titanium ion optics, a simple method was to operate the thruster initially without beam extraction to heat the ion optics. Another possible method is to apply high voltage to the grids prior to igniting the discharge because power deposition to the grids from the plasma is lower with beam extraction than without. Further testing would be required to confirm this approach.
NASA Astrophysics Data System (ADS)
Delcroix, Stefaan; Fisher, Michael J.
2012-07-01
In this paper, we compute the Hausdorff dimension of a graph-directed set when the underlying multigraph is a Cartesian product or a tensor product of several multigraphs. We give explicit formulas in terms of the eigenvalues of the graph and the similarity ratios used with each graph.
Movement coordination during conversation.
Latif, Nida; Barbosa, Adriano V; Vatikiotis-Bateson, Eric; Vatiokiotis-Bateson, Eric; Castelhano, Monica S; Munhall, K G
2014-01-01
Behavioral coordination and synchrony contribute to a common biological mechanism that maintains communication, cooperation and bonding within many social species, such as primates and birds. Similarly, human language and social systems may also be attuned to coordination to facilitate communication and the formation of relationships. Gross similarities in movement patterns and convergence in the acoustic properties of speech have already been demonstrated between interacting individuals. In the present studies, we investigated how coordinated movements contribute to observers' perception of affiliation (friends vs. strangers) between two conversing individuals. We used novel computational methods to quantify motor coordination and demonstrated that individuals familiar with each other coordinated their movements more frequently. Observers used coordination to judge affiliation between conversing pairs but only when the perceptual stimuli were restricted to head and face regions. These results suggest that observed movement coordination in humans might contribute to perceptual decisions based on availability of information to perceivers. PMID:25119189
Movement Coordination during Conversation
Latif, Nida; Barbosa, Adriano V.; Vatiokiotis-Bateson, Eric; Castelhano, Monica S.; Munhall, K. G.
2014-01-01
Behavioral coordination and synchrony contribute to a common biological mechanism that maintains communication, cooperation and bonding within many social species, such as primates and birds. Similarly, human language and social systems may also be attuned to coordination to facilitate communication and the formation of relationships. Gross similarities in movement patterns and convergence in the acoustic properties of speech have already been demonstrated between interacting individuals. In the present studies, we investigated how coordinated movements contribute to observers’ perception of affiliation (friends vs. strangers) between two conversing individuals. We used novel computational methods to quantify motor coordination and demonstrated that individuals familiar with each other coordinated their movements more frequently. Observers used coordination to judge affiliation between conversing pairs but only when the perceptual stimuli were restricted to head and face regions. These results suggest that observed movement coordination in humans might contribute to perceptual decisions based on availability of information to perceivers. PMID:25119189
Basal ganglia outputs map instantaneous position coordinates during behavior.
Barter, Joseph W; Li, Suellen; Sukharnikova, Tatyana; Rossi, Mark A; Bartholomew, Ryan A; Yin, Henry H
2015-02-11
The basal ganglia (BG) are implicated in many movement disorders, yet how they contribute to movement remains unclear. Using wireless in vivo recording, we measured BG output from the substantia nigra pars reticulata (SNr) in mice while monitoring their movements with video tracking. The firing rate of most nigral neurons reflected Cartesian coordinates (either x- or y-coordinates) of the animal's head position during movement. The firing rates of SNr neurons are either positively or negatively correlated with the coordinates. Using an egocentric reference frame, four types of neurons can be classified: each type increases firing during movement in a particular direction (left, right, up, down), and decreases firing during movement in the opposite direction. Given the high correlation between the firing rate and the x and y components of the position vector, the movement trajectory can be reconstructed from neural activity. Our results therefore demonstrate a quantitative and continuous relationship between BG output and behavior. Thus, a steady BG output signal from the SNr (i.e., constant firing rate) is associated with the lack of overt movement, when a stable posture is maintained by structures downstream of the BG. Any change in SNr firing rate is associated with a change in position (i.e., movement). We hypothesize that the SNr output quantitatively determines the direction, velocity, and amplitude of voluntary movements. By changing the reference signals to downstream position control systems, the BG can produce transitions in body configurations and initiate actions.
Basal ganglia outputs map instantaneous position coordinates during behavior.
Barter, Joseph W; Li, Suellen; Sukharnikova, Tatyana; Rossi, Mark A; Bartholomew, Ryan A; Yin, Henry H
2015-02-11
The basal ganglia (BG) are implicated in many movement disorders, yet how they contribute to movement remains unclear. Using wireless in vivo recording, we measured BG output from the substantia nigra pars reticulata (SNr) in mice while monitoring their movements with video tracking. The firing rate of most nigral neurons reflected Cartesian coordinates (either x- or y-coordinates) of the animal's head position during movement. The firing rates of SNr neurons are either positively or negatively correlated with the coordinates. Using an egocentric reference frame, four types of neurons can be classified: each type increases firing during movement in a particular direction (left, right, up, down), and decreases firing during movement in the opposite direction. Given the high correlation between the firing rate and the x and y components of the position vector, the movement trajectory can be reconstructed from neural activity. Our results therefore demonstrate a quantitative and continuous relationship between BG output and behavior. Thus, a steady BG output signal from the SNr (i.e., constant firing rate) is associated with the lack of overt movement, when a stable posture is maintained by structures downstream of the BG. Any change in SNr firing rate is associated with a change in position (i.e., movement). We hypothesize that the SNr output quantitatively determines the direction, velocity, and amplitude of voluntary movements. By changing the reference signals to downstream position control systems, the BG can produce transitions in body configurations and initiate actions. PMID:25673860
Cloud Computing for the Grid: GridControl: A Software Platform to Support the Smart Grid
2012-02-08
GENI Project: Cornell University is creating a new software platform for grid operators called GridControl that will utilize cloud computing to more efficiently control the grid. In a cloud computing system, there are minimal hardware and software demands on users. The user can tap into a network of computers that is housed elsewhere (the cloud) and the network runs computer applications for the user. The user only needs interface software to access all of the cloud’s data resources, which can be as simple as a web browser. Cloud computing can reduce costs, facilitate innovation through sharing, empower users, and improve the overall reliability of a dispersed system. Cornell’s GridControl will focus on 4 elements: delivering the state of the grid to users quickly and reliably; building networked, scalable grid-control software; tailoring services to emerging smart grid uses; and simulating smart grid behavior under various conditions.
Wang, Hsiang-Hsu; Taam, Ronald E.; Yen, David C. C.
2015-11-15
Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two-dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and self-gravitational forces are relatively straightforward for attaining second-order accuracy. However, in polar coordinates, a second-order calculation of self-gravitational forces is required for matching the second-order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second-order accuracy without artificial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly linear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.
Gridded electron reversal ionizer
NASA Technical Reports Server (NTRS)
Chutjian, Ara (Inventor)
1993-01-01
A gridded electron reversal ionizer forms a three dimensional cloud of zero or near-zero energy electrons in a cavity within a filament structure surrounding a central electrode having holes through which the sample gas, at reduced pressure, enters an elongated reversal volume. The resultant negative ion stream is applied to a mass analyzer. The reduced electron and ion space-charge limitations of this configuration enhances detection sensitivity for material to be detected by electron attachment, such as narcotic and explosive vapors. Positive ions may be generated by generating electrons having a higher energy, sufficient to ionize the target gas and pulsing the grid negative to stop the electron flow and pulsing the extraction aperture positive to draw out the positive ions.
Smart Grid Demonstration Project
Miller, Craig; Carroll, Paul; Bell, Abigail
2015-03-11
The National Rural Electric Cooperative Association (NRECA) organized the NRECA-U.S. Department of Energy (DOE) Smart Grid Demonstration Project (DE-OE0000222) to install and study a broad range of advanced smart grid technologies in a demonstration that spanned 23 electric cooperatives in 12 states. More than 205,444 pieces of electronic equipment and more than 100,000 minor items (bracket, labels, mounting hardware, fiber optic cable, etc.) were installed to upgrade and enhance the efficiency, reliability, and resiliency of the power networks at the participating co-ops. The objective of this project was to build a path for other electric utilities, and particularly electrical cooperatives, to adopt emerging smart grid technology when it can improve utility operations, thus advancing the co-ops’ familiarity and comfort with such technology. Specifically, the project executed multiple subprojects employing a range of emerging smart grid technologies to test their cost-effectiveness and, where the technology demonstrated value, provided case studies that will enable other electric utilities—particularly electric cooperatives— to use these technologies. NRECA structured the project according to the following three areas: Demonstration of smart grid technology; Advancement of standards to enable the interoperability of components; and Improvement of grid cyber security. We termed these three areas Technology Deployment Study, Interoperability, and Cyber Security. Although the deployment of technology and studying the demonstration projects at coops accounted for the largest portion of the project budget by far, we see our accomplishments in each of the areas as critical to advancing the smart grid. All project deliverables have been published. Technology Deployment Study: The deliverable was a set of 11 single-topic technical reports in areas related to the listed technologies. Each of these reports has already been submitted to DOE, distributed to co-ops, and
Poirot, Jordan; De Luna, Paolo; Rainer, Gregor
2016-04-01
We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. PMID:26843607
Wireless Communications in Smart Grid
NASA Astrophysics Data System (ADS)
Bojkovic, Zoran; Bakmaz, Bojan
Communication networks play a crucial role in smart grid, as the intelligence of this complex system is built based on information exchange across the power grid. Wireless communications and networking are among the most economical ways to build the essential part of the scalable communication infrastructure for smart grid. In particular, wireless networks will be deployed widely in the smart grid for automatic meter reading, remote system and customer site monitoring, as well as equipment fault diagnosing. With an increasing interest from both the academic and industrial communities, this chapter systematically investigates recent advances in wireless communication technology for the smart grid.
Grid integrated distributed PV (GridPV).
Reno, Matthew J.; Coogan, Kyle
2013-08-01
This manual provides the documentation of the MATLAB toolbox of functions for using OpenDSS to simulate the impact of solar energy on the distribution system. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feeder on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions. Each function in the toolbox is documented with the function use syntax, full description, function input list, function output list, example use, and example output.
NASA Technical Reports Server (NTRS)
Stocker, Erich Franz
2007-01-01
NASA's Tropical Rainfall Measuring Mission (TRMM) has many products that contain instantaneous or gridded rain rates often among many other parameters. However, these products because of their completeness can often seem intimidating to users just desiring surface rain rates. For example one of the gridded monthly products contains well over 200 parameters. It is clear that if only rain rates are desired, this many parameters might prove intimidating. In addition, for many good reasons these products are archived and currently distributed in HDF format. This also can be an inhibiting factor in using TRMM rain rates. To provide a simple format and isolate just the rain rates from the many other parameters, the TRMM product created a series of gridded products in ASCII text format. This paper describes the various text rain rate products produced. It provides detailed information about parameters and how they are calculated. It also gives detailed format information. These products are used in a number of applications with the TRMM processing system. The products are produced from the swath instantaneous rain rates and contain information from the three major TRMM instruments: radar, radiometer, and combined. They are simple to use, human readable, and small for downloading.
NASA Technical Reports Server (NTRS)
Banks, D. W.; Hafez, M. M.
1996-01-01
Grid adaptation for structured meshes is the art of using information from an existing, but poorly resolved, solution to automatically redistribute the grid points in such a way as to improve the resolution in regions of high error, and thus the quality of the solution. This involves: (1) generate a grid vis some standard algorithm, (2) calculate a solution on this grid, (3) adapt the grid to this solution, (4) recalculate the solution on this adapted grid, and (5) repeat steps 3 and 4 to satisfaction. Steps 3 and 4 can be repeated until some 'optimal' grid is converged to but typically this is not worth the effort and just two or three repeat calculations are necessary. They also may be repeated every 5-10 time steps for unsteady calculations.
Progress in Grid Generation: From Chimera to DRAGON Grids
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Kao, Kai-Hsiung
1994-01-01
Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are
Enhancing control of grid distribution in algebraic grid generation
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Shih, T. I.-P.; Roelke, R. J.
1992-01-01
Three techniques are presented to enhance the control of grid-point distribution for a class of algebraic grid generation methods known as the two-, four- and six-boundary methods. First, multidimensional stretching functions are presented, and a technique is devised to construct them based on the desired distribution of grid points along certain boundaries. Second, a normalization procedure is proposed which allows more effective control over orthogonality of grid lines at boundaries and curvature of grid lines near boundaries. And third, interpolating functions based on tension splines are introduced to control curvature of grid lines in the interior of the spatial domain. In addition to these three techniques, consistency conditions are derived which must be satisfied by all user-specified data employed in the grid generation process to control grid-point distribution. The usefulness of the techniques developed in this study was demonstrated by using them in conjunction with the two- and four-boundary methods to generate several grid systems, including a three-dimensional grid system in the coolant passage of a radial turbine blade with serpentine channels and pin fins.
GridTool: A surface modeling and grid generation tool
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1995-01-01
GridTool is designed around the concept that the surface grids are generated on a set of bi-linear patches. This type of grid generation is quite easy to implement, and it avoids the problems associated with complex CAD surface representations and associated surface parameterizations. However, the resulting surface grids are close to but not on the original CAD surfaces. This problem can be alleviated by projecting the resulting surface grids onto the original CAD surfaces. GridTool is designed primary for unstructured grid generation systems. Currently, GridTool supports VGRID and FELISA systems, and it can be easily extended to support other unstructured grid generation systems. The data in GridTool is stored parametrically so that once the problem is set up, one can modify the surfaces and the entire set of points, curves and patches will be updated automatically. This is very useful in a multidisciplinary design and optimization process. GridTool is written entirely in ANSI 'C', the interface is based on the FORMS library, and the graphics is based on the GL library. The code has been tested successfully on IRIS workstations running IRIX4.0 and above. The memory is allocated dynamically, therefore, memory size will depend on the complexity of geometry/grid. GridTool data structure is based on a link-list structure which allows the required memory to expand and contract dynamically according to the user's data size and action. Data structure contains several types of objects such as points, curves, patches, sources and surfaces. At any given time, there is always an active object which is drawn in magenta, or in their highlighted colors as defined by the resource file which will be discussed later.
Running GCM physics and dynamics on different grids: Algorithm and tests
NASA Astrophysics Data System (ADS)
Molod, A.
2006-12-01
The major drawback in the use of sigma coordinates in atmospheric GCMs, namely the error in the pressure gradient term near sloping terrain, leaves the use of eta coordinates an important alternative. A central disadvantage of an eta coordinate, the inability to retain fine resolution in the vertical as the surface rises above sea level, is addressed here. An `alternate grid' technique is presented which allows the tendencies of state variables due to the physical parameterizations to be computed on a vertical grid (the `physics grid') which retains fine resolution near the surface, while the remaining terms in the equations of motion are computed using an eta coordinate (the `dynamics grid') with coarser vertical resolution. As a simple test of the technique a set of perpetual equinox experiments using a simplified lower boundary condition with no land and no topography were performed. The results show that for both low and high resolution alternate grid experiments, much of the benefit of increased vertical resolution for the near surface meridional wind (and mass streamfield) can be realized by enhancing the vertical resolution of the `physics grid' in the manner described here. In addition, approximately half of the increase in zonal jet strength seen with increased vertical resolution can be realized using the `alternate grid' technique. A pair of full GCM experiments with realistic lower boundary conditions and topography were also performed. It is concluded that the use of the `alternate grid' approach offers a promising way forward to alleviate a central problem associated with the use of the eta coordinate in atmospheric GCMs.
Lithographic tool dynamic coordinate calibration for CDU improvement
NASA Astrophysics Data System (ADS)
Yang, Zhiyong; Mao, Fanglin; Bourov, Anatoly; Cheng, Jianrui; He, Le
2012-03-01
In lithographic scanner, many different physical factors could impact to image quality and CD uniformity. In optical systems, the pupil filling quality (source shape), wavefront error and stray light can decrease the intensity contrast and shrink the process window. In mechanical domain, the vibration and scanning synchronization error have the similar effect to imaging process. Imaging in scanner is a dynamic exposure process and in this process, aerial image should keep the same relative position to the wafer. It requests the lithographic tool must have a very stable mechanical frame and very good motion control performance. In addition, the wafer stage, reticle stage's coordinate and projection lens' grid should be matched exactly, include the scanning direction and velocity ratio. The tool's alignment system can calibrate the statistic coordinate for overlay, but it cannot calibrate the dynamic coordinate in scanning direction very well because projection lens' grid has a small asymmetric signiture. This systematic error should be calibrated for CDU improvement. An imaging model considering the motion blurring is represented in this paper and based on this model, the dynamic coordinate's error could be analyzed. Furthermore, exposure method can be used to calibrate the dynamic coordinate and improve the CD uniformity. Exposure latitude will be used to check and calibrate the lithographic tool's dynamic coordinate. We designed a special calibration process to obtain the best dynamic coordinate setting for scanner. In this process, some tool's coordinate parameters (scanning skew and scale) have been changed for every field to obtain the multi-dimensions' exposure information. Exposure window can be represented from this result, and in this exposure window, the best dynamic coordinate setting could be found. After the dynamic coordinate calibrated, the CDU is improved.
Grid crusher apparatus and method
McDaniels, J.D. Jr.
1994-01-11
A grid crusher apparatus and method are provided for a nuclear fuel rod consolidation system. Spacer grids are crushed within a basket which is then placed in a storage canister. The grid crusher apparatus has a ram assembly and a basket driving mechanism. The ram assembly has a sleeve ram and a central ram. The sleeve ram surrounds the central ram which is longitudinally movable within the sleeve ram. The central ram protrudes from the sleeve ram at a ram contact end and is retractable upon application of a preselected force to the central ram so that the central ram is flush with the sleeve ram at the ram contact end. The basket driving mechanism is configured to move the basket containing a spacer grid towards the ram contact end so that the spacer grid is crushed within the basket. The spacer grid is crushed by the combination of successive forces from the central ram and the sleeve ram, respectively. Essentially, the central portion of the spacer grid is crushed first, and then the remaining outer portion of the spacer grid is crushed to complete the crushing action of the spacer grid. The foregoing process is repeated for other spacer grids until the basket reaches a predetermined allowable capacity, and then the basket is stored in a storage canister. 11 figs.
Evaluating the Information Power Grid using the NAS Grid Benchmarks
NASA Technical Reports Server (NTRS)
VanderWijngaartm Rob F.; Frumkin, Michael A.
2004-01-01
The NAS Grid Benchmarks (NGB) are a collection of synthetic distributed applications designed to rate the performance and functionality of computational grids. We compare several implementations of the NGB to determine programmability and efficiency of NASA's Information Power Grid (IPG), whose services are mostly based on the Globus Toolkit. We report on the overheads involved in porting existing NGB reference implementations to the IPG. No changes were made to the component tasks of the NGB can still be improved.
Study on the grid-based distributed virtual geo-environment (DVGE-G)
NASA Astrophysics Data System (ADS)
Tang, Lu-liang; Li, Qing-quan
2005-10-01
It is publicly considered that the next generational Internet technology is grid computing, which supports the sharing and coordinated use of diverse resources in dynamic virtual organizations from geographically and organizationally distributed components. Grid computing characters strong computing ability and broad width information exchange. After analyzing the characteristic of grid computing, this paper expatiates on current application status of grid computing with middleware technology on DVGE-G and the problems it faces. Cooperating with IBM, Microsoft and HP, Globus Toolkit as a standard for grid computing is widely used to develop application on grid, which can run on Unix and Windows operation systems. On the basis of "the five-tiers sandglass structure" and web services technology, Globus presented Open Grid Services Architecture (OGSA), which centered on grid services. According to the characteristic of DVGE-G and the development of current grid computing, this paper put forward the Grid-Oriented Distributed Network Model for DVGE-G. Virtual group is corresponding with the Virtual Organization in OGSA service, which is easier and more directly for the dynamic virtual groups in GDNM to utilize the grid source and communication each other. The GDNM is not only more advantage to the distributed database consistency management, but also it is more convenient to the virtual group users acquiring the DVGE-G data information, The architecture of DVGE-G designed in this paper is based on OGSA and web services, which is keep to "the five-tiers sandglass structure" of the OGSA. This architecture is more convenient to utilizing grid service and decreasing the conflict with the grid environment. At last, this paper presents the implementation of DVGE-G and the interfaces of Grid Service.
Finite difference grid generation by multivariate blending function interpolation
NASA Technical Reports Server (NTRS)
Anderson, P. G.; Spradley, L. W.
1980-01-01
The General Interpolants Method (GIM) code which solves the multidimensional Navier-Stokes equations for arbitrary geometric domains is described. The geometry module in the GIM code generates two and three dimensional grids over specified flow regimes, establishes boundary condition information and computes finite difference analogs for use in the GIM code numerical solution module. The technique can be classified as an algebraic equation approach. The geometry package uses multivariate blending function interpolation of vector-values functions which define the shapes of the edges and surfaces bounding the flow domain. By employing blending functions which conform to the cardinality conditions the flow domain may be mapped onto a unit square (2-D) or unit cube (3-D), thus producing an intrinsic coordinate system for the region of interest. The intrinsic coordinate system facilitates grid spacing control to allow for optimum distribution of nodes in the flow domain.
The Volume Grid Manipulator (VGM): A Grid Reusability Tool
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
This document is a manual describing how to use the Volume Grid Manipulation (VGM) software. The code is specifically designed to alter or manipulate existing surface and volume structured grids to improve grid quality through the reduction of grid line skewness, removal of negative volumes, and adaption of surface and volume grids to flow field gradients. The software uses a command language to perform all manipulations thereby offering the capability of executing multiple manipulations on a single grid during an execution of the code. The command language can be input to the VGM code by a UNIX style redirected file, or interactively while the code is executing. The manual consists of 14 sections. The first is an introduction to grid manipulation; where it is most applicable and where the strengths of such software can be utilized. The next two sections describe the memory management and the manipulation command language. The following 8 sections describe simple and complex manipulations that can be used in conjunction with one another to smooth, adapt, and reuse existing grids for various computations. These are accompanied by a tutorial section that describes how to use the commands and manipulations to solve actual grid generation problems. The last two sections are a command reference guide and trouble shooting sections to aid in the use of the code as well as describe problems associated with generated scripts for manipulation control.
GridPP: the UK grid for particle physics.
Britton, D; Cass, A J; Clarke, P E L; Coles, J; Colling, D J; Doyle, A T; Geddes, N I; Gordon, J C; Jones, R W L; Kelsey, D P; Lloyd, S L; Middleton, R P; Patrick, G N; Sansum, R A; Pearce, S E
2009-06-28
The start-up of the Large Hadron Collider (LHC) at CERN, Geneva, presents a huge challenge in processing and analysing the vast amounts of scientific data that will be produced. The architecture of the worldwide grid that will handle 15 PB of particle physics data annually from this machine is based on a hierarchical tiered structure. We describe the development of the UK component (GridPP) of this grid from a prototype system to a full exploitation grid for real data analysis. This includes the physical infrastructure, the deployment of middleware, operational experience and the initial exploitation by the major LHC experiments. PMID:19451101
GridPP: the UK grid for particle physics.
Britton, D; Cass, A J; Clarke, P E L; Coles, J; Colling, D J; Doyle, A T; Geddes, N I; Gordon, J C; Jones, R W L; Kelsey, D P; Lloyd, S L; Middleton, R P; Patrick, G N; Sansum, R A; Pearce, S E
2009-06-28
The start-up of the Large Hadron Collider (LHC) at CERN, Geneva, presents a huge challenge in processing and analysing the vast amounts of scientific data that will be produced. The architecture of the worldwide grid that will handle 15 PB of particle physics data annually from this machine is based on a hierarchical tiered structure. We describe the development of the UK component (GridPP) of this grid from a prototype system to a full exploitation grid for real data analysis. This includes the physical infrastructure, the deployment of middleware, operational experience and the initial exploitation by the major LHC experiments.
Multidimensional discretization of conservation laws for unstructured polyhedral grids
Burton, D.E.
1994-08-22
To the extent possible, a discretized system should satisfy the same conservation laws as the physical system. The author considers the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH) which is an extension of a ID scheme due to von Neumann and Richtmyer (VNR). The term staggered refers to spatial centering in which position, velocity, and kinetic energy are centered at nodes, while density, pressure, and internal energy are at cell centers. Traditional SGH formulations consider mass, volume, and momentum conservation, but tend to ignore conservation of total energy, conservation of angular momentum, and requirements for thermodynamic reversibility. The author shows that, once the mass and momentum discretizations have been specified, discretization for other quantities are dictated by the conservation laws and cannot be independently defined. The spatial discretization method employs a finite volume procedure that replaces differential operators with surface integrals. The method is appropriate for multidimensional formulations (1D, 2D, 3D) on unstructured grids formed from polygonal (2D) or polyhedral (3D) cells. Conservation equations can then be expressed in conservation form in which conserved currents are exchanged between control volumes. In addition to the surface integrals, the conservation equations include source terms derived from physical sources or geometrical considerations. In Cartesian geometry, mass and momentum are conserved identically. Discussion of volume conservation will be temporarily deferred. The author shows that the momentum equation leads to a form-preserving definition for kinetic energy and to an exactly conservative evolution equation for internal energy. Similarly, the author derives a form-preserving definition and corresponding conservation equation for a zone-centered angular momentum.
Spatial grid services for adaptive spatial query optimization
NASA Astrophysics Data System (ADS)
Gao, Bingbo; Xie, Chuanjie; Sheng, Wentao
2008-10-01
Spatial information sharing and integration has now become an important issue of Geographical Information Science (GIS). Web Service technologies provide a easy and standard way to share spatial resources over network, and grid technologies which aim at sharing resources such as data, storage, and computational powers can help the sharing go deeper. However, the dynamic characteristic of grid brings complexity to spatial query optimization which is more stressed in GIS domain because spatial operations are both CPU intensive and data intensive. To address this problem, a new grid framework is employed to provide standard spatial services which can also manage and report their state information to the coordinator which is responsible for distributed spatial query optimization.
Adventures in Computational Grids
NASA Technical Reports Server (NTRS)
Walatka, Pamela P.; Biegel, Bryan A. (Technical Monitor)
2002-01-01
Sometimes one supercomputer is not enough. Or your local supercomputers are busy, or not configured for your job. Or you don't have any supercomputers. You might be trying to simulate worldwide weather changes in real time, requiring more compute power than you could get from any one machine. Or you might be collecting microbiological samples on an island, and need to examine them with a special microscope located on the other side of the continent. These are the times when you need a computational grid.
and Drayton Munster, Miroslav Stoyanov
2013-09-20
Sparse Grids are the family of methods of choice for multidimensional integration and interpolation in low to moderate number of dimensions. The method is to select extend a one dimensional set of abscissas, weights and basis functions by taking a subset of all possible tensor products. The module provides the ability to create global and local approximations based on polynomials and wavelets. The software has three components, a library, a wrapper for the library that provides a command line interface via text files ad a MATLAB interface via the command line tool.
2013-09-20
Sparse Grids are the family of methods of choice for multidimensional integration and interpolation in low to moderate number of dimensions. The method is to select extend a one dimensional set of abscissas, weights and basis functions by taking a subset of all possible tensor products. The module provides the ability to create global and local approximations based on polynomials and wavelets. The software has three components, a library, a wrapper for the library thatmore » provides a command line interface via text files ad a MATLAB interface via the command line tool.« less
ERIC Educational Resources Information Center
Varlet, Manuel; Marin, Ludovic; Lagarde, Julien; Bardy, Benoit G.
2011-01-01
The goal of the current study was to investigate whether a visual coupling between two people can produce spontaneous interpersonal postural coordination and change their intrapersonal postural coordination involved in the control of stance. We examined the front-to-back head displacements of participants and the angular motion of their hip and…
2014-05-01
Any complex operation requires a system for management. In most societies, disaster management is the responsibility of the government. Coordination and control is a system that provides the oversight for all of the disaster management functions. The roles and responsibilities of a coordination and control centre include: (1) planning; (2) maintenance of inventories; (3) activation of the disaster response plan; (4) application of indicators of function; (5) surveillance; (6) information management; (7) coordination of activities of the BSFs; (8) decision-making; (9) priority setting; (10) defining overarching goal and objectives for interventions; (11) applying indicators of effectiveness; (12) applying indicators of benefit and impact; (13) exercising authority; (14) managing resources; (15) initiating actions; (16) preventing influx of unneeded resources; (17) defining progress; (18) providing information; (19) liasing with responding organisations; and (20) providing quality assurance. Coordination and control is impossible without communications. To accomplish coordination and control, three factors must be present: (1) mandate; (2) power and authority; and (3) available resources. Coordination and control is responsible for the evaluation of the effectiveness and benefits/impacts of all interventions. Coordination and control centres (CCCs) are organised hierarchically from the on-scene CCCs (incident command) to local provincial to national CCCs. Currently, no comprehensive regional and international CCCs have been universally endorsed. Systems such as the incident command system, the unified command system, and the hospital incident command system are described as are the humanitarian reform movement and the importance of coordination and control in disaster planning and preparedness.
IVS Technology Coordinator Report
NASA Technical Reports Server (NTRS)
Whitney, Alan
2013-01-01
This report of the Technology Coordinator includes the following: 1) continued work to implement the new VLBI2010 system, 2) the 1st International VLBI Technology Workshop, 3) a VLBI Digital- Backend Intercomparison Workshop, 4) DiFX software correlator development for geodetic VLBI, 5) a review of progress towards global VLBI standards, and 6) a welcome to new IVS Technology Coordinator Bill Petrachenko.
Heyne, Matthias; Derrick, Donald
2015-12-01
Tongue surface measurements from midsagittal ultrasound scans are effectively arcs with deviations representing tongue shape, but smoothing-spline analysis of variances (SSANOVAs) assume variance around a horizontal line. Therefore, calculating SSANOVA average curves of tongue traces in Cartesian Coordinates [Davidson, J. Acoust. Soc. Am. 120(1), 407-415 (2006)] creates errors that are compounded at tongue tip and root where average tongue shape deviates most from a horizontal line. This paper introduces a method for transforming data into polar coordinates similar to the technique by Mielke [J. Acoust. Soc. Am. 137(5), 2858-2869 (2015)], but using the virtual origin of a radial ultrasound transducer as the polar origin-allowing data conversion in a manner that is robust against between-subject and between-session variability.
Prepares Overset Grids for Processing
1998-04-22
Many large and complex computational problems require multiple, structured, generically overlapped (overset) grids to obtain numerical solutions in a timely manner. BREAKUP significantly reduces required compute times by preparing overset grids for processing on massively parallel computers. BREAKUP subdivides the original grids for use on a user-specified number of parallel processors. Grid-to-grid and intragrid communications are maintained in the parallel environment via connectivity tables generated by BREAKUP. The subgrids are formed to be statically loadmore » balanced and to incur a minimum of communication between the subgrids. When the output of BREAKUP is submitted to an appropriately modified flow solver, subgrid solutions will be updated simultaneously. This contrasts to the much less efficient solution method of updating each original grid sequentially as done in the past.« less
Prepares Overset Grids for Processing
Barnette, Daniel W.
1998-04-22
Many large and complex computational problems require multiple, structured, generically overlapped (overset) grids to obtain numerical solutions in a timely manner. BREAKUP significantly reduces required compute times by preparing overset grids for processing on massively parallel computers. BREAKUP subdivides the original grids for use on a user-specified number of parallel processors. Grid-to-grid and intragrid communications are maintained in the parallel environment via connectivity tables generated by BREAKUP. The subgrids are formed to be statically load balanced and to incur a minimum of communication between the subgrids. When the output of BREAKUP is submitted to an appropriately modified flow solver, subgrid solutions will be updated simultaneously. This contrasts to the much less efficient solution method of updating each original grid sequentially as done in the past.
Recent Progress on the Parallel Implementation of Moving-Body Overset Grid Schemes
NASA Technical Reports Server (NTRS)
Wissink, Andrew; Allen, Edwin (Technical Monitor)
1998-01-01
Viscous calculations about geometrically complex bodies in which there is relative motion between component parts is one of the most computationally demanding problems facing CFD researchers today. This presentation documents results from the first two years of a CHSSI-funded effort within the U.S. Army AFDD to develop scalable dynamic overset grid methods for unsteady viscous calculations with moving-body problems. The first pan of the presentation will focus on results from OVERFLOW-D1, a parallelized moving-body overset grid scheme that employs traditional Chimera methodology. The two processes that dominate the cost of such problems are the flow solution on each component and the intergrid connectivity solution. Parallel implementations of the OVERFLOW flow solver and DCF3D connectivity software are coupled with a proposed two-part static-dynamic load balancing scheme and tested on the IBM SP and Cray T3E multi-processors. The second part of the presentation will cover some recent results from OVERFLOW-D2, a new flow solver that employs Cartesian grids with various levels of refinement, facilitating solution adaption. A study of the parallel performance of the scheme on large distributed- memory multiprocessor computer architectures will be reported.
On unstructured grids and solvers
NASA Technical Reports Server (NTRS)
Barth, T. J.
1990-01-01
The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
None, None
2014-10-15
The combined team of GE Global Research, Federal Express, National Renewable Energy Laboratory, and Consolidated Edison has successfully achieved the established goals contained within the Department of Energy’s Smart Grid Capable Electric Vehicle Supply Equipment funding opportunity. The final program product, shown charging two vehicles in Figure 1, reduces by nearly 50% the total installed system cost of the electric vehicle supply equipment (EVSE) as well as enabling a host of new Smart Grid enabled features. These include bi-directional communications, load control, utility message exchange and transaction management information. Using the new charging system, Utilities or energy service providers will now be able to monitor transportation related electrical loads on their distribution networks, send load control commands or preferences to individual systems, and then see measured responses. Installation owners will be able to authorize usage of the stations, monitor operations, and optimally control their electricity consumption. These features and cost reductions have been developed through a total system design solution.
NASA Technical Reports Server (NTRS)
Hu, Chaumin
2007-01-01
IPG Execution Service is a framework that reliably executes complex jobs on a computational grid, and is part of the IPG service architecture designed to support location-independent computing. The new grid service enables users to describe the platform on which they need a job to run, which allows the service to locate the desired platform, configure it for the required application, and execute the job. After a job is submitted, users can monitor it through periodic notifications, or through queries. Each job consists of a set of tasks that performs actions such as executing applications and managing data. Each task is executed based on a starting condition that is an expression of the states of other tasks. This formulation allows tasks to be executed in parallel, and also allows a user to specify tasks to execute when other tasks succeed, fail, or are canceled. The two core components of the Execution Service are the Task Database, which stores tasks that have been submitted for execution, and the Task Manager, which executes tasks in the proper order, based on the user-specified starting conditions, and avoids overloading local and remote resources while executing tasks.
Vision guided automatic measuring in coordinate metrology
NASA Astrophysics Data System (ADS)
Qin, Yuhong; Wang, Lei; Xie, Lusheng; Huang, Yuanqing
2008-12-01
A novel automatically measuring planning method in coordinate metrology based on computer vision is presented in this paper. An active stereo vision system is established by attaching a CCD camera to the mechanical probe of the coordinate measuring machine (CMM). Through the movement of the probe of the CMM, as well as the camera, 3D edge characters of the object can be acquired, which are used as clues for automatically coordinate measuring. A multi-baseline matching method is presented to overcome the ambiguity in stereo matching, and a quadratic interpolating is used in sub pixel matching to get continuous depth image. The matching is only done on character edges in images, so it is much faster and more robust. Two methods of measuring path planning are put forward, in one way, a 2D characteristic edge image which are often stand for rapidly changes in depth or curvature of object surface can be acquired by projecting 3D edge characters to a scanning plane, and then the sampling points of mechanical probe are selected depending on the edge image. In the other way, surface patches are fitted to these 3D edges, and the sampling grid is determined by the type and area of every patch. Using these techniques, a highly automated high-speed, high-precision, 3-D coordinate acquisition system based on multiple-sensor integration can be developed. It has potential applications in manufacturing problems as metrology, inspection, and reverse engineering.
NASA Technical Reports Server (NTRS)
Peltier, L. J.; Biringen, S.
1993-01-01
The present numerical simulation explores a thermal-convective mechanism for oscillatory thermocapillary convection in a shallow Cartesian cavity for a Prandtl number 6.78 fluid. The computer program developed for this simulation integrates the two-dimensional, time-dependent Navier-Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces are assumed. The instability is shown to depend upon temporal coupling between large scale thermal structures within the flow field and the temperature sensitive free surface. A primary result of this study is the development of a stability diagram presenting the critical Marangoni number separating steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. Within this range, a minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20,000 are predicted below which steady convection is found.
Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; Kempel, Leo
2010-08-27
Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(N_{s}^{2}N_{t}^{2}), where N_{s} and N_{t} are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The first scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N_{s}N_{t}log^{2}N_{t}). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.
Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; Kempel, Leo
2010-08-27
Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(Ns2Nt2), where Ns and Nt are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The first scheme identifies a convolution relation inmore » time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(NsNtlog2Nt). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.« less
López-Muñoz, F; Alamo, C
2011-03-01
The relationship between physical and functional alterations in the pineal gland, the 'passions' (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that 'passions' were sensitive movements that the soul, located in the pineal gland, experienced due to its union with the body, by circulating animal spirits. Descartes described sadness as one of the six primitive passions of the soul, which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century and during much of the 18th century, but the link between the pineal gland and psychiatric disorders it was definitively highlighted in the 20th century, with the discovery of melatonin in 1958. The recent development of a new pharmacological agent acting through melatonergic receptors (agomelatine) has confirmed the close link between the pineal gland and affective disorders.
NASA Astrophysics Data System (ADS)
Cai, Tao
2016-04-01
In this paper, we have described a 'stratified' semi-implicit spectral method to study compressible convection in Cartesian geometry. The full set of compressible hydrodynamic equations are solved in conservative forms. The numerical scheme is accurate and efficient, based on fast Fourier/sin/cos spectral transforms in the horizontal directions, Chebyshev spectral transform or second-order finite difference scheme in the vertical direction, and second order semi-implicit scheme in time marching of linear terms. We have checked the validity of both the fully pseudo-spectral scheme and the mixed finite-difference pseudo-spectral scheme by studying the onset of compressible convection. The difference of the critical Rayleigh number between our numerical result and the linear stability analysis is within two percent. Besides, we have computed the Mach numbers with different Rayleigh numbers in compressible convection. It shows good agreement with the numerical results of finite difference methods and finite volume method. This model has wide application in studying laminar and turbulent flow. Illustrative examples of application on horizontal convection, gravity waves, and long-lived vortex are given in this paper.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)
2002-01-01
The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.
OGC and Grid Interoperability in enviroGRIDS Project
NASA Astrophysics Data System (ADS)
Gorgan, Dorian; Rodila, Denisa; Bacu, Victor; Giuliani, Gregory; Ray, Nicolas
2010-05-01
EnviroGRIDS (Black Sea Catchment Observation and Assessment System supporting Sustainable Development) [1] is a 4-years FP7 Project aiming to address the subjects of ecologically unsustainable development and inadequate resource management. The project develops a Spatial Data Infrastructure of the Black Sea Catchment region. The geospatial technologies offer very specialized functionality for Earth Science oriented applications as well as the Grid oriented technology that is able to support distributed and parallel processing. One challenge of the enviroGRIDS project is the interoperability between geospatial and Grid infrastructures by providing the basic and the extended features of the both technologies. The geospatial interoperability technology has been promoted as a way of dealing with large volumes of geospatial data in distributed environments through the development of interoperable Web service specifications proposed by the Open Geospatial Consortium (OGC), with applications spread across multiple fields but especially in Earth observation research. Due to the huge volumes of data available in the geospatial domain and the additional introduced issues (data management, secure data transfer, data distribution and data computation), the need for an infrastructure capable to manage all those problems becomes an important aspect. The Grid promotes and facilitates the secure interoperations of geospatial heterogeneous distributed data within a distributed environment, the creation and management of large distributed computational jobs and assures a security level for communication and transfer of messages based on certificates. This presentation analysis and discusses the most significant use cases for enabling the OGC Web services interoperability with the Grid environment and focuses on the description and implementation of the most promising one. In these use cases we give a special attention to issues such as: the relations between computational grid and
Coordination sequences and coordination waves in matter
Rau, V. G. Pugaev, A. A.; Rau, T. F.
2006-01-15
A possible way of partitioning a space into polycubes (n-dimensional modifications of Golomb polyominoes, which are generally nonconvex) is used as a basic model of ordered matter structure. It is suggested that layer-by-layer growth of a structure, occurring along the geodetics of the digraph of a net defined by the local rules of bonding of polycubes, justifies the phenomenological laws of shaping (self-similarity during the growth, independence of the polyhedron shape on the 'seed,' the symmetry of the growth polyhedron, etc.). Specific results of the analysis of number sequences of the increase in coordination circles for planar periodic partitions of model and real crystal structures, as well as the preliminary results of investigation of standing coordination topological waves, revealed for the first time in computer experiments, are reported.
New coordinates for the amplitude parameter space of continuous gravitational waves
NASA Astrophysics Data System (ADS)
Whelan, John T.; Prix, Reinhard; Cutler, Curt J.; Willis, Joshua L.
2014-03-01
The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters (signal frequency and frequency derivatives, and parameters such as sky position which determine the Doppler modulation of the signal). The division is useful in part because of the existence of a set of functions known as the Jaranowski-Królak-Schutz (JKS) coordinates, which are a set of four coordinates on the amplitude parameter space such that the GW signal can be written as a linear combination of four template waveforms (which depend on the phase-evolution parameters) with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which can be more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as circular polarization factored (CPF) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. A further coordinate transformation can be made, within each subspace, between CPF and so-called root-radius coordinates, whose radial coordinate is the fourth root of the radial coordinate in CPF-polar coordinates. We illustrate some simplifying applications for these various coordinate systems, such as a calculation of the Jacobian for the transformation between JKS or CPF coordinates and the physical amplitude parameters (amplitude, inclination, polarization and initial phase); a demonstration that the Jacobian between root-radius coordinates and the physical parameters is a constant; an illustration of the signal coordinate singularities associated with left- and right
Application of wall functions to generalized nonorthogonal curvilinear coordinate systems
NASA Astrophysics Data System (ADS)
Sondak, Douglas L.; Pletcher, Richard H.
1995-01-01
A method has been developed for the application of wall functions to generalized curvilinear coordinate systems with nonorthogonal grids. Two test cases have been computed using this method with the k-epsilon turbulence model: flow over a flat plate at 0-deg angle of attack using a nonorthogonal grid at the wall and flow over a prolate hemispheroid with a hemispherical nose cap at 0-deg angle of attack. All results are compared with experimental data. In addition, the hemispheroid results are compared with computations using the Baldwin-Lomax algebraic turbulence model and the Chien low-Reynolds-number k-epsilon turbulence model.
Grid Generation Techniques Utilizing the Volume Grid Manipulator
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1998-01-01
This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.
From the grid to the smart grid, topologically
NASA Astrophysics Data System (ADS)
Pagani, Giuliano Andrea; Aiello, Marco
2016-05-01
In its more visionary acceptation, the smart grid is a model of energy management in which the users are engaged in producing energy as well as consuming it, while having information systems fully aware of the energy demand-response of the network and of dynamically varying prices. A natural question is then: to make the smart grid a reality will the distribution grid have to be upgraded? We assume a positive answer to the question and we consider the lower layers of medium and low voltage to be the most affected by the change. In our previous work, we analyzed samples of the Dutch distribution grid (Pagani and Aiello, 2011) and we considered possible evolutions of these using synthetic topologies modeled after studies of complex systems in other technological domains (Pagani and Aiello, 2014). In this paper, we take an extra important step by defining a methodology for evolving any existing physical power grid to a good smart grid model, thus laying the foundations for a decision support system for utilities and governmental organizations. In doing so, we consider several possible evolution strategies and apply them to the Dutch distribution grid. We show how increasing connectivity is beneficial in realizing more efficient and reliable networks. Our proposal is topological in nature, enhanced with economic considerations of the costs of such evolutions in terms of cabling expenses and economic benefits of evolving the grid.
New Global Bathymetry and Topography Model Grids
NASA Astrophysics Data System (ADS)
Smith, W. H.; Sandwell, D. T.; Marks, K. M.
2008-12-01
A new version of the "Smith and Sandwell" global marine topography model is available in two formats. A one-arc-minute Mercator projected grid covering latitudes to +/- 80.738 degrees is available in the "img" file format. Also available is a 30-arc-second version in latitude and longitude coordinates from pole to pole, supplied as tiles covering the same areas as the SRTM30 land topography data set. The new effort follows the Smith and Sandwell recipe, using publicly available and quality controlled single- and multi-beam echo soundings where possible and filling the gaps in the oceans with estimates derived from marine gravity anomalies observed by satellite altimetry. The altimeter data have been reprocessed to reduce the noise level and improve the spatial resolution [see Sandwell and Smith, this meeting]. The echo soundings database has grown enormously with new infusions of data from the U.S. Naval Oceanographic Office (NAVO), the National Geospatial-intelligence Agency (NGA), hydrographic offices around the world volunteering through the International Hydrographic Organization (IHO), and many other agencies and academic sources worldwide. These new data contributions have filled many holes: 50% of ocean grid points are within 8 km of a sounding point, 75% are within 24 km, and 90% are within 57 km. However, in the remote ocean basins some gaps still remain: 5% of the ocean grid points are more than 85 km from the nearest sounding control, and 1% are more than 173 km away. Both versions of the grid include a companion grid of source file numbers, so that control points may be mapped and traced to sources. We have compared the new model to multi-beam data not used in the compilation and find that 50% of differences are less than 25 m, 95% of differences are less than 130 m, but a few large differences remain in areas of poor sounding control and large-amplitude gravity anomalies. Land values in the solution are taken from SRTM30v2, GTOPO30 and ICESAT data