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1

NSDL National Science Digital Library

This lesson is designed to develop students' understanding of the Cartesian coordinate plane. Topics include plotting coordinates and slope. This lesson provides links to discussions and activities related to the Cartesian coordinate system as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

2011-05-24

2

Coordinates and the Cartesian Plane

NSDL National Science Digital Library

The lesson begins with a short refresher lecture on how points are written in (x,y) format and orientation with the Cartesian plane axes. The lecture also covers which directions are positive and which are negative on an x-y plane. Students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points. Prerequisite knowledge: Familiarity with the coordinate plane, coordinates, and equations are helpful, but not required.

2011-03-31

3

The 3D Euler solutions using automated Cartesian grid generation

NASA Technical Reports Server (NTRS)

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.

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

4

Coordinates and the Cartesian Plane

NSDL National Science Digital Library

A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.

VU Bioengineering RET Program, School of Engineering,

5

Conversion of Cartesian coordinates from and to Generalized Balanced Ternary addresses

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.

van Roessel, Jan W.

1988-01-01

6

Flow Simulations on Cartesian Grids involving Complex Moving Geometries

and a set of ghost cells, so that cell updates are performed on regular grid cells. #12;2 H. Forrer, M. Berger To obtain ghost cell values in our method, the ow is extrapolated beyond the boundary by a mirror. We use this mirror ow to develop a Cartesian grid method to treat the cells along a re ecting

Berger, Marsha J.

7

A Cartesian grid-based unified gas kinetic scheme

NASA Astrophysics Data System (ADS)

A Cartesian grid-based unified gas kinetic scheme is developed. In this approach, any oriented boundary in a Cartesian grid is represented by many directional boundary points. The numerical flux is evaluated on each boundary point. Then, a boundary flux interpolation method (BFIM) is constructed to distribute the boundary effect to the flow evolution on regular Cartesian grid points. The BFIM provides a general strategy to implement any kind of boundary condition on Cartesian grid. The newly developed technique is implemented in the unified gas kinetic scheme, where the scheme is reformulated into a finite difference format. Several typical test cases are simulated with different geometries. For example, the thermophoresis phenomenon for a plate with infinitesimal thickness immersed in a rarefied flow environment is calculated under different orientations on the same Cartesian grid. These computational results validate the BFIM in the unified scheme for the capturing of different thermal boundary conditions. The BFIM can be extended to the moving boundary problems as well.

Chen, Songze; Xu, Kun

2014-12-01

8

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

NASA Technical Reports Server (NTRS)

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.

Soler, T.

1976-01-01

9

Efficient Fluid Dynamic Design Optimization Using Cartesian Grids

NASA Technical Reports Server (NTRS)

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.

Dadone, A.; Grossman, B.; Sellers, Bill (Technical Monitor)

2004-01-01

10

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

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.

Quirk, James J.

1994-01-01

11

The Approach to Steady State Using Homogeneous and Cartesian Coordinates

Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work further develops this line of thought and compares the relative merits of using a homogeneous or a Cartesian coordinate system. PMID:23983812

Gochberg, D. F.; Ding, Z.

2013-01-01

12

Triangle geometry processing for surface modeling and cartesian grid generation

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.

Aftosmis, Michael J. (San Mateo, CA) [San Mateo, CA; Melton, John E. (Hollister, CA) [Hollister, CA; Berger, Marsha J. (New York, NY) [New York, NY

2002-09-03

13

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

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.

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

14

A Multi-solver Scheme for Viscous Flows Using Adaptive Cartesian Grids and Meshless Grid

A Multi-solver Scheme for Viscous Flows Using Adaptive Cartesian Grids and Meshless Grid to fill the majority of the computational domain. An edge-based meshless scheme is used in the interface efficient scheme with sharp feature reso- lution. The use of a meshless flow solver to interface the body

Jameson, Antony

15

A novel cartesian grid method for complex aerodynamic CFD applications

A novel automatic grid-generation method for Euler and RANS computations of flows over complex geometries has been developed. This is driven by the need of the industrial CFD practitioner to reduce the turnaround time from an initial CAD geometry to obtaining a flow solution. The method uses a subdivision strategy. allowing hanging nodes in a Cartesian unstructured-mesh environment, and is combined with a non-overlapping, semi-structured surface grid. Unusually, the surface grid is the end rather than the starting point of the present approach. The capabilities of the method are demonstrated by reference to an inviscid and a viscous-flow solution for a realistic complex configuration at a transonic flow condition, using the Fluent Inc. code Rampant v4.0.

Smith, R.J.; Leschziner, M.A. [UMIST, Manchester (United Kingdom)

1996-12-31

16

GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows

NASA Technical Reports Server (NTRS)

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.

2003-01-01

17

A cartesian grid embedded boundary method for hyperbolic conservation laws

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.

Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J.; Modiano, David

2004-10-03

18

Ghost-Cell Method with far-field coarsening and mesh adaptation for Cartesian grids

Cartesian grid methods for inviscid computational fluid dynamics offer great promise for the development of very rapid conceptual design tools. The present paper deals with a number of new features for Cartesian grid methods which appear to be particularly well suited for this application. A key ingredient is the implementation of non-penetration boundary conditions at solid walls which is based

A. Dadone; B. Grossman

2006-01-01

19

A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries

A Cartesian grid method for computing flows with complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. A mixed Eulerian–Lagrangian framework is employed, which allows us to treat the immersed moving boundary as a sharp interface. The incompressible Navier–Stokes equations are discretized

H. S. Udaykumar; R. Mittal; P. Rampunggoon; A. Khanna

2001-01-01

20

Various parameterizations of "latitude" equation - Cartesian to geodetic coordinates transformation

NASA Astrophysics Data System (ADS)

The paper presents a solution to one of the basic problems of computational geodesy - conversion between Cartesian and geodetic coordinates on a biaxial ellipsoid. The solution is based on what is known in the literature as "latitude equation". The equation is presented in three different parameterizations commonly used in geodesy - geodetic, parametric (reduced) and geocentric latitudes. Although the resulting equations may be derived in many ways, here, we present a very elegant one based on vectors orthogonality. As the "original latitude equations" are trigonometric ones, their representation has been changed into an irrational form after Fukushima (1999, 2006). Furthermore, in order to avoid division operations we have followed Fukushima's strategy again and rewritten the equations in a fractional form (a pair of iterative formulas). The resulting formulas involving parametric latitude are essentially the same as those introduced by Fukushima (2006) (considered the most efficient today). All the resulting variants are solved with Newton's second-order and Halley's third-order formulas. It turns out that all parameterizations of the "latitude equation" show a comparable level of performance.

Ligas, M.

2013-09-01

21

NASA Astrophysics Data System (ADS)

A primitive, pressure-velocity variable, finite difference code was developed to predict turbulent three dimensional transient flows in cylindrical and cartesian coordinates. Three applications of the code are considered: local destratification near the release structure of a reservoir, deflection of a jet entering normally into a uniform crossflow, and dilution jets in gas turbine combustors. The prediction procedure is based on the transient two dimensional SOLA technique (for laminar flows), which is a finite difference scheme based on the Marker and Cell Methods. The procedure incorporates displaced grids for the three velocity components, which are placed between the nodes where pressure and other variables are stored. The pressure is deduced from the continuity equation and the latest velocity field, using a pressure-velocity iteration procedure. The developed three dimensional turbulent computer code is shown to be a simplified yet effective prediction procedure for use by persons with little or no experience in computational fluid dynamics.

Busnaina, A. A.

1983-12-01

22

A second order accurate level set method on non-graded adaptive cartesian grids

on non-graded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells to demonstrate the accuracy of the method. Ó 2006 Published by Elsevier Inc. Keywords: Level set method; Ghost,4,9,27,44,66] have the advantage of being volume preserving since the mass fraction in each cell is being tracked

Smereka, Peter

23

Ghost-Cell Method for Inviscid Three-Dimensional Flows with Moving Body on Cartesian Grids

NASA Astrophysics Data System (ADS)

This paper depicts a ghost cell method to solve the three dimensional compressible time-dependent Euler equations using Cartesian grids for static or moving bodies. In this method, there is no need for special treatment corresponding to cut cells, which complicate other Cartesian mesh methods, and the method avoids the small cell problem. As an application, we present some numerical results for a special moving body using this method, which demonstrates the efficiency of the proposed method.

Liu, Jianming; Zhao, Ning; Hu, Ou

24

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.

OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.

2000-06-27

25

Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation

NASA Technical Reports Server (NTRS)

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.

Buning, Pieter G.; Pulliam, Thomas H.

2011-01-01

26

The Ghost Cell Method for Inviscid Compressible Flow on Adaptive Tree Cartesian Grids

NASA Astrophysics Data System (ADS)

In this paper, a new immersed boundary algorithm is developed by combining the ghost cell method with adaptive tree Cartesian grid method. Furthermore, the presented method has been successfully used to evaluate an inviscid compressible flow with immersed boundary. Numerical example shows the present method be effective.

Liu, Jianming; Zhao, Ning; Hu, Ou

2010-05-01

27

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

for the parabolic terms, such as the heat equation and Navier-Stokes viscosity. The most intricate aspect of anyAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure

Bejerano, Gill

28

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We addressAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R

Fedkiw, Ron

29

Development and application of a 3D Cartesian grid Euler method

NASA Technical Reports Server (NTRS)

This report describes recent progress in the development and application of 3D Cartesian grid generation and Euler flow solution techniques. Improvements to flow field grid generation algorithms, geometry representations, and geometry refinement criteria are presented, including details of a procedure for correctly identifying and resolving extremely thin surface features. An initial implementation of automatic flow field refinement is also presented. Results for several 3D multi-component configurations are provided and discussed.

Melton, John E.; Aftosmis, Michael J.; Berger, Marsha J.; Wong, Michael D.

1995-01-01

30

Ghost-cell method for analysis of inviscid three-dimensional flows on Cartesian-grids

The present paper deals with the implementation of non-penetration boundary conditions at solid walls for three-dimensional inviscid flow computations on Cartesian grids. 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

Andrea Dadone; Bernard Grossman

2007-01-01

31

Grid-coordinate generation program

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.

Cosner, Oliver J.; Horwich, Esther

1974-01-01

32

NASA Technical Reports Server (NTRS)

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.

Finley, Dennis B.

1995-01-01

33

Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates

NASA Astrophysics Data System (ADS)

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.

Briggs, Andrew; Camblong, Horacio E.; Ordóńez, Carlos R.

2013-06-01

34

A Cartesian Grid Embedded Boundary Method for the Incompressible Navier Stokes Equations

We present a second-order accurate projection method to solve the incompressible Navier-Stokes equations on irregular domains in two or three dimensions. We use a finite-volume discretization obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing a conservative discretization of the advective terms with a stable, nonconservative discretization at

M. Barad; P. Colella; D. T. Graves; P. Schwartz; B. van Straalen; D. Trebotich

2009-01-01

35

Active stiffness control of a manipulator in cartesian coordinates

A method of actively controlling the apparent stiffness of a manipulator end effecter is presented. The approach allows the programmer to specify the three transnational and three rotational stiffness of a frame located arbitrarily in hand coordinates. Control of the nominal position of the hand then permits simultaneous position and force control. Stiffness may be changed under program control to

J. Kenneth Salisbury

1980-01-01

36

This paper presents an e-cient Euler method on Cartesian grids coupled with an integral Boundary-Layer method. The unsteady Euler equations are solved using cell-centered flnite volume method by the implicit-explicit dual-time stepping scheme. The wall boundary con- ditions on the wing are implemented on the wing chord plane by flrst order approximation so that non-moving Cartesian grids can be used.

Zhichao Zhang; Feng Liu; David M. Schuster

37

Computing reaching dynamics in motor cortex with Cartesian spatial coordinates

How neurons in the primary motor cortex control arm movements is not yet understood. Here we show that the equations of motion governing reaching simplify when expressed in spatial coordinates. In this fixed reference frame, joint torques are the sums of vector cross products between the spatial positions of limb segments and their spatial accelerations and velocities. The consequences that follow from this model explain many properties of neurons in the motor cortex, including directional broad, cosinelike tuning, nonuniformly distributed preferred directions dependent on the workspace, and the rotation of the population vector during arm movements. Remarkably, the torques can be directly computed as a linearly weighted sum of responses from cortical motoneurons, and the muscle tensions can be obtained as rectified linear sums of the joint torques. This allows the required muscle tensions to be computed rapidly from a trajectory in space with a feedforward network model. PMID:23114209

Sejnowski, Terrence J.

2013-01-01

38

On the new analytical solution for a well in Cartesian coordinates with MODFLOW comparisons.

In this paper, the comparison process of Batu (2012) generalized three-dimensional well hydraulics solution for confined aquifers in Cartesian coordinates with MODFLOW is presented. First, a brief description of Batu (2012) solution along with the governing equations and some of its key features are described. The final average drawdown expression in an observation well is given with the conversion expressions from Cartesian to radial coordinates. A generalized comparison using Batu (2012), Hantush (1964), and MODFLOW (Harbaugh et al. 2000), for vertical wells in horizontally isotropic aquifers, that is, ayx ?=?Ky /Kx ?=?1, is presented. Comparisons are also presented with Batu (2012) and MODFLOW for horizontally anisotropic aquifers, that is, ayx ???1. After that comparisons are presented for horizontal wells between Batu (2012) and MODFLOW. PMID:24236933

Batu, Vedat

2014-01-01

39

\\u000a René Descartes (1596–1650) is often credited with the invention of the xy-plane, but Pierre de Fermat (1601–1665) was probably the first inventor. In 1636 Fermat was working on a treatise titled\\u000a Ad locus planos et solidos isagoge, which outlined what we now call analytic geometry. Unfortunately, Fermat never published his treatise, although he shared his ideas with other mathematicians such

John Vince

40

A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains

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.

Johansen, H. [Univ. of California, Berkeley, CA (United States). Dept. of Mechanical Engineering; Colella, P. [Lawrence Berkeley National Lab., CA (United States). Center for Computational Sciences and Engineering

1997-01-31

41

A Cartesian-grid integrated-RBF method for viscoelastic flows

NASA Astrophysics Data System (ADS)

This paper is concerned with the use of integrated radial-basis-function networks (IRBFNs), Cartesian-grids and point collocation for numerically solving 2D flows of viscoelastic fluids. In the proposed method, RBFNs, which are constructed through integration, are employed to approximate the field variables including stresses, and the governing equations are discretised by means of point collocation. Advantages gained from the integration process over differentiated RBFNs process are (i) better accuracy (ii) more straightforward implementation of boundary conditions and (iii) more stable solutions. The method is verified through several test problems, e.g. planar Poiseuille flow and fully-developed flow in a square duct, with different types of viscoelastic fluids, namely Oldroyd-B and CEF. The obtained results show that (i) The proposed method is easy to implement; (ii) Its pre-processing is simple and (iii) Accurate results are obtained using relatively-coarse grids.

Ho-Minh, D.; Mai-Duy, N.; Tran-Cong, T.

2010-06-01

42

NASA Astrophysics Data System (ADS)

Aims:We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to demonstrate that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations while offering advantages, such as the absence of a grid singularity, for certain applications, e.g., circumbinary disks and disk-jet simulations. Methods: We employ the Pencil Code, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation of state. Planets and stars are treated as particles evolved with an N-body scheme. Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle. Results: We find that Cartesian grids are well-suited for accretion disk problems. The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence, in good agreement with published results achieved with cylindrical codes. Models without an inner boundary do not show the spurious build-up of magnetic pressure and Reynolds stress seen in the models with boundaries, but the global stresses and alpha viscosities are similar in the two cases. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 ± 0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of Maxwell to Reynolds stresses decreases with increasing temperature, dropping from 5 to 1 when the sound speed was raised by a factor 4, maintaing the same field strength. We also study the dynamics of solid boulders in the hydromagnetic turbulence, by making use of 106 Lagrangian particles embedded in the Eulerian grid. The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer, forming instead a layer of solids of finite vertical thickness. The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0 ± 0.2 for a model with ??10-3 and 0.78 ± 0.06 for a model with ??10-1. That is, the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase. The average bulk density of solids in the turbulent flow is quite low (?p = 6.0×10-11 kg m-3), but in the high pressure regions, significant overdensities are observed, where the solid-to-gas ratio reached values as great as 85, corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01.

Lyra, W.; Johansen, A.; Klahr, H.; Piskunov, N.

2008-03-01

43

A Cartesian grid method for simulation of the unsteady aerodynamics of microscale flapping flight

NASA Astrophysics Data System (ADS)

Recent improvements in MEMS technology is making it possible to develop microscale mechanical devices capable of operating in gases and liquids at low Reynolds number. In the current work a method has been developed to be able to simulate the operation of such devices computationally. The method imposes arbitrary solid/fluid boundaries on Cartesian grids, thus avoiding complexities with body-fitted grid methods. This thesis explains the numerical approximations used for solving the governing equations, the discretization of the equations, and the implementation of the immersed fluid/solid boundary conditions. The method is validated by comparing computed results of flows over an infinitely thin plate, a cylinder, and a sphere, and it is found that the method predicts both steady and unsteady flows with sufficient accuracy. The method performs similarly whether the solid objects translates through the grid or remains fixed in the grid with an imposed flow field. The method was then used to compute the fluid dynamics and force generation of a microscale flapping cantilever beam propulsion device. Both two-dimensional and three-dimensional flow features were explored, and the investigation showed that the cantilever produces thrust and can therefore potentially be used as a simple propulsion mechanism. Finally, the method was used to simulate an idealized model of fruit fly wing in hovering flight. The computed flow fields and force dynamics compared well with an equivalent experimental model, although some discrepancies were found due to a thicker wing being used in the computations for numerical reasons.

Emblemsvag, Jo-Einar

44

Tensor decomposition in electronic structure calculations on 3D Cartesian grids

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.

Khoromskij, B.N. [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig (Germany)], E-mail: bokh@mis.mpg.de; Khoromskaia, V.; Chinnamsetty, S.R. [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig (Germany); Flad, H.-J. [TU Berlin, Sekretariat MA 3-3, Strasse des 17, Juni 136, D-10623 Berlin (Germany)

2009-09-01

45

A Cut-Cell Approach for 2D Cartesian Meshes that Preserves Orthogonal Grid Sweep Ordering

In this paper, we present a cut-cell methodology for solving the two-dimensional neutral-particle transport equation on an orthogonal Cartesian grid. We allow the rectangular cell to be subdivided into two polygonal subcells. We ensure that this division (or cut) conserves the volumes of the materials in the subcells and we utilize a step-characteristics (SC) slice balance approach (SBA) to calculate the angular fluxes exiting the cell as well as the average scalar fluxes in each subcell. Solving the discrete ordinates transport equation on an arbitrary mesh has historically been difficult to parallelize while maintaining good parallel efficiency. However on Cartesian meshes, the KBA algorithm maintains good parallel efficiency using a direct solve. The ability to preserve this algorithm was a driving factor in the development of our cut-cell method. This method also provides a more accurate depiction of a material interface in a cell, which leads to more accurate solutions downstream of this cell. As a result, fewer spatial cells can be utilized, resulting in reduced memory requirements. We apply this approach in the 2D/3D discrete ordinates neutral-particle transport code Denovo, where we analyze a 2D 3 x 3 lattice of pincells. We show that, for eigenvalue problems, a significant increase in accuracy for a given mesh size is gained by utilizing the cut-cell, SC equations instead of the standard homogenized-cell, SC equations.

Jarrell, Joshua J [ORNL] [ORNL; Grove, Robert E [ORNL] [ORNL; Evans, Thomas M [ORNL] [ORNL

2011-01-01

46

A Cartesian grid embedded boundary method for the heat equation on irregular domains

We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60--85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank--Nicolson time discretization is unstable, requiring us to use the L{sub 0}-stable implicit Runge--Kutta method of Twizell, Gumel, and Arigu.

McCorquodale, Peter; Colella, Phillip; Johansen, Hans

2001-03-14

47

NASA Astrophysics Data System (ADS)

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.

Chen, XinJian

2012-12-01

48

. The Cartesian grids with ghost cell im- mersed boundary method for arbitrarily complex geometries is also are equipped with ghost cells using the immersed boundary. When cut cells become very small, however there are many different techniques, ghost cell method or immersed boundary method for its simplification still

Li, Tiejun

49

A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids

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 assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities – obtained with both linear and nonlinear Poisson-Boltzmann equation – for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers. PMID:21984876

Boschitsch, Alexander H.; Fenley, Marcia O.

2011-01-01

50

Coordinate Grids: The Key to the City - solving real world problems using the coordinate grid

NSDL National Science Digital Library

This lesson contains a small group activity in which students use previous knowledge of graphing in a 4 quadrant coordinate grid and individually solve a real world problem involving finding distance on a coordinate grid. Students must utilize their knowledge of absolute value as well as subtracting integers to determine distances between points.

Patty Sisson

2012-07-05

51

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

NASA Astrophysics Data System (ADS)

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

52

NASA Technical Reports Server (NTRS)

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.

Finley, Dennis B.; Karman, Steve L., Jr.

1996-01-01

53

NASA Technical Reports Server (NTRS)

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.

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2000-01-01

54

Features of CPB: a Poisson-Boltzmann solver that uses an adaptive cartesian grid.

The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (?rf ) of the electrostatic potential (?), eliminating the charge-induced singularities in ?. CPB can also use a least-squares reconstruction method to improve estimates of ? at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ? and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software. PMID:25430617

Fenley, Marcia O; Harris, Robert C; Mackoy, Travis; Boschitsch, Alexander H

2015-02-01

55

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. PMID:20512873

Meng, Yuguang; Lei, Hao

2010-06-01

56

We investigate C1-smooth univariate curvature-based cubic L1 interpolating splines in Cartesian and polar coordinates. The coefficients of these splines are calculated by minimizing the L1 norm of curvature. We compare these curvature-based cubic L1 splines with second-derivative-based cubic L1 splines and with cubic L2 splines based on the L2 norm of curvature and of the second derivative. In computational experiments

John E. Lavery

2002-01-01

57

A numerical method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in curvilinear coordinates is presented. The non-staggered-grid method originally developed by C. M. Rhie and W. L. Chow (AIAAJ.21, 1525 (1983)) for steady state problems is extended to compute unsteady flows. In the computational space, the Cartesian velocity components and the pressure are defined at the center of a control

Yan Zang; Jeffrey R. Koseff

1994-01-01

58

A method is presented for representing curved boundaries for the solution of the Navier–Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell

M. P. Kirkpatrick; S. W. Armfield; J. H. Kent

2003-01-01

59

Surface Mesh Generation for Dirty Geometries by Shrink Wrapping using Cartesian Grid Approach

A Cartesian shrink wrapping technique has been investigated in this study to construct triangular surface meshes for three-dimensional\\u000a dirty geometries. The geometries dealt in this paper are defined by faceted representation with dirtiness such as nonconforming\\u000a edges, gaps and overlaps. The objective of the proposed technique is to deliver a way constructing triangular surface meshes\\u000a for upstream solutions in design

Y. K. Lee; Chin K. Lim; Hamid Ghazialam; Harsh Vardhan; Erling Eklund

2006-01-01

60

NASA Astrophysics Data System (ADS)

In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.

Chung, Eric T.; Ciarlet, Patrick; Yu, Tang Fei

2013-02-01

61

NASA Astrophysics Data System (ADS)

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.

Blanc, Emilie; Chiavassa, Guillaume; Lombard, Bruno

2014-10-01

62

NASA Astrophysics Data System (ADS)

Techniques are presented to solve problems involving high speed material interactions that can lead to large deformations followed by fragmentation. To simulate such problems in an Eulerian framework on a fixed Cartesian mesh, interfaces (free surfaces as well as interacting material interfaces) are tracked as levelsets; to resolve shocks and interfaces, a quadtree adaptive mesh is employed. This paper addresses issues associated with the treatment of all interfaces as sharp entities by defining ghost fields on each side of the interface. Collisions between embedded objects are resolved using an efficient collision detection algorithm and appropriate interfacial conditions are supplied. Key issues of supplying interfacial conditions at the precise location of the sharp interface and populating the ghost cells with physically consistent values during and beyond fragmentation events are addressed. Numerous examples pertaining to impact, penetration, void collapse and fragmentation phenomena are presented along with careful benchmarking to establish the validity, accuracy and versatility of the approach.

Sambasivan, S.; Kapahi, A.; Udaykumar, H. S.

2013-02-01

63

Augmented weighted diamond form of the linear nodal scheme for Cartesian coordinate systems

The equations of the high order linear nodal numerical scheme are cast in an augmented weighted difference form for three-dimensional Cartesian nodes. The coupling exhibited by these equations indicate that this new algorithm is simpler and hence faster than previous nodal schemes of this degree of accuracy. A well-logging problem and a fast reactor problem are examined. The new scheme developed here is compared with the classical linear-linear nodal scheme and the diamond difference scheme. For the well-logging problem, it is found that the new scheme is both faster and simpler than the classical linear-linear nodal scheme while sacrificing little in accuracy. Even though the new scheme is more accurate than the diamond difference scheme for the reactor problem, the results indicate that state of the art acceleration methods are needed for nodal schemes.

Walters, W.F.

1985-01-01

64

NSDL National Science Digital Library

This introduction to the labeling of points on a plane by their Cartesian coordinates can optionally be extended to coordinates in 3-dimensional space, to plane polar coordinates and to 3-dimensional polar coordinates. Students should learn to use Cartesian coordinates (x,y) for defining the position of a point in two dimensions and to use Cartesian coordinates (x,y,z) in 3-dimensional space and learn to appreciate the two ways of defining the z axis. Students should also become familiar with some of the tools and terms used by surveyors such as theodolite, azimuth, elevation, and zenith. Optional items for students familiar with trigonometry and with the theorem of Pythagoras are polar coordinates (r,f ) on the plane, Converting (r,f) to (x,y) and vice versa, at least for r, and Spherical polar coordinates (r,q, f) in 3-dimensional space.

David Stern

65

A conservative discretization of the Poisson-Nernst-Planck equations on adaptive Cartesian grids

NASA Astrophysics Data System (ADS)

In this paper we present a novel hybrid finite-difference/finite-volume method for the numerical solution of the nonlinear Poisson-Nernst-Planck (PNP) equations on irregular domains. The method is described in two spatial dimensions but can be extended to three dimensional problems as well. The boundary of the irregular domain is represented implicitly via the zero level set of a signed distance function and quadtree data structures are used to systematically generate adaptive grids needed to accurately capture the electric double layer near the boundary. To handle the nonlinearity in the PNP equations efficiently, a semi-implicit time integration method is utilized. An important feature of our method is that total number of ions in the system is conserved by carefully imposing the boundary conditions, by utilizing a conservative discretization of the diffusive and, more importantly, the nonlinear migrative flux term. Several numerical experiments are conducted which illustrate that the presented method is first-order accurate in time and second-order accurate in space. Moreover, these tests explicitly indicate that the algorithm is also conservative. Finally we illustrate the applicability of our method in the study of the charging dynamics of porous supercapacitors.

Mirzadeh, Mohammad; Gibou, Frédéric

2014-10-01

66

To produce images of tissue elasticity, the vibro-elastography technique involves applying a steady-state multi-frequency vibration to tissue, estimating displacements from ultrasound echo data, and using the estimated displacements in an inverse elasticity problem with the shear modulus spatial distribution as the unknown. In order to fully solve the inverse problem, all three displacement components are required. However, using ultrasound, the axial component of the displacement is measured much more accurately than the other directions. Therefore, simplifying assumptions must be used in this case. Usually, the equations of motion are transformed into a Helmholtz equation by assuming tissue incompressibility and local homogeneity. The local homogeneity assumption causes significant imaging artifacts in areas of varying elasticity. In this paper, we remove the local homogeneity assumption. In particular we introduce a new finite element based direct inversion technique in which only the coupling terms in the equation of motion are ignored, so it can be used with only one component of the displacement. Both Cartesian and cylindrical coordinate systems are considered. The use of multi-frequency excitation also allows us to obtain multiple measurements and reduce artifacts in areas where the displacement of one frequency is close to zero. The proposed method was tested in simulations and experiments against a conventional approach in which the local homogeneity is used. The results show significant improvements in elasticity imaging with the new method compared to previous methods that assumes local homogeneity. For example in simulations, the contrast to noise ratio (CNR) for the region with spherical inclusion increases from an average value of 1.5-17 after using the proposed method instead of the local inversion with homogeneity assumption, and similarly in the prostate phantom experiment, the CNR improved from an average value of 1.6 to about 20. PMID:25906038

Honarvar, M; Lobo, J; Mohareri, O; Salcudean, S E; Rohling, R

2015-05-01

67

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.

Götze, Jan P.; Karasulu, Bora; Thiel, Walter [Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)] [Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)

2013-12-21

68

NSDL National Science Digital Library

Students observe Pascal's law, Archimedes' principle and the ideal gas law as a Cartesian diver moves within a closed system. The Cartesian diver is neutrally buoyant and begins to sink when an external pressure is applied to the closed system. A basic explanation and proof of this process is provided in this activity, and supplementary ideas for more extensive demonstrations and independent group activities are presented.

National Science Foundation GK-12 and Research Experience for Teachers (RET) Programs,

69

G-GPE Squares on a coordinate grid

NSDL National Science Digital Library

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In the picture below a square is outlined whose vertices lie on the coordinate grid points: The area of this particular square is 16 square units. For ...

70

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

NASA Technical Reports Server (NTRS)

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.

Deane, Anil E.

1996-01-01

71

NSDL National Science Digital Library

In this quick activity (page 1 of the PDF), learners will build a simple Cartesian Diver in an empty 2-liter bottle. Use this activity to demonstrate the principle of buoyancy, similar to the bladder system many fish rely on to move up and down in their watery environment. Relates to the linked video, DragonflyTV GPS: California Fish.

Twin Cities Public Television, Inc.

2006-01-01

72

Federal Register 2010, 2011, 2012, 2013, 2014

...NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN); Middleware and Grid Interagency...Coordination (MAGIC) Team AGENCY: The Networking and Information Technology Research...MAGIC Team reports to the Large Scale Networking (LSN) Coordinating Group...

2012-09-20

73

78 FR 70076 - Large Scale Networking (LSN)-Middleware and Grid Interagency Coordination (MAGIC) Team

Federal Register 2010, 2011, 2012, 2013, 2014

...NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN)--Middleware and Grid Interagency...Coordination (MAGIC) Team AGENCY: The Networking and Information Technology Research...MAGIC Team reports to the Large Scale Networking (LSN) Coordinating Group...

2013-11-22

74

78 FR 7464 - Large Scale Networking (LSN)-Middleware And Grid Interagency Coordination (MAGIC) Team

Federal Register 2010, 2011, 2012, 2013, 2014

...NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN)--Middleware And Grid Interagency...Coordination (MAGIC) Team AGENCY: The Networking and Information Technology Research...MAGIC Team reports to the Large Scale Networking (LSN) Coordinating Group...

2013-02-01

75

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, R.K., E-mail: RKCrockett@txcorp.co [Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Colella, P.; Graves, D.T. [Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720 (United States)

2011-04-01

76

Recognizing Patterns In Log-Polar Coordinates

NASA Technical Reports Server (NTRS)

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.

Weiman, Carl F. R.

1992-01-01

77

76 FR 70721 - Voltage Coordination on High Voltage Grids; Notice of Staff Workshop

Federal Register 2010, 2011, 2012, 2013, 2014

...Docket No. AD12-5-000] Voltage Coordination on High Voltage Grids; Notice of Staff Workshop Take notice that the Federal Energy...will hold a Workshop on Voltage Coordination on High Voltage Grids on Thursday, December 1, 2011 from 9 a.m. to 4:30...

2011-11-15

78

76 FR 72203 - Voltage Coordination on High Voltage Grids; Notice of Reliability Workshop Agenda

Federal Register 2010, 2011, 2012, 2013, 2014

...Docket No. AD12-5-000] Voltage Coordination on High Voltage Grids; Notice of Reliability Workshop Agenda As announced in the...003 Staff Workshop on Voltage Coordination on High Voltage Grids December 1, 2011 9 a.m.-4:30 p.m. Agenda...

2011-11-22

79

NSDL National Science Digital Library

This activity has students create a Cartesian diver, which will act in some ways like a submarine. Students will adjust the amount of air and water in an inverted test tube (the "diver") so that it at first barely floats in a water-filled bottle. Then, they will squeeze the closed bottle to create higher water pressure, causing the diver to sink. Releasing the bottle allows the diver to float again. Written instructions, a list of materials, and illustrations are included.

2001-06-08

80

A Global Ocean Model Based on Icosahedral-Hexagonal Grids With a Hybrid Vertical Coordinate

This talk will present results from a new ocean general circulation model (OGCM). The ocean model uses an icosahedral-hexagonal grid to tile the surface of the sphere and hybrid (floating) coordinates to discretize the vertical depth of the ocean. The use of icosahedral-hexagonal grids leads to a highly uniform and isotropic discretization of the sphere and eliminates problematic grid singularities

T. D. Ringler; J. Baumgardner; D. A. Randall

2003-01-01

81

Coordinate control of distributed generations with power converters in a micro grid

For extensive utilization of distributed generation with the objectives of more efficient use of energy and introduction of renewable energy sources, the construction of a micro grid at demand end is inevitable. The micro grid should operate independently and have a good neighbor relation with the power grid, which supplies base power to it. A coordinate control scheme of distributed

S. Kusagawa; E. Masada; J. Baba; M. Ohshima; I. Nagy

2005-01-01

82

NASA Astrophysics Data System (ADS)

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.

Trost, Nico; Jiménez, Javier; Imke, Uwe; Sanchez, Victor

2014-06-01

83

NASA Astrophysics Data System (ADS)

A numerical method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in curvilinear coordinates is presented. The non-staggered-grid method originally developed by C. M. Rhie and W. L. Chow ( AIAAJ.21, 1525 (1983)) for steady state problems is extended to compute unsteady flows. In the computational space, the Cartesian velocity components and the pressure are defined at the center of a control volume, while the volume fluxes are defined at the mid-point on their corresponding cell faces. The momentum equations are integrated semi-implicitly by the approximate factorization technique. The intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure Poisson equation, which is solved iteratively with a multigrid method. The compatibility condition of the pressure Poisson equation is satisfied in the same manner as in a staggered-grid method; mass conservation can be satisfied to machine accuracy. The pressure boundary condition is derived from the momentum equations. Solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method.

Zang, Yan; Street, Robert L.; Koseff, Jeffrey R.

1994-09-01

84

NASA Astrophysics Data System (ADS)

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.

Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.

2014-09-01

85

Discretization formulas for unstructured grids

NASA Astrophysics Data System (ADS)

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.

86

Discretization formulas for unstructured grids

NASA Technical Reports Server (NTRS)

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.

1988-01-01

87

controller to shift their computation load towards data centers in regions with cheaper electricity. On the other hand, distributed data centers also provide opportunities to help the smart grid to improve loadCoordination of the Smart Grid and Distributed Data Centers: A Nested Game-Based Optimization

Pedram, Massoud

88

Coordination of Cloud Computing and Smart Power Grids

increasing the load at locations where they are built. However, data centers and cloud computing also provide building massive, energy-hungry, and geograph- ically distributed data centers. Due to their enormous energy consumption, data centers are expected to have major impact on the electric grid by significantly

Mohsenian-Rad, Hamed

89

A new vertical coordinate system for a 3D unstructured-grid model

NASA Astrophysics Data System (ADS)

We present a new vertical coordinate system for cross-scale applications. Dubbed LSC2 (Localized Sigma Coordinates with Shaved Cell), the new system allows each node of the grid to have its own vertical grid, while still maintaining reasonable smoothness across horizontal and vertical dimensions. Furthermore, the staircase created by the mismatch of vertical levels at adjacent nodes is eliminated with a simple shaved-cell like approach using the concept of degenerate prisms. The new system is demonstrated to have the benefits of both terrain-following and Z-coordinate systems, while minimizing their adverse effects. We implement LSC2 in a 3D unstructured-grid model (SELFE) and demonstrate its superior performance with test cases on lake and ocean stratification.

Zhang, Yinglong J.; Ateljevich, Eli; Yu, Hao-Cheng; Wu, Chin H.; Yu, Jason C. S.

2015-01-01

90

Coordinated Control of DFIG's Rotor and Grid Side Converters During Network Unbalance

This paper proposes a coordinated control of the rotor side converters (RSCs) and grid side converters (GSCs) of doubly-fed induction generator (DFIG) based wind generation systems under unbalanced voltage conditions. System behaviors and operations of the RSC and GSC under unbalanced voltage are illustrated. To provide enhanced operation, the RSC is controlled to eliminate the torque oscillations at double supply

Lie Xu

2008-01-01

91

An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows

NASA Astrophysics Data System (ADS)

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 flows.

Wongwathanarat, A.; Hammer, N. J.; Müller, E.

2010-05-01

92

Coordinated control of grid-connected three-level NPC converter under distorted grid voltage

This paper presents complete control algorithm for grid-connected Pulse Width Modulated (PWM) AC\\/DC converter intended for industrial drives and renewable energy applications. The objective of control is to limit current harmonics distortion and provide ride through capability during voltage dips. Following improvements to Voltage Oriented Control are presented: synchronization loop with positive sequence extraction, resonant current controllers for higher harmonics

Krzysztof Rafal; Malgorzata Bobrowska-Rafal; Szymon Piasecki; Marek Jasinski

2011-01-01

93

Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection

NASA Technical Reports Server (NTRS)

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.

Rubincam, D. P.

1980-01-01

94

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

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

95

Logarithmic spiral grids for image processing

NASA Technical Reports Server (NTRS)

A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.

Weiman, C. F. R.; Chaikin, G. M.

1979-01-01

96

A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh

NASA Astrophysics Data System (ADS)

We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable nonaxisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios and on quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows such as accretion disks and mass-transferring binary systems.

Byerly, Zachary D.; Adelstein-Lelbach, Bryce; Tohline, Joel E.; Marcello, Dominic C.

2014-06-01

97

Hall MHD on Block-Adaptive Grids

NASA Astrophysics Data System (ADS)

This proceedings paper is based on a much longer research paper that was published during the conference (Toth et al. 2008). We present a conservative second order accurate finite volume discretization of the magnetohydrodynamics equations including the Hall term on three dimensional block adaptive grids with Cartesian or generalized coordinates. Both explicit and implicit time integration schemes are developed. The parallel scaling and robustness are demonstrated by three dimensional simulations of planetary magnetospheres.

Tóth, G.; Ma, Y.-J.; Gombosi, T. I.

2009-04-01

98

Automatic off-body overset adaptive Cartesian mesh method based on an octree approach

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.

Peron, Stephanie, E-mail: stephanie.peron@onera.fr [ONERA - The French Aerospace Lab, F-92322 Chatillon (France)] [ONERA - The French Aerospace Lab, F-92322 Chatillon (France); Benoit, Christophe, E-mail: christophe.benoit@onera.fr [ONERA - The French Aerospace Lab, F-92322 Chatillon (France)] [ONERA - The French Aerospace Lab, F-92322 Chatillon (France)

2013-01-01

99

This dissertation presents an efficient inviscid-viscous coupling method for airplane wing flutter prediction. For the inviscid part, the Euler method is employed for accurate resolution of shock-waves and vorticity. For viscous effects, an integral boundary-layer method is developed and coupled with the Euler solver in a semi-inverse manner. In order to avoid the burden of generating body-fitted grids as well

Zhichao Zhang

2005-01-01

100

A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids

NASA Technical Reports Server (NTRS)

An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.

Benson, Rusty A.; Mcrae, D. S.

1991-01-01

101

CARTESIAN MECHANICS* Sophie Roux

. T.H. = Fermat, Oeuvres de Fermat. E.N. = Galileo, Le Opere di Galileo Galilei. T.W.B. = Mersenne Galileo.1 The purpose of this paper is not to refute this big picture, but to qualify it from a Cartesian

Boyer, Edmond

102

Flexible Two-Dimensional Square-Grid Coordination Polymers: Structures and Functions

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

Kajiro, Hiroshi; Kondo, Atsushi; Kaneko, Katsumi; Kanoh, Hirofumi

2010-01-01

103

Multi-Agent Based Techniques for Coordinating the Distribution of Electricity in a Micro-Grid will be required which incor- porates intermittent renewable resources, micro-generators, micro-storage devices and agent managed microgrids. Fred Schweppe, a recognised world leader in the field of electric power

Southampton, University of

104

Design and Control of a Nano-precision Cartesian Platform

In this article, a Cartesian coordinate nano-scale positioning platform driven by stack-type piezoelectric actuator associated with flexure hinge mechanism is developed. Structural design and analysis, system identification, and feedforward controller design to deal with the hysteresis effect, as well as and the feedback PID controller designed by use of Ziegler-Nichols method and the genetic algorithm are included. The developed Cartesian

Yung Ting; Chun-chung Li; Ho-chin Jar; Chang-wei Chiang

2006-01-01

105

Rapid Structured Volume Grid Smoothing and Adaption Technique

NASA Technical Reports Server (NTRS)

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.

Alter, Stephen J.

2006-01-01

106

Filling the Void: Interpolating in Cartesian Cut Cells A. Hendriks*

is not compatible with finite-element based algorithms). In this paper, we present an algorithm to generate simple, the actual task of creating the grid becomes complex, potentially labor intensive and time visualization algorithms are finite-element based. For Cartesian meshes, the definition of the boundary

Peraire, Jaime

107

Game Coloring the Cartesian Product

Game Coloring the Cartesian Product of Graphs Xuding Zhu1,2 1DEPARTMENT OF APPLIED MATHEMATICS to each vertex a set of n degree 1 neighbors. If G has game coloring number m and G has acyclic chromatic number k, then the Cartesian product G G has game chromatic number at most k(k+m - 1). As a consequence

Zhu, Xuding

108

CARTESIAN CONTROL OF VGT MANIPULATORS

-2979 Phone: (740) 593-1096 Fax: (740) 593-0476 E-mail: bobw@bobcat.ent.ohiou.edu #12;CARTESIAN CONTROL OF VGT bobw@bobcat.ent.ohiou.edu ABSTRACT This paper introduces a novel method for Cartesian trajectory

Williams II, Robert L.

109

On Cartesian trees and range minimum queries

We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree ...

Demaine, Erik D.

110

A Cartesian embedded boundary method for hyperbolic conservation laws

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.

Sjogreen, B; Petersson, N A

2006-12-04

111

NASA Astrophysics Data System (ADS)

A conservative second-order difference scheme for solving the equations of ideal hydrodynamics is described. Although it is capable of dealing with general orthogonal curvilinear coordinates, it was mainly developed for calculating the axisymmetric collapse of rotating stellar cores in spherical coordinates. The basic features of the scheme are: (i) variables are assigned to "volume centers" of the computational cells and not to "geometrical cell centers" as usual; (ii) the spatial discretization is of second-order accuracy and includes monotonicity constraints; (iii) advectional changes are calculated by using a "volume advection scheme" instead of evaluating interface integrals of the advection fluxes; (iv) the time evolution is described by an explicit, second-order accurate discretization (v) a moving non-equidistant, staggered grid can be used. In addition a Poisson solver for axially symmetric mass distributions is incorporated into the scheme. In this paper it is demonstrated that for the simple but important test problem of a spherical dust collapse the proposed difference scheme avoids the pitfalls occurring whenever a discretization scheme originally developed for straight coordinates is applied to curvilinear Eulerian coordinates in a straightforward way.

Monchmeyer, R.; Muller, E.

1989-06-01

112

NASA Astrophysics Data System (ADS)

Perfectly matched layer (PML) is an efficient absorbing technique for numerical wave simulations. Since it appeared, various improvements have been made. The complex frequency-shifted PML (CFS-PML) improves the absorbing performance for near-grazing incident waves and evanescent waves. The auxiliary differential equation (ADE) formulation of the PML provides a convenient unsplit-field PML implementation that can be directly used with high order time marching schemes. The multi-axial PML (MPML) stabilizes the PML on anisotropic media. However, these improvements were generally developed for Cartesian grids. In this paper, we extend the ADE CFS-PML to general curvilinear (non-orthogonal) grids for elastic wave modelling. Unlike the common implementations to absorb the waves in the computational space, we apply the damping along the perpendicular direction of the PML layer in the local Cartesian coordinates. Further, we relate the perpendicular and parallel components of the gradient operator in the local Cartesian coordinates to the derivatives in the curvilinear coordinates, to avoid mapping the wavefield to the local Cartesian coordinates. It is thus easy to be incorporated with numerical schemes on curvilinear grids. We derive the PML equations for the interior region and for the free surface separately because the free surface boundary condition modifies the elastic wave equations. We show that the elastic wave modelling on curvilinear grids exhibits anisotropic effects in the computational space, which may lead to unstable simulations. To stabilize the simulation, we adapt the MPML strategy to also absorb the wavefield along the two parallel directions of the PML. We illustrate the stability of this ADE CFS-MPML for finite-difference elastic wave simulations on curvilinear grids by two numerical experiments.

Zhang, Zhenguo; Zhang, Wei; Chen, Xiaofei

2014-07-01

113

NASA Technical Reports Server (NTRS)

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.

Lopez, Isaac; Follen, Gregory J.; Gutierrez, Richard; Foster, Ian; Ginsburg, Brian; Larsson, Olle; Martin, Stuart; Tuecke, Steven; Woodford, David

2000-01-01

114

Coordinating the Global Information Grid Initiative with the NG9-1-1 Initiative

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.

Michael Schmitt

2008-05-01

115

NASA Technical Reports Server (NTRS)

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.

Smith, R. E.

1981-01-01

116

In geometry optimizations and molecular dynamics calculations, it is often necessary to transform a geometry step that has been determined in internal coordinates to Cartesian coordinates. A new method for performing such transformations, the high-order path-expansion (HOPE) method, is here presented. The new method treats the nonlinear relation between internal and Cartesian coordinates by means of automatic differentiation. The method is reliable, applicable to any system of internal coordinates, and computationally more efficient than the traditional method of iterative back transformations. As a bonus, the HOPE method determines not just the Cartesian step vector but also a continuous step path expressed in the form of a polynomial, which is useful for determining reaction coordinates, for integrating trajectories, and for visualization. PMID:23703109

Rybkin, Vladimir V; Ekström, Ulf; Helgaker, Trygve

2013-08-01

117

Digital Topology on Adaptive Octree Grids

The theory of digital topology is used in many different image processing and computer graphics algorithms. Most of the existing theories apply to uniform cartesian grids, and they are not readily extensible to new algorithms targeting at adaptive cartesian grids. This article provides a rigorous extension of the classical digital topology framework for adaptive octree grids, including the characterization of adjacency, connected components, and simple points. Motivating examples, proofs of the major propositions, and algorithm pseudocodes are provided. PMID:20072715

Bai, Ying; Han, Xiao; Prince, Jerry L.

2009-01-01

118

Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling

NASA Astrophysics Data System (ADS)

We compare different finite-difference schemes for two-dimensional (2-D) acoustic frequency-domain forward modelling. The schemes are based on staggered-grid stencils of various accuracy and grid rotation strategies to discretize the derivatives of the wave equation. A combination of two staggered-grid stencils on the classical Cartesian coordinate system and the 45° rotated grid is the basis of the so-called mixed-grid stencil. This method is compared with a parsimonious staggered-grid method based on a fourth-order approximation of the first derivative operator. Averaging of the mass acceleration can be incorporated in the two stencils. Sponge-like perfectly matched layer absorbing boundary conditions are also examined for each stencil and shown to be effective. The deduced numerical stencils are examined for both the wavelength content and azimuthal variation. The accuracy of the fourth-order staggered-grid stencil is slightly superior in terms of phase velocity dispersion to that of the mixed-grid stencil when averaging of the mass acceleration term is applied to the staggered-grid stencil. For fourth-order derivative approximations, the classical staggered-grid geometry leads to a stencil that incorporates 13 grid nodes. The mixed-grid approach combines only nine grid nodes. In both cases, wavefield solutions are computed using a direct matrix solver based on an optimized multifrontal method. For this 2-D geometry, the staggered-grid strategy is significantly less efficient in terms of memory and CPU time requirements because of the enlarged bandwidth of the impedance matrix and increased number of coefficients in the discrete stencil. Therefore, the mixed-grid approach should be suggested as the routine scheme for 2-D acoustic wave propagation modelling in the frequency domain.

Hustedt, Bernhard; Operto, Stéphane; Virieux, Jean

2004-06-01

119

Cartesian control of redundant robots

NASA Technical Reports Server (NTRS)

A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.

Colbaugh, R.; Glass, K.

1989-01-01

120

On automating domain connectivity for overset grids

NASA Technical Reports Server (NTRS)

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.

Chiu, Ing-Tsau

1994-01-01

121

NSDL National Science Digital Library

In this activity, students enter in coordinates then the applet places a house at that location, or the location is decided first then the student must enter in the coordinates of the house. This activity allows students to practice with coordinates and ordered pairs in the Cartesian coordinate system. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

2011-05-26

122

Adjoint Formulation for an Embedded-Boundary Cartesian Method

NASA Technical Reports Server (NTRS)

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t 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 Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.

2004-01-01

123

Sink or Swim: The Cartesian Diver.

ERIC Educational Resources Information Center

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)

Pinkerton, K. David

2001-01-01

124

Index integral representations for connection between cartesian, cylindrical, and spheroidal systems

In this paper, we present two new index integral representations for connection between cartesian, cylindrical, and spheroidal coordinate systems in terms of Bessel, MacDonald, and conical functions. Our result is mainly motivated by solution of the boundary value problems in domains composed of both cartesian and hyperboloidal boundaries, and the need for new integral representations that facilitate the transformation between these coordinates. As a by-product, the special cases of our results will produce new proofs to known index integrals and provide some new integral identities.

Passian, Ali [ORNL; Koucheckian, Sherwin [University of South Florida, Tampa; Yakubovich, Semyon [University of Porto, Portugal

2011-01-01

125

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.

2014-01-01

126

Curvilinear coordinate systems in five-, seven-, and nine-spot symmetry element models have been used to achieve a more realistic representation of reservoir flow behavior. The grid pattern is chosen to approximate the streamtubes, and near each well this can be made the same as for history-matched single-well radial models. Consequently, the parameters obtained in a history match of a single well can be used directly in the curvilinear system, thereby obviating the need to adapt them for use in a cartesian one. In this way individual well behavior, including cusping and coning effects, can be realistically modeled. Comparison runs have been made for a single-layer inverted nine-spot model with a favorable mobility ratio using two curvilinear and two cartesian grid patterns. Significant differences in the well performances are obtained, with the cartesian models yielding more optimistic results. Satisfactory history matches of production performance were obtained for a typical drainage point in the Kharaib reservoir of the Lekhwair field using a multilayer single-well radial model. The parameters obtained were applied directly in curvilinear areal grid configurations of five-, seven-, and nine-spot symmetry elements to obtain predictions of waterflood behavior. Since the mobility ratio (M= 0.7) of the system is favorable, high recoveries are obtained for all the pattern flood models--namely, + or - 56% of stock-tank oil initially in place (STOIIP) in the Kharaib. The equivalent result for natural depletion is 10%.

Cottrell, C.W.

1983-07-01

127

NASA Astrophysics Data System (ADS)

The computational efficiency of iterative and direct solution methods in viscous flows calculated on curvilinear coordinate systems is studied for cases including a series of two-dimensional planar channels with progressive skewness of the grid system and a kidney-shaped channel. The iterative method convergence rate, less rapid than that of the direct method, decreases monotonically with increasing global mesh skewness and Reynolds number, while the direct method is seen as insensitive to these variables. It is shown that the increased complexity of the equations in curvilinear coordinates causes the storage requirements and cost per iteration of the direct method to be higher than in corresponding Cartesian coordinate methods. Therefore, increases in grid size increase CPU time and computer storage needs of the direct method more severely than the iterative method.

Braaten, M. E.; Shyy, W.

1986-06-01

128

. .................. ................. . .................. ................. . ................... ....................................... ................... ..................... ................... E T © Let q = ai + bj be the position vector of the point Q. Then applying Pythagoras's Theorem. ¨ ¨ ¨¨ ¨ ¨¨ ¨ ¨¨¨ ¨¨ .......................... ........................ s s s . .................. ................. . .................. .................. ....................................... O Q R q r ck (length |c|) Applying Pythagoras's Theorem to triangle OQR gives: |r| = | - OR

Banaji,. Murad

129

Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

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.

Rumsey, Christopher Lockwood

1991-01-01

130

Graphing and the Coordinate Plane

NSDL National Science Digital Library

This lesson is designed to introduce students to graphing coordinates and lines in the Cartesian coordinate plane. This lesson provides links to discussions and activities related to graphing as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

2011-05-24

131

Recommended coordinate systems for thin spherocylindrical lenses.

Because the set of thin spherocylindrical lenses forms a vector space, any such lens can be expressed in terms of its cartesian coordinates with respect to whatever set of basis lenses we may choose. Two types of cartesian coordinate systems have become prominent, those having coordinates associated with the lens power matrix and those having coordinates associated with the Humphrey Vision Analyzer. This paper emphasizes the value of a particular cartesian coordinate system of the latter type, and the cylindrical coordinate system related to it, by showing how it can simplify the trigonometry of adding lenses and how it preserves symmetry in depicting the sets of all spherical lenses, all Jackson crossed-cylinders, and all cylindrical lenses. It also discusses appropriate coordinates for keeping statistics on lenses and shows that an easy extension of the lens vector space to include general optical systems is not possible. PMID:8515971

Deal, F C; Toop, J

1993-05-01

132

A spectral element shallow water model on spherical geodesic grids

NASA Astrophysics Data System (ADS)

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. The Finite Element Method for Engineers. Wiley, New York, 1995; Karniadakis GE, Sherwin SJ. Spectral/hp Element Methods for CFD. Oxford University Press, New York, 1999; and Szabó B, Babu\\vska I. Finite Element Analysis. Wiley, New York, 1991) can be used. Results for six test cases are presented to confirm the accuracy and stability of the new method. Published in 2001 by John Wiley & Sons, Ltd.

Giraldo, Francis X.

2001-04-01

133

NASA Technical Reports Server (NTRS)

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.

Moore, Reagan W.; Jagatheesan, Arun; Rajasekar, Arcot; Wan, Michael; Schroeder, Wayne

2004-01-01

134

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

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.

Coirier, William J.; Powell, Kenneth G.

1996-01-01

135

Coping with curvilinear coordinates in fluid mechanics

The method of local Cartesian coordinates introduced in the first part of a series of three articles on curvilinear coordinates was applied in the second article to some solid mechanics problems. In this final, third article of the series, the method is applied to fluid mechanics and for intrinsic coordinates. The use of the principle of virtual power is advocated

J. Paavola

136

GECCO 2012 tutorial: cartesian genetic programming

Cartesian Genetic Programming (CGP) is an increasingly popular and efficient form of Genetic Programming that was developed by Julian Miller in 1999 and 2000. In its classic form, it uses a very simple integer based genetic representation of a program in the form of a directed graph. Graphs are very useful program representations and can be applied to many domains

Julian Francis Miller; Simon Harding

2012-01-01

137

GECCO 2011 tutorial: cartesian genetic programming

Cartesian Genetic Programming (CGP) is an increasingly popular and efficient form of Genetic Programming that was developed by Julian Miller in 1999 and 2000. In its classic form, it uses a very simple integer based genetic representation of a program in the form of a directed graph. Graphs are very useful program representations and can be applied to many domains

Julian F. Miller; Simon L. Harding

2011-01-01

138

Automated Parameter Studies Using a Cartesian Method

A modular process for performing general parametric studies about an aerodynamic configuration using a Cartesian method is described. A novel part of this process is the automatic handling of general control surfaces deflections based upon simple, user- specified inputs. The article focuses on the use of aerodynamic databases in the design process. Database fly-through is used to develop and analyze

Scott M. Murman; Michael J. Aftosmis; Marian Nemec

139

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.

Tao, Liang; McCurdy, Bill; Rescigno, Tom

2010-06-10

140

Further on Non-Cartesian Systems Elemer E Rosinger

the state space given by the Cartesian product E Ă? F. Classical physical systems are in this sense Cartesian, respectively, then the state space of the composite quantum system "X and Y " is the tensor product E F. And indeed, this is a considerably larger space than the Cartesian product E Ă? F, since we have the injective

Boyer, Edmond

141

Development of a 2-D black-oil reservoir simulator using a unique grid-block system

effective in reducing the grid orientation effect than the Cartesian grid. The HGB grid performs better by consistently giving a smaller relative difference between HGB parallel grid and HGB diagonal grid in pore volume recovered (6.0, 4.5, 3.3, and 2.2...

Chong, Emeline E

2006-04-12

142

NASA Technical Reports Server (NTRS)

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.

Swinbank, Richard; Purser, James

2006-01-01

143

NASA Astrophysics Data System (ADS)

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.

de Zelicourt, Diane; Ge, Liang; Sotiropoulos, Fotis; Yoganathan, Ajit

2008-11-01

144

On automating domain connectivity for overset grids

NASA Technical Reports Server (NTRS)

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.

Chiu, Ing-Tsau; Meakin, Robert L.

1995-01-01

145

This paper presents an example of compliant manipulator control implemented on a DSP chip. Drake and Hsia (1993) discussed the algorithms for computing the manipulator forward and inverse kinematics, Jacobian, J(?), J-1, J˙?˙, and Newton-Euler inverse dynamics. These algorithms were unified under a common coordinate system and optimized. Here, these tools have been augmented by a six D.O.F Cartesian trajectory

T. A. Lasky; T. C. Hsia

1994-01-01

146

Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries

NASA Technical Reports Server (NTRS)

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.

Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)

2002-01-01

147

Inflow-outflow boundary conditions along arbitrary directions in Cartesian lake models

NASA Astrophysics Data System (ADS)

Specifying point sources and sinks of water near boundaries is presented as a flexible approach to prescribe inflows and outflows along arbitrary directions in Cartesian grid lake models. Implementing the approach involves a straightforward modification of the governing equations, to include a first order source term in the continuity and momentum equations. The approach is implemented in a Cartesian grid model and applied to several test cases. First, the flow along a straight flat bottom channel with its axis forming different angles with the grid directions is simulated and the results are compared against well-known analytical solutions. Point-sources are then used to simulate unconfined inflows into a reservoir (a small river entering a reservoir in a jet-like manner), which occur at an angle with the grid directions. The model results are assessed in terms of a mixing ratio between lake and river water, evaluated at a cross section downstream of the inflow boundary. Those results are particularly sensitive to changes in the inflow angle. It is argued that differences in mixing rates near the inflow sections could affect the fate of river-borne substances in model simulations.

Ramón, C. L.; Cortés, A.; Rueda, F. J.

2015-01-01

148

Arbitrary order permanent Cartesian multipolar electrostatic interactions

NASA Astrophysics Data System (ADS)

Recently, there has been a concerted effort to implement advanced classical potential energy surfaces by adding higher order multipoles to fixed point charge electrostatics in a bid to increase the accuracy of simulations of condensed phase systems. One major hurdle is the unwieldy nature of the expressions which in part has limited developers mostly to including only dipoles and quadrupoles. In this paper, we present a generalization of the Cartesian formulation of electrostatic multipolar interactions that enables the specification of an arbitrary order of multipoles. Specifically, we derive formulas for arbitrary order implementation of the particle mesh Ewald method and give a closed form formula for the stress tensor in the reciprocal space. In addition, we provide recurrence relations for common electrostatic potentials employed in molecular simulations, which allows for the generalization to arbitrary order and guarantees a computational cost that scales as O(p3) for Cartesian multipole interactions of order p.

Boateng, H. A.; Todorov, I. T.

2015-01-01

149

Surface Generation and Cartesian Mesh Support

NASA Technical Reports Server (NTRS)

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.

Haimes, Robert

2004-01-01

150

A Cartesian Adaptive Level Set Method for Two-Phase Flows

NASA Technical Reports Server (NTRS)

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.

Ham, F.; Young, Y.-N.

2003-01-01

151

Self modifying Cartesian Genetic Programming: Parity

Self Modifying CGP (SMCGP) is a developmental form of Cartesian Genetic Programming(CGP). It differs from CGP by including primitive functions which modify the pro- gram. Beginning with the evolved genotype the self-modifying functions produce a new program (phenotype) at each iteration. In this paper we have applied it to a well known digital circuit building problem: even-parity. We show that

Simon Harding; Julian Francis Miller; Wolfgang Banzhaf

2009-01-01

152

76 FR 46279 - Smart Grid Advisory Committee

Federal Register 2010, 2011, 2012, 2013, 2014

...Institute of Standards and Technology Smart Grid Advisory Committee AGENCY: Department...SUMMARY: The Smart Grid Advisory Committee (SGAC or Committee...Office of the National Coordinator for Smart Grid Interoperability, National Institute...

2011-08-02

153

FUTURE POWER GRID INITIATIVE Future Power Grid

for grid operation and planning and ensure a more secure, efficient and reliable future grid. Building on the Electricity Infrastructure Operations Center (EIOC), the Pacific Northwest National Laboratory's (PNNL robust controllers (DHRC) - Improve transient stability of system over wide operating range - Coordinate

154

NASA Technical Reports Server (NTRS)

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.

Kaul, Upender K.

2005-01-01

155

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

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.

Coirier, William J.; Powell, Kenneth G.

1995-01-01

156

A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction

NASA Technical Reports Server (NTRS)

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.

Hood, Caroline; Frendi, Abdelkader

2006-01-01

157

Tolerating Correlated Failures for Generalized Cartesian Distributions via Bipartite Matching

Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale systems. A key ingredient of any approach to fault tolerance is effective support for fault tolerant data storage. A typical application execution consists of phases in which certain data structures are modified while others are read-only. Often, read-only data structures constitute a large fraction of total memory consumed. Fault tolerance for read-only data can be ensured through the use of checksums or parities, without resorting to expensive in-memory duplication or checkpointing to secondary storage. In this paper, we present a graph-matching approach to compute and store parity data for read-only matrices that are compatible with fault tolerant linear algebra (FTLA). Typical approaches only support blocked data distributions with each process holding one block with the parity located on additional processes. The matrices are assumed to be blocked by a cartesian grid with each block assigned to a process. We consider a generalized distribution in which each process can be assigned arbitrary blocks. We also account for the fact that multiple processes might be part of the same failure unit, say an SMP node. The flexibility enabled by our novel application of graph matching extends fault tolerance support to data distributions beyond those supported by prior work. We evaluate the matching implementations and cost to compute the parity and recover lost data, demonstrating the low overhead incurred by our approach.

Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.

2011-05-05

158

A numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics. The governing equations are discretized on a hybrid staggered\\/non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual-time-stepping, artificial compressibility iteration scheme. Unstructured,

Anvar Gilmanov; Fotis Sotiropoulos

2005-01-01

159

OVERGRID: A Unified Overset Grid Generation Graphical Interface

NASA Technical Reports Server (NTRS)

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.

Chan, William M.; Akien, Edwin W. (Technical Monitor)

1999-01-01

160

Material translations in the Cartesian brain.

This article reexamines the controversial doctrine of the pineal gland in Cartesian psychophysiology. It argues initially that Descartes' combined metaphysics and natural philosophy yield a distinctly human subject who is rational, willful, but also a living and embodied being in the world, formed in the union and through the dynamics of the interaction between the soul and the body. However, Descartes only identified one site at which this union was staged: the brain, and more precisely, the pineal gland, the small bulb of nervous tissue at the brain's center. The pineal gland was charged with the incredible task of ensuring the interactive mutuality between the soul and body, while also maintaining the necessary ontological incommensurability between them. This article reconsiders the theoretical obligations placed on the pineal gland as the site of the soul-body union, and looks at how the gland was consequently forced to adopt a very precarious ontological status. The article ultimately questions how successfully the Cartesian human could be localized in the pineal gland, while briefly considering the broader historical consequences of the ensuing equivalence of the self and brain. PMID:22326094

Bassiri, Nima

2012-03-01

161

NASA Technical Reports Server (NTRS)

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.

Coirier, William J.; Powell, Kenneth G.

1994-01-01

162

NASA Technical Reports Server (NTRS)

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.

Coirier, William J.; Powell, Kenneth G.

1995-01-01

163

Biangular Coordinates Redux: Discovering a New Kind of Geometry

ERIC Educational Resources Information Center

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…

Winkel, Brian; Naylor, Michael

2010-01-01

164

SMCGP2: self modifying cartesian genetic programming in two dimensions

Self Modifying Cartesian Genetic Programming is a general purpose, graph-based, developmental form of Cartesian Genetic Programming. Using a combination of computational functions and special functions that can modify the phenotype at runtime, it has been employed to find general solutions to certain Boolean circuits and mathematical problems. In the present work, a new version, of SMCGP is proposed and demonstrated.

Simon Harding; Julian F. Miller; Wolfgang Banzhaf

2011-01-01

165

Cartesian Factoring of Polyhedra in Linear Relation Analysis

Cartesian Factoring of Polyhedra in Linear Relation Analysis N. Halbwachs and D. Merchat and C.Halbwachs,David.Merchat,Catherine.Parent}@imag.fr Abstract. Linear Relation Analysis [CH78] suffers from the cost of op- erations on convex polyhedra, which to detect when a polyhedron is a Cartesian product of polyhedra of lower dimen- sions, i.e., when groups

Paris-Sud XI, UniversitĂ© de

166

Developmental Plasticity in Cartesian Genetic Programming Artificial Neural Networks

Developmental Plasticity in Cartesian Genetic Programming Artificial Neural Networks Maryam Mahsal developmental plasticity in Artificial Neural Networks using Carte- sian Genetic Programming. This is inspired. The network architecture used is that of a static Cartesian Genetic Programming ANN, which has recently been

Fernandez, Thomas

167

Configuration space representation in parallel coordinates

NASA Technical Reports Server (NTRS)

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).

Fiorini, Paolo; Inselberg, Alfred

1989-01-01

168

A Finite-Volume Method with Hexahedral Multiblock Grids for Modeling Flow in Porous Media

This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and\\/or unstructured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids. These

S. H. Lee; P. Jenny; H. A. Tchelepi

2002-01-01

169

A finite-volume method with hexahedral multiblock grids for modeling flow in porous media

This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and\\/or unstruc- tured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids.

S. H. Lee; P. Jenny; H. A. Tchelepi

2002-01-01

170

``Yin-Yang grid'': An overset grid in spherical geometry

NASA Astrophysics Data System (ADS)

A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on their boundaries. Each component grid is a low-latitude part of the latitude-longitude grid. Therefore the grid spacing is quasi-uniform, and the metric tensors are simple and analytically known. One can directly apply mathematical and numerical resources that have been written in the spherical polar coordinates or latitude-longitude grid. The complemental combination of the two identical component grids enables us to make efficient and concise programs. Simulation codes for geodynamo and mantle convection simulations using finite difference scheme based on the Yin-Yang grid are developed and tested. The Yin-Yang grid is suitable for massively parallel computers.

Kageyama, Akira; Sato, Tetsuya

2004-09-01

171

Graphing Equations on the Cartesian Plane: Slope

NSDL National Science Digital Library

The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slope occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y- axes on the plane in both the positive and negative directions.

2011-03-31

172

Calibrating a Cartesian Robot with Eye-on-Hand Configuration Independent of Eye-to-Hand Relationship

A new approach is described for geometric calibration of Cartesian robots. This is part of a set of procedures for real-time 3-D robotics eye, eye-to-hand, and hand calibration which uses a common setup and calibration object, common coordinate systems, matrices, vectors, symbols, and operations and is especially suited to machine vision systems. The robot makes a series of automatically planned

REIMAR K. LENZ; Roger Y. Tsai

1989-01-01

173

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Adjoint 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 optimization. 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 (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et 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 Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian; Aftosmis, Michael J.

2004-01-01

174

Black-hole excision with multiple grid patches

NASA Astrophysics Data System (ADS)

When using black-hole excision to numerically evolve a black-hole spacetime with no continuous symmetries, most 3 + 1 finite differencing codes use a Cartesian grid. It is difficult to do excision on such a grid because the natural r = constant excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth 'LEGO1 sphere' which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme which uses multiple {r × (angular coordinates)} grid patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth r = constant 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries (I use a ghost-zone scheme), the number and shape of the patches (I use a 6-patch 'inflated-cube' scheme), the details of how the ghost zones are 'synchronized' by interpolation from neighbouring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN \\tilde{\\Gamma}^i (I use a scheme which requires ghost zones which are twice as wide for the BSSN conformal factor phgr as for \\tilde{\\Gamma}^i and the other BSSN field variables). I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using fourth-order finite differencing in space and time. Using Kerr initial data with J/m2 = 0.6, I present evolutions to t gap 1500m. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme.

Thornburg, Jonathan

2004-08-01

175

A Survey of Self Modifying Cartesian Genetic Programming

\\u000a Self-Modifying Cartesian Genetic Programming (SMCGP) is a general purpose, graph-based, developmental form of Cartesian Genetic\\u000a Programming. In addition to the usual computational functions found in CGP, SMCGP includes functions that can modify the evolved\\u000a program at run time. This means that programs can be iterated to produce an infinite sequence of phenotypes from a single\\u000a evolved genotype. Here, we discuss

Simon Harding; Wolfgang Banzhaf; Julian F. Miller

2011-01-01

176

Developments in Cartesian Genetic Programming: self-modifying CGP

Self-modifying Cartesian Genetic Programming (SMCGP) is a general purpose, graph-based, developmental form of Genetic Programming\\u000a founded on Cartesian Genetic Programming. In addition to the usual computational functions, it includes functions that can\\u000a modify the program encoded in the genotype. This means that programs can be iterated to produce an infinite sequence of programs\\u000a (phenotypes) from a single evolved genotype. It

Simon HardingJulian; Julian F. Miller; Wolfgang Banzhaf

2010-01-01

177

Coloring the square of the Cartesian product of two cycles

Coloring the square of the Cartesian product of two cycles Â´Eric Sopena and Jiaojiao Wu Universit Abstract The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most 2 in G are joined by an edge. We study the chromatic number of the square of the Cartesian

Paris-Sud XI, UniversitĂ© de

178

Mars Transverse Mercator (MTM) Map Series Updated with Planetocentric Grid

NASA Astrophysics Data System (ADS)

The Mars Transverse Mercator (MTM) map series has been updated to use planetocentric coordinates with positive east longitude as the primary grid with a secondary grid showing the planetographic coordinates with positive west longitude.

Rosiek, M. R.; Howington-Kraus, E.; Hare, T. M.; Redding, B. L.

2003-03-01

179

77 FR 71169 - Smart Grid Advisory Committee Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

...the Committee's report and to receive presentations on cybersecurity coordination and the NIST Smart Grid Program Plan. The...the Committee's report and to receive presentations on cybersecurity coordination and the NIST Smart Grid Program Plan....

2012-11-29

180

Equipartition Principle for Internal Coordinate Molecular Dynamics.

The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has ˝kT of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordinates and includes cross-terms. Due to this coupled structure, no such equipartition principle holds for ICMD models. In this paper we introduce non-canonical modal coordinates to recover some of the structural simplicity of Cartesian models and develop a new equipartition principle for ICMD models. We derive low-order recursive computational algorithms for transforming between the modal and physical coordinates. The equipartition principle in modal coordinates provides a rigorous method for initializing velocities in ICMD simulations thus replacing the ad hoc methods used until now. It also sets the basis for calculating conformational entropy using internal coordinates. PMID:23341754

Jain, Abhinandan; Park, In-Hee; Vaidehi, Nagarajan

2012-08-14

181

Conservation equations of gasdynamics in curvilinear coordinate systems

NASA Technical Reports Server (NTRS)

Description of a new method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms. It is thus possible to readily apply difference schemes derived for Cartesian coordinates which conserve mass, momentum, and energy in the total flow field. The method is derived for orthogonal coordinates, and then extended to cover the most general class of coordinate transformations, using general tensor analysis. Several special features of the equations are discussed.

Vinokur, M.

1974-01-01

182

Plasticity of Intermediate Mechanics Students' Coordinate System Choice

ERIC Educational Resources Information Center

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…

Sayre, Eleanor C.; Wittman, Michael C.

2008-01-01

183

In the title compound, {[Ag2Fe(CN)4(H2O)2]·2C12H10N2}n, the asymmetric unit contains one FeII cation, two water molecules, two dicyanidoargentate(I) anions and two uncoordinating 1,2-bis(pyridin-2-yl)ethylene (2,2?-bpe) molecules. Each FeII atom is six-coordinated in a nearly regular octahedral geometry by four N atoms from dicyanidoargentate(I) bridges and two coordinating water molecules. The FeII atoms are bridged by dicyanidoargentate(I) units to give a two-dimensional layer with square-grid spaces. The intergrid spaces with interlayer distance of 6.550?(2)?Ĺ are occupied by 2,2?-bpe guest molecules which form O—H?N hydrogen bonds to the host layers. This leads to an extended three-dimensional supramolecular architecture. The structure of the title compound is compared with some related compounds containing dicyanidoargentate(I) ligands and N-donor organic co-ligands. PMID:25249868

Othong, Jintana; Wannarit, Nanthawat; Pakawatchai, Chaveng; Youngme, Sujittra

2014-01-01

184

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 ?-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:24729762

Branduardi, Davide; Faraldo-Gómez, José D

2013-09-10

185

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

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.

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

186

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

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.

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

187

GEAR Tech-21 Geographic Coordinates

GEAR Tech-21 Geographic Coordinates Throughout the activity, look for and record the definitions and two others on the grid below: Important Terms #12;GEAR Tech-21 Geographic Coordinates How Far Are They: Miles: #12;GEAR Tech-21 Geographic Coordinates Try It! Use the Satellites page on your handheld GPS

Farritor, Shane

188

NASA Astrophysics Data System (ADS)

A numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics. The governing equations are discretized on a hybrid staggered/non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual-time-stepping, artificial compressibility iteration scheme. Unstructured, triangular meshes are employed to discretize complex immersed boundaries. The nodes of the surface mesh constitute a set of Lagrangian control points used to track the motion of the flexible body. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. Grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity, which show that the method is second-order accurate. The method is validated by applying it to calculate flow in a Cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing. The ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish-like body and flow past an anatomically realistic planktonic copepod performing an escape-like maneuver.

Gilmanov, Anvar; Sotiropoulos, Fotis

2005-08-01

189

Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers

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

Zanchi, Marta G.; Pauly, John M.; Scott, Greig C.

2010-01-01

190

A new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains

SUMMARY This paper describes a new fast hybrid adaptive grid generation technique for arbitrary two- dimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution

Mohamed S. Ebeida; Roger L. Davis; Roland W. Freund

2010-01-01

191

Three-Dimensional Deformable Grid Electromagnetic Particle-in-cell for Parallel Computers

NASA Technical Reports Server (NTRS)

We describe a new parallel, non-orthogonal grid, three-dimensional electromagnetic particle-in-cell (EMPIC) code based on a finite-volume formulation. This code uses a logically Cartesian grid of deformable hexahedral cells, a discrete surface integral (DSI) algorithm to calculate the electromagnetic field, and a hybrid logical-physical space algorithm to push particles.

Wang, J.; Kondrashov, D.; Liewer, P. C.; Karmesin, S. R.

1998-01-01

192

Implicit Approaches for Moving Boundaries in a 3-D Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan

2003-01-01

193

ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach

NASA Astrophysics Data System (ADS)

In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM) is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat-long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.

Jähn, M.; Knoth, O.; König, M.; Vogelsberg, U.

2015-02-01

194

NSDL National Science Digital Library

This map displays the Universal Transverse Mercator (UTM) grid across the globe. Links are provided to convert between UTM and latitude/longitude coordinates and for more details on referencing coordinates within each UTM zone.

2002-12-24

195

Compact-range coordinate system established using a laser tracker.

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.

Gallegos, Floyd H.; Bryce, Edwin Anthony

2006-12-01

196

Vertex and edge PI indices of Cartesian product graphs

The Padmakar–Ivan (PI) index of a graph G is the sum over all edges uv of G of the number of edges which are not equidistant from u and v. In this paper, the notion of vertex PI index of a graph is introduced. We apply this notion to compute an exact expression for the PI index of Cartesian product

M. H. Khalifeh; H. Yousefi-azari; A. R. Ashrafi

2008-01-01

197

The Cartesian Diver as an Aid for Teaching Respiratory Physiology

ERIC Educational Resources Information Center

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…

Fitch, Greg K.

2004-01-01

198

Self Modifying Cartesian Genetic Programming: Fibonacci, Squares, Regression and Summing

Self Modifying CGP (SMCGP) is a developmental form of Cartesian Genetic Programming(CGP). It is able to modify its own phe- notype during execution of the evolved program. This is done by the inclusion of modification operators in the function set. Here we present the use of the technique on several different sequence generation and regression problems.

Simon Harding; Julian Francis Miller; Wolfgang Banzhaf

2009-01-01

199

The Structure of Integral Dimensions: Contrasting Topological and Cartesian Representations

ERIC Educational Resources Information Center

Diverse evidence shows that perceptually integral dimensions, such as those composing color, are represented holistically. However, the nature of these holistic representations is poorly understood. Extant theories, such as those founded on multidimensional scaling or general recognition theory, model integral stimulus spaces using a Cartesian…

Jones, Matt; Goldstone, Robert L.

2013-01-01

200

A THREE-DIMENSIONAL CARTESIAN TREE-CODE AND

A THREE-DIMENSIONAL CARTESIAN TREE-CODE AND APPLICATIONS TO VORTEX SHEET ROLL-UP by Keith Lindsay . . . . . . . . . . . . . . . . . . . 11 2.2.3 Discretization . . . . . . . . . . . . . . . . . . . . . 13 2.3 Vortex Rings SIMULATIONS . . . . . 29 3.1 Mesh Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Tree

201

Self-Modifying Cartesian Genetic Programming Simon Harding

of Cartesian Genetic Programming that includes self-modification operations. One advantage of this approach of problems and demonstrate the characteristics and advantages that self-modification brings. Categories into their phenotypes are not merely the string of bases in the DNA. Such a view would be akin to the once domi- nant

Fernandez, Thomas

202

Coevolution of Intelligent Agents using Cartesian Genetic Programming

inspired by the biological neurons. Agents have a health which is related to their actions and encountersCoevolution of Intelligent Agents using Cartesian Genetic Programming Gul Muhammad Khan Electronics for two antagonistic agents is presented. The agents are controlled by a new kind of computational network

Fernandez, Thomas

203

Self Modifying Cartesian Genetic Programming: Fibonacci, Squares, Regression and Summing

the subsequent genetic expression [1, 2]. The concept of self-modification can be a unifying way of looking that by utilizing self-modification opera- tions within an existing computational method (a form of geneticSelf Modifying Cartesian Genetic Programming: Fibonacci, Squares, Regression and Summing Simon

Fernandez, Thomas

204

MARS TERRAIN IMAGE CLASSIFICATION USING CARTESIAN GENETIC PROGRAMMING

to drive on another planet using semiautonomous, purely-reactive terrain navigation [2]. The current MarsMARS TERRAIN IMAGE CLASSIFICATION USING CARTESIAN GENETIC PROGRAMMING J. Leitner, S. Harding, A. F for classification tasks performed on a panorama image collected by the Mars Exploration Rover Spirit. 1

Fernandez, Thomas

205

A Lot of Good Physics in the Cartesian Diver

ERIC Educational Resources Information Center

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…

De Luca, Roberto; Ganci, Salvatore

2011-01-01

206

The Cartesian Diver, Surface Tension and the Cheerios Effect

ERIC Educational Resources Information Center

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…

Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai

2014-01-01

207

Grid spacing control with variation diminishing splines

NASA Technical Reports Server (NTRS)

Methods used to specify and control two and three dimensional grids on which numerical solutions of partial differential equations may be obtained were studied. While initially focusing on grid generation, the research will evolve into a consideration of the interaction of grid generation with the solution of a partial differential equation. The multisurface method of grid generation was used to continuously patch a grid onto an existing grid. In the resulting grid the elements of the Jacobian matrix must be continuous across the boundary between the original grid and the patched grid. Programs were written which accept as input the coordinates of the original grid and the desired new boundary, and then use the three-surface or four-surface version of the multisurface method to extend the original grid out to a new boundary.

Smith, P. W.

1983-01-01

208

Enhanced Elliptic Grid Generation

NASA Technical Reports Server (NTRS)

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 determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.

2007-01-01

209

The Overgrid Interface for Computational Simulations on Overset Grids

NASA Technical Reports Server (NTRS)

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.

Chan, William M.; Kwak, Dochan (Technical Monitor)

2002-01-01

210

General noncommuting curvilinear coordinates and fluid Mechanics

We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The cartesian, circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U(1) gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg-Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange to Euler map in fluid mechanics.

S. A. Alavi

2006-08-16

211

TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide

NASA Technical Reports Server (NTRS)

A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.

Miller, David P.

1994-01-01

212

Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates

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.

Nagaitsev, S.; /Fermilab; Kharkov, Y.; Morozov, I.A.; /Novosibirsk, IYF; Zolkin, T.V.; /Chicago U.

2012-05-01

213

Internal coordinate molecular dynamics: a foundation for multiscale dynamics.

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

Vaidehi, Nagarajan; Jain, Abhinandan

2015-01-29

214

SU-E-I-41: Non-Cartesian MR Image Reconstruction with Integrated Gradient Non-Linearity Correction

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 that corrects for gradient nonlinearities during — rather than after — reconstruction, and thus better preserves image resolution than traditional interpolation-based methods. This approach is expected to be especially advantageous when imaging with non-standard magnet geometries. NIH RR018898; NIH EB10065.

Tao, S; Trzasko, JD; Polley, TW; Shu, Y; Bernstein, MA [Mayo Clinic, Rochester, MN (United States)

2014-06-01

215

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

NASA Technical Reports Server (NTRS)

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.

Liu, Yen; Vinokur, Marcel

1997-01-01

216

Simulations of 6-DOF Motion with a Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)

2003-01-01

217

Approximate Cartesian state transition matrix. [for spacecraft navigation

NASA Technical Reports Server (NTRS)

Based on a Taylor series expansion, an easily-computed approximation to the Cartesian state transition matrix is presented for a general velocity-independent force field. Suitable for the short time intervals encountered in onboard navigation applications of the extended Kalman filter, it provides approximately five decimal digits of accuracy for earth orbiting spacecraft with update intervals of one minute, and better accuracy for shorter intervals.

Markley, F. L.

1986-01-01

218

NASA Astrophysics Data System (ADS)

This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.

Wu, C. S.; Young, D. L.; Chiu, C. L.

2013-12-01

219

Quality-based generation of weather radar Cartesian products

NASA Astrophysics Data System (ADS)

Weather radar data volumes are commonly processed to obtain various 2-D Cartesian products based on the transfer from polar to Cartesian representations through a certain interpolation method. In this research, an algorithm of the spatial interpolation of polar reflectivity data with respect to QI (quality index) data is applied to find the Cartesian reflectivity as PPI (plan position indicator) product and generate a corresponding QI field. On this basis, quality-based versions of standard algorithms for the generation of the following products have been developed: ETOP (echo top), MAX (maximum of reflectivity), and VIL (vertically integrated liquid water). Moreover, as an example of a higher-level product, a CONVECTION (detection of convection) has been defined as a specific combination of the above-listed standard products. A corresponding QI field is determined for each generated product, taking into account the quality of the pixels from which a given product was determined and how large a fraction of the investigated heights was scanned. Examples of such quality-based products are presented in the paper.

O?ródka, K.; Szturc, J.

2014-11-01

220

Frequency-Offset Cartesian Feedback for MRI Power Amplifier Linearization

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

Zanchi, Marta Gaia; Stang, Pascal; Kerr, Adam; Pauly, John Mark; Scott, Greig Cameron

2011-01-01

221

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. PMID:23679541

Van Gorder, Robert A

2013-04-01

222

A Hybrid Solar Wind Model of the CESE+HLL Method with a Yin-Yang Overset Grid and an AMR Grid

NASA Astrophysics Data System (ADS)

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.

Feng, Xueshang; Zhang, Shaohua; Xiang, Changqing; Yang, Liping; Jiang, Chaowei; Wu, S. T.

2011-06-01

223

NASA Technical Reports Server (NTRS)

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 different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Coirier, William John

1994-01-01

224

Ontology-Based Resource Matching in the Grid - The Grid Meets the Semantic Web

The Grid is an emerging technology for enabling resource sharing and coordinated problem solving in dynamic multi-institutional virtual organizations. In the Grid environment, shared resources and users typically span different orga- nizations. The resource matching problem in the Grid involves assigning resources to tasks in order to satisfy task requirements and resource policies. These require- ments and policies are often

Hongsuda Tangmunarunkit; Stefan Decker; Carl Kesselman

2003-01-01

225

NSDL National Science Digital Library

TeraGrid is an open scientific discovery infrastructure combining leadership class resources at nine partner sites to create an integrated, persistent computational resource. Using high-performance network connections, the TeraGrid integrates high-performance computers, data resources and tools, and high-end experimental facilities around the country. These integrated resources include more than 102 teraflops of computing capability and more than 15 petabytes (quadrillions of bytes) of online and archival data storage with rapid access and retrieval over high-performance networks. Through the TeraGrid, researchers can access over 100 discipline-specific databases. With this combination of resources, the TeraGrid is the world's largest, most comprehensive distributed cyberinfrastructure for open scientific research. TeraGrid is coordinated through the Grid Infrastructure Group (GIG) at the University of Chicago, working in partnership with the Resource Provider sites: Indiana University, Oak Ridge National Laboratory, National Center for Supercomputing Applications, Pittsburgh Supercomputing Center, Purdue University, San Diego Supercomputer Center, Texas Advanced Computing Center, University of Chicago/Argonne National Laboratory, and the National Center for Atmospheric Research.

226

NASA Astrophysics Data System (ADS)

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.

Mignone, A.

2014-08-01

227

Internal coordinate density of state from molecular dynamics simulation.

The vibrational density of states (DoS), calculated from the Fourier transform of the velocity autocorrelation function, provides profound information regarding the structure and dynamic behavior of a system. However, it is often difficult to identify the exact vibrational mode associated with a specific frequency if the DoS is determined based on velocities in Cartesian coordinates. Here, the DoS is determined based on velocities in internal coordinates, calculated from Cartesian atomic velocities using a generalized Wilson's B-matrix. The DoS in internal coordinates allows for the correct detection of free dihedral rotations that may be mistaken as hindered rotation in Cartesian DoS. Furthermore, the pronounced enhancement of low frequency modes in Cartesian DoS for macromolecules should be attributed to the coupling of dihedral and angle motions. The internal DoS, thus deconvolutes the internal motions and provides fruitful insights to the dynamic behaviors of a system. © 2015 Wiley Periodicals, Inc. PMID:25565300

Lai, Pin-Kuang; Lin, Shiang-Tai

2015-03-30

228

Taxonomy of Grid Business Models

Grid Computing, initially intended to provide access to computational resources for high-performance computing applications, broadened its focus by addressing computational needs of enterprises. It became concerned with coordinating the on-demand, usage-based allocation of resources in dynamic, multi-institutional virtual organizations, and eventually creating new business models based on this technology. This trend in Grid computing holds a lot of potential in

Jörn Altmann; Mihaela Ion; Ashraf Adel Bany Mohammed

2007-01-01

229

Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids

NASA Astrophysics Data System (ADS)

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 discretizationsare 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.

Burton, Donald E.

1994-10-01

230

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

NASA Technical Reports Server (NTRS)

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

Berger, Marsha; Aftosmis, Michael J.

2011-01-01

231

Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle

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.

Li, Tingwen; Dietiker, Jean-Francois; Zhang, Yongmin; Shahnam, Mehrdad

2011-12-01

232

A Cartesian Grid Method for Compressible Inviscid Flows M. Asif Farooq

by merging those cut-cells with neighboring cells [7]. Cut cells are avoided altogether by ghost point variables in ghost cells or at ghost points near solid boundaries [15, 16, 17, 12, 18, 19]. In the ghost ghost point treatment for compressible inviscid flows with immersed boundaries. In the simplified ghost

Müller,Bernhard

233

Multi-moment advection schemes for Cartesian grids and cut cells

Computational fluid dynamics has progressed to the point where it is now possible to simulate flows with large eddy turbulence, free surfaces and other complex features. However, the success of these models often depends ...

Ferrier, Richard James

2014-11-27

234

Coil Compression for Accelerated Imaging with Cartesian Sampling

MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression algorithms are effective in mitigating this problem by compressing data from many channels into fewer virtual coils. In Cartesian sampling there often are fully sampled k-space dimensions. In this work, a new coil compression technique for Cartesian sampling is presented that exploits the spatially varying coil sensitivities in these non-subsampled dimensions for better compression and computation reduction. Instead of directly compressing in k-space, coil compression is performed separately for each spatial location along the fully-sampled directions, followed by an additional alignment process that guarantees the smoothness of the virtual coil sensitivities. This important step provides compatibility with autocalibrating parallel imaging techniques. Its performance is not susceptible to artifacts caused by a tight imaging fieldof-view. High quality compression of in-vivo 3D data from a 32 channel pediatric coil into 6 virtual coils is demonstrated. PMID:22488589

Zhang, Tao; Pauly, John M.; Vasanawala, Shreyas S.; Lustig, Michael

2012-01-01

235

Field Inhomogeneity Correction based on Gridding Reconstruction for Magnetic Resonance Imaging

1 Field Inhomogeneity Correction based on Gridding Reconstruction for Magnetic Resonance Imaging H in magnetic resonance images if disregarded in reconstruction. With non-Cartesian k-space sampling, they often and a balance between reconstruction and correction accuracy. Index Terms-- Magnetic resonance imaging, image re

236

Skew grids and irrotational flow

NASA Astrophysics Data System (ADS)

Finite-difference computation of incompressible flow through regions of arbitrary shape often requires the implementation of boundary-fitted coordinates for which the grid lines may be non-orthogonal (skew). When the governing equations are expressed in terms of pressure and velocity, conservation of mass is maintained by the gradient of the pressure. In principle, the gradient is irrotational and should have no effect on the existing circulation in the flow field; but if the grid lines are skew, the discrete representation of the gradient can generate spurious vorticity near the boundaries. In the present work this difficulty is eliminated for uniform skew grids, and markedly reduced for non-uniform skew grids, by adopting a discrete formulation of the pressure gradient that helps maintain irrotationality near boundaries. The procedure is applicable for staggered grids with either Poisson or Chorin equations for pressure.

Bernard, Robert S.

1988-03-01

237

In this introductory chapter, we lay the groundwork for the rest of the book by providing a more detailed picture of the expected\\u000a purpose, shape, and architecture of future grid systems. We structure the chapter in terms of six questions that we believe\\u000a are central to this discussion: Why do we need computational grids? What types of applications will grids

Ian T. Foster; Carl Kesselman

2000-01-01

238

Basic equations of horizontal two dimensional debris flow analysis in general coordinate system

NASA Astrophysics Data System (ADS)

Horizontal two dimensional debris flow models are developed by many researchers and all of those equations are written in Cartesian coordinate system. Basic equations in Cartesian coordinate system are simple and are easy to be used. However, numerical frictions are happened at the side edges of the debris flow when the channel geometry is not a straight channel. We can find many meandering channels in mountainous rivers and, in general, width-depth ration is smaller in the mountainous rivers. Hence, the numerical frictions at the side edge of the debris affect on the flow characteristics of debris flow very well and basic equations in the boundary fitted coordinate system can reduce the numerical friction at the side edge of the debris flow in meandering channels. In this study, basic equations of horizontal two dimensional debris flow analysis are written in general coordinate system and simulate the debris flow in the meandering channels by use of the basic equations of horizontal two dimensional debris flow analysis in general coordinate system. Furthermore, the debris flow in the meandering channels is simulated by use of the basic equations in Cartesian coordinate system and the difference of the flow velocity and flow depth between them discussed. Results show that the depth and the velocity of the debris flow simulated by use of the basic equations in general coordinate system is smaller and faster than those by use of the basic equations in Cartesian coordinate system, respectively. Underestimation of the flow velocity indicates that the underestimation of fluid power of debris flow on the river structures, houses and son. Furthermore, the escape time of people tends to be overestimated, when the basic equations in Cartesian coordinate system are used.

Takebayashi, Hiroshi; Fujita, Masaharu

2014-05-01

239

The National Grid Project: A system overview

NASA Technical Reports Server (NTRS)

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.

Gaither, Adam; Gaither, Kelly; Jean, Brian; Remotigue, Michael; Whitmire, John; Soni, Bharat; Thompson, Joe; Dannenhoffer,, John; Weatherill, Nigel

1995-01-01

240

Coriolis weighting on unstructured staggered grids

NASA Astrophysics Data System (ADS)

There is an increasing interest to move ocean codes from classical Cartesian staggered mesh schemes to unstructured staggered grids. By using unstructured grid models one may construct meshes that follow the coastlines more accurately, and it is easy to apply a finer resolution in areas of special interest. In this paper we focus on how to approximate the Coriolis terms in such unstructured staggered grid models using equivalents of the Arakawa C-grid for the linear equations governing the propagation of the inertia-gravity waves. We base the analysis on a Delaunay triangulation of the region in question and use the Voronoi points and the midpoints on the triangle edges to define a staggered grid for the sea elevation and the velocity orthogonal to the edges of the triangles. It is shown that a standard method for the Coriolis weighting may create unphysical growth of the numerical solutions. A modified Coriolis weighting that conserves the total energy is suggested. In real applications diffusion is often introduced both for physical reasons, but often also in order to stabilise the numerical experiments. The growing modes associated with the unstructured staggered grids and equal weighting may force us to enhance the diffusion more than we would like from physical considerations. The modified weighting offers a simple solution to this problem.

Espelid, Terje O.; Berntsen, Jarle

241

Cartesian Impedance Control Techniques for Torque Controlled LightWeight Robots

The paper compares various approaches to imple- menting a compliant Cartesian behavior for robotic manipulators: impedance, admittance and stifiness control. A new controller structure is proposed, which consists of an impedance controller enhanced by lo- cal stifiness control. This structure consistently takes into account the two time scale property of the joint and Cartesian control loops. The DLR light-weight robot,

Alin Albu-schäffer; Gerd Hirzinger

2002-01-01

242

The Role of Dynamic Models in Cartesian Force Control of Manipulators

Dynamic models are as important in Cartesian force control as they are in position control. A variety of Cartesian force control schemes are examined, comprising some that do incorporate a dynamic model into the control loop (resolved acceleration force control, operational space method, and impedance control) and some that do not (hybrid control and stiffness control). Stability analyses and experimental

Chae H. An; John M. Hollerbach

1989-01-01

243

Practical Conversion from Torsion Space to Cartesian Space for In Silico Protein Synthesis

Practical Conversion from Torsion Space to Cartesian Space for In Silico Protein Synthesis JEROD Experiment Station, Texas A&M University, College Station, Texas 77843 2 Los Alamos National Laboratory, Los: conversion; torsion space; Cartesian space; protein synthesis Introduction The backbones of common biological

244

Cartesian Compliant Control Strategies for LightWeight, Flexible Joint Robots

The paper focuses on theoretical and experimental aspects related to the Cartesian compliant control of flexible joint robots with joint torque measurement. While the Cartesian impedance control for rigid robots, as well as the joint level control of flexible joint robots have been studied in detail, their combined implementation on robots with six or seven joints still leaves many open

Alin Albu-Schäffer; Gerd Hirzinger

245

MESH2D GRID GENERATOR DESIGN AND USE

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.

Flach, G.; Smith, F.

2012-01-20

246

ERIC Educational Resources Information Center

Proposes that narrow columns provide a flexible system of organization for designers. Notes that grids serve the content on the pages, help to develop a layout that will clearly direct the reader to information; and prevent visual monotony. Concludes when grid layouts are used, school publications look as good as professional ones. (PM)

Barrington, Linda; Carter, Jacky

2003-01-01

247

KOALA: a co-allocating grid scheduler

SUMMARY In multicluster systems, and more generally in grids, jobs may require co-allocation, that is, the simul- taneous or coordinated access of single applications to resources of possibly multiple types in multiple locations managed by different resource managers. Co-allocation presents new challenges to resource management in grids, such as locating sufficient resources in geographically distributed sites, allocating and managing resources

Hashim H. Mohamed; Dick H. J. Epema

2008-01-01

248

Unstructured Grid Generation Techniques and Software

NASA Technical Reports Server (NTRS)

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.

Posenau, Mary-Anne K. (editor)

1993-01-01

249

Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method

This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specific preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.

Cantrell, J Nathan [ORNL] [ORNL; Inclan, Eric J [ORNL] [ORNL; Joshi, Abhijit S [ORNL] [ORNL; Popov, Emilian L [ORNL] [ORNL; Jain, Prashant K [ORNL] [ORNL

2012-01-01

250

Polar Coordinates and Multiplication In the last chapter we wrote complex numbers in the form x + iy where x and y are real numbers. We can think of this as writing complex numbers using Cartesian coordinates. Every complex number is the sum of a number on the real axis and a number on the imaginary axis

Wortman, Kevin

251

Iterative reconstruction method for three-dimensional non-cartesian parallel MRI

NASA Astrophysics Data System (ADS)

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 image from a separate body coil scan were used to verify the fidelity of reconstruction to the reference. Region of interest (ROI) signal to noise ratio (SNR), two-data SNR and background noise were used to validate the quality of the reconstruction. The proposed method showed higher ROI SNR, two-data SNR, and lower background noise over conventional method with comparable RMSE, NMI and JE to the reference image at reduced computer resource requirement.

Jiang, Xuguang

252

Multi-fault Tolerance for Cartesian Data Distributions

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.

Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.

2013-06-01

253

Numerical solution of the full potential equation using a chimera grid approach

NASA Technical Reports Server (NTRS)

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.

Holst, Terry L.

1995-01-01

254

NSDL National Science Digital Library

This activity allows the user to explore the polar coordinate system. The applet is similar to GraphIt, but instead allows users to explore the representation of a function in the polar coordinate system.

255

NSDL National Science Digital Library

Become familiar with the coordinate plane. Learn the quadrants and how to graph points and read points on a coordinate plane. You are required to do the assignment and take the quiz. The other resources are to help prepare you for the quiz and book assignment. This is a quick review of the lesson.The Coordinate Plane This is a game to practice plotting and reading points.coordinates game *Assignment: Watch Powerpoint 3.3 and fill in your ...

olsen

2010-10-07

256

Run-time Optimization for Grid Workflow Applications

The execution of workflow applications on the Grid is a complex issue because of its dynamic and heterogeneous nature. While the Grid provides good potential for achieving high performance, it also introduces a broad set of unpredictable overheads and possible failures. In this paper we present new methods for scalable and fault tolerant coordination of workflows in dynamic Grid environments,

Rubing Duan; Radu Prodan; Thomas Fahringer

257

A Vertical Grid Module for Baroclinic Models of the Atmosphere

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

John B. Drake; John B

2008-01-01

258

Solving Partial Differential Equations on Overlapping Grids

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.

Henshaw, W D

2008-09-22

259

Grid systems for Earth radiation budget experiment applications

NASA Technical Reports Server (NTRS)

Spatial coordinate transformations are developed for several global grid systems of interest to the Earth Radiation Budget Experiment. The grid boxes are defined in terms of a regional identifier and longitude-latitude indexes. The transformations associate longitude with a particular grid box. The reverse transformations identify the center location of a given grid box. Transformations are given to relate the rotating (Earth-based) grid systems to solar position expressed in an inertial (nonrotating) coordinate system. The FORTRAN implementations of the transformations are given, along with sample input and output.

Brooks, D. R.

1981-01-01

260

An assessment of unstructured grid technology for timely CFD analysis

NASA Technical Reports Server (NTRS)

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.

Kinard, Tom A.; Schabowski, Deanne M.

1995-01-01

261

Coordinate transformation by minimizing correlations between parameters

NASA Technical Reports Server (NTRS)

This investigation was to determine the transformation parameters (three rotations, three translations and a scale factor) between two Cartesian coordinate systems from sets of coordinates given in both systems. The objective was the determination of well separated transformation parameters with reduced correlations between each other, a problem especially relevant when the sets of coordinates are not well distributed. The above objective is achieved by preliminarily determining the three rotational parameters and the scale factor from the respective direction cosines and chord distances (these being independent of the translation parameters) between the common points, and then computing all the seven parameters from a solution in which the rotations and the scale factor are entered as weighted constraints according to their variances and covariances obtained in the preliminary solutions. Numerical tests involving two geodetic reference systems were performed to evaluate the effectiveness of this approach.

Kumar, M.

1972-01-01

262

NASA Astrophysics Data System (ADS)

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

263

We present an unconditionally stable second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive Cartesian grids. We employ quadtree and octree data structures as an efficient means to represent the grid. We use the supra-convergent Poisson solver of [C.-H. Min, F. Gibou, H. Ceniceros, A supra-convergent finite difference scheme for the variable coefficient Poisson equation on

Chohong Min; Frédéric Gibou

2006-01-01

264

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

265

Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver

NASA Astrophysics Data System (ADS)

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.

Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre

2014-06-01

266

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

267

Evolution, development and learning using self-modifying cartesian genetic programming

Self-Modifying Cartesian Genetic Programming (SMCGP) is a form of genetic programming that integrates developmental (self-modifying) features as a genotype-phenotype mapping. This paper asks: Is it possible to evolve a learning algorithm using SMCGP?

Simon Harding; Julian Francis Miller; Wolfgang Banzhaf

2009-01-01

268

A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates

The results of minimizing the action for string-like systems on a simply-connected world sheet are shown to encode the Cartesian components of real null momentum four-vectors into co-ordinates on the world sheet. This identification arises consistently from different approaches to the problem.

David B. Fairlie

2008-05-15

269

Cartesian Compliant Control Strategies for LightWeight, Flexible Joint Robots

The paper focuses on theoretical and experimental aspects related to the Cartesian compliant control of flexible joint robots\\u000a with joint torque measurement. While the Cartesian impedance control for rigid robots, as well as the joint level control\\u000a of flexible joint robots have been studied in detail, their combined implementation on robots with six or seven joints still\\u000a leaves many open

Alin Albu-Schäffer; Gerd Hirzinger

270

NASA Astrophysics Data System (ADS)

A conservative staggered-grid finite difference method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H, and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model (Kuvshinov & Pankratov 1994), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres (Martinec 1998).

Uyeshima, M.; Schultz, A.

2000-03-01

271

NSDL National Science Digital Library

With this interactive Shockwave applet students practice recognizing various types of numbers, including factors, multiples, and prime numbers. Each level presents several grids of numbers, each with a specific rule. Users select all numbers in the grid that satisfy the rule. Level 1 involves parity (odd/even) and multiplication facts of 2, 3, 4, 5 and 10. Level 2 includes multiplication facts up to 10 x 10, primes, and square numbers. Level 3 also covers powers of 2, triangle numbers less than 100, and lower cube numbers. A Key Ideas window explains each type of number. Cross Number puzzle printouts are available for further practice.

2000-01-01

272

A description of the finite differencing used by the B-grid dynamical core

levels may gradually transform to pressure coordinate surfaces in the upper model levels. The horizontal grid has been switched to the Arakawa B-grid (Arakawa and Lamb 1977). This has several advantages over fluxes near the pole of the E-grid has been eliminated in the B-grid. An additional benefit

273

A computer program for converting rectangular coordinates to latitude-longitude coordinates

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)

Rutledge, A.T.

1989-01-01

274

Multiscale geometric modeling of macromolecules I: Cartesian representation

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 polarized curvature, for the prediction of protein binding sites. PMID:24327772

Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei

2013-01-01

275

Multiscale geometric modeling of macromolecules I: Cartesian representation

NASA Astrophysics Data System (ADS)

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 polarized curvature, for the prediction of protein binding sites.

Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2014-01-01

276

Multiscale geometric modeling of macromolecules I: Cartesian representation

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 polarized curvature, for the prediction of protein binding sites.

Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States)] [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States)] [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States)] [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States)] [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States) [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)

2014-01-15

277

Multiscale geometric modeling of macromolecules I: Cartesian representation.

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 polarized curvature, for the prediction of protein binding sites. PMID:24327772

Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei

2014-01-01

278

FUTURE POWER GRID INITIATIVE GridPACK: Grid Parallel Advanced

Operations Center (EIOC), the Pacific Northwest National Laboratory's (PNNL) national electric grid research Grid Initiative (FPGI) will deliver next-generation concepts and tools for grid operation and planning and ensure a more secure, efficient and reliable future grid. Building on the Electricity Infrastructure

279

A Vertical Grid Module for Baroclinic Models of the Atmosphere

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 ?, isentropic ? 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.

Drake, John B [ORNL

2008-04-01

280

Determination of Ship Approach Parameters in the Polar Coordinates System

NASA Astrophysics Data System (ADS)

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

Banachowicz, Andrzej; Wolski, Adam

2014-06-01

281

Geometry optimization of periodic systems using internal coordinates.

An algorithm is proposed for the structural optimization of periodic systems in internal (chemical) coordinates. Internal coordinates may include in addition to the usual bond lengths, bond angles, out-of-plane and dihedral angles, various "lattice internal coordinates" such as cell edge lengths, cell angles, cell volume, etc. The coordinate transformations between Cartesian (or fractional) and internal coordinates are performed by a generalized Wilson B-matrix, which in contrast to the previous formulation by Kudin et al. [J. Chem. Phys. 114, 2919 (2001)] includes the explicit dependence of the lattice parameters on the positions of all unit cell atoms. The performance of the method, including constrained optimizations, is demonstrated on several examples, such as layered and microporous materials (gibbsite and chabazite) as well as the urea molecular crystal. The calculations used energies and forces from the ab initio density functional theory plane wave method in the projector-augmented wave formalism. PMID:15836398

Bucko, Tomás; Hafner, Jürgen; Angyán, János G

2005-03-22

282

NSDL National Science Digital Library

The celestial coordinate system is a projection of earth's coordinate system into the celestial sphere. Being just like Earth's system it contains an "equator", lines of "latitude" and "longitude", and even poles. (Though we don't use the same words for it.) One suggestion one might have would be to just extend the Earth's latitude, longitude, and equator out into the night sky, but the Earth is constantly spinning. For the Celestial coordinates, we have to pick some fixed reference to go by.

David Joiner

283

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

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.

Florinski, V. [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States)] [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States); Guo, X. [Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States)] [Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Balsara, D. S.; Meyer, C. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States)] [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States)

2013-04-01

284

Easing The Calculation Of Bolt-Circle Coordinates

NASA Technical Reports Server (NTRS)

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.

Burley, Richard K.

1995-01-01

285

On deriving nonreflecting boundary conditions in generalized curvilinear coordinates

In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12, 2050-2058, 1990). A thorough Fourier analysis of the linearized Euler equation is performed to determine the eigenvalues and the eigenvectors that are then used to derive the appropriate inflow and outflow boundary conditions. The analysis lacks rigorous proof of the well-posedness in the general case, which is open to investigation (a weak assumption is introduced here to complete the boundary conditions). The boundary conditions derived here are not tested on specific applications.

Adrian Sescu

2015-01-20

286

NASA Astrophysics Data System (ADS)

The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.

Kuczy?ski, Pawe?; Bia?ecki, Ryszard

2014-06-01

287

The NCRC Grid Scheduling Environment

In support of the NCRC, a joint computing center between NOAA and ORNL, a grid-based scheduling infrastructure was designed to allow geographically separate computing resources to be used as production resources in climate and weather research workflows. These workflows require job coordination between the two centers in order to provide a complete workflow of data staging, computation, post-analysis and archival. This paper details the design, implementation and initial production phase of the infrastructure and lessons learned from the process.

Indiviglio, Frank M [ORNL; Maxwell, Don E [ORNL

2011-01-01

288

NSDL National Science Digital Library

This interactive Java applet lets users explore the coordinate plane through the use of a Geoboard. The user places bands on the board where each peg is at an integer coordinate. Once a band has been placed, the applet outputs the perimeter and area of the shape or, if bands are placed as line segments, the applet outputs the distance and slope of the segment.

1999-01-01

289

Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey.

1. We studied the responses of 103 neurons in visual area V4 of anesthetized macaque monkeys to two novel classes of visual stimuli, polar and hyperbolic sinusoidal gratings. We suspected on both theoretical and experimental grounds that these stimuli would be useful for characterizing cells involved in intermediate stages of form analysis. Responses were compared with those obtained with conventional Cartesian sinusoidal gratings. Five independent, quantitative analyses of neural responses were carried out on the entire population of cells. 2. For each cell, responses to the most effective Cartesian, polar, and hyperbolic grating were compared directly. In 18 of 103 cells, the peak response evoked by one stimulus class was significantly different from the peak response evoked by the remaining two classes. Of the remaining 85 cells, 74 had response peaks for the three stimulus classes that were all within a factor of 2 of one another. 3. An information-theoretic analysis of the trial-by-trial responses to each stimulus showed that all but two cells transmitted significant information about the stimulus set as a whole. Comparison of the information transmitted about each stimulus class showed that 23 of 103 cells transmitted a significantly different amount of information about one class than about the remaining two classes. Of the remaining 80 cells, 55 had information transmission rates for the three stimulus classes that were all within a factor of 2 of one another. 4. To identify cells that had orderly tuning profiles in the various stimulus spaces, responses to each stimulus class were fit with a simple Gaussian model. Tuning curves were successfully fit to the data from at least one stimulus class in 98 of 103 cells, and such fits were obtained for at least two classes in 87 cells. Individual neurons showed a wide range of tuning profiles, with response peaks scattered throughout the various stimulus spaces; there were no major differences in the distributions of the widths or positions of tuning curves obtained for the different stimulus classes. 5. Neurons were classified according to their response profiles across the stimulus set with two objective methods, hierarchical cluster analysis and multidimensional scaling. These two analyses produced qualitatively similar results. The most distinct group of cells was highly selective for hyperbolic gratings. The majority of cells fell into one of two groups that were selective for polar gratings: one selective for radial gratings and one selective for concentric or spiral gratings. There was no group whose primary selectivity was for Cartesian gratings. 6. To determine whether cells belonging to identified classes were anatomically clustered, we compared the distribution of classified cells across electrode penetrations with the distribution that would be expected if the cells were distributed randomly. Cells with similar response profiles were often anatomically clustered. 7. A position test was used to determine whether response profiles were sensitive to precise stimulus placement. A subset of Cartesian and non-Cartesian gratings was presented at several positions in and near the receptive field. The test was run on 13 cells from the present study and 28 cells from an earlier study. All cells showed a significant degree of invariance in their selectivity across changes in stimulus position of up to 0.5 classical receptive field diameters. 8. A length and width test was used to determine whether cells preferring non-Cartesian gratings were selective for Cartesian grating length or width. Responses to Cartesian gratings shorter or narrower than the classical receptive field were compared with those obtained with full-field Cartesian and non-Cartesian gratings in 29 cells. Of the four cells that had shown significant preferences for non-Cartesian gratings in the main test, none showed tuning for Cartesian grating length or width that would account for their non-Cartesian res PMID:8899641

Gallant, J L; Connor, C E; Rakshit, S; Lewis, J W; Van Essen, D C

1996-10-01

290

FUTURE POWER GRID INITIATIVE GridOPTICSTM

-generation concepts and tools for grid operation and planning and ensure a more secure, efficient and reliable future grid. Building on the Electricity Infrastructure Operations Center (EIOC), the Pacific NorthwestFUTURE POWER GRID INITIATIVE GridOPTICSTM : A Software Framework for Power System Operations

291

Programming Grid Applications with GRID Superscalar

The aim of GRID superscalar is to reduce the development complexity of Grid applications to the minimum, in such a way that writing an application for a computational Grid may be as easy as writing a sequential application. Our assumption is that Grid applica- tions would be in a lot of cases composed of tasks, most of them repetitive. The

Rosa M. Badia; Jesús Labarta; Raúl Sirvent; Josep M. Pérez; José M. Cela; Rogeli Grima

2003-01-01

292

NASA Astrophysics Data System (ADS)

An immersed boundary methodology to solve the compressible Navier-Stokes equations around complex geometries in Cartesian fluid dynamics solvers is described. The objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts. A standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended. Boundary conditions on the surface are enforced by an approach inspired by analytic continuation. Each fluid field is extended independently, constrained only by the boundary condition associated with that field. Unlike most existing methods, no jump conditions or explicit derivation of them from the boundary conditions are required in this approach. Numerical stiffness that arises when the fluid-solid interface is close to grid points of the mesh is addressed by preconditioning. In addition, the embedded geometry technique is coupled with a stable high-order adaptive discretization that is enabled around the object boundary to enhance resolution. The stencils used to transition the order of accuracy of the discretization are derived using the summation-by-parts technique that ensures stability. Applications to shock reflections, shock-ramp interactions, and supersonic and low-Mach number flows over two- and three-dimensional geometries are presented.

Uddin, H.; Kramer, R. M. J.; Pantano, C.

2014-04-01

293

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.

Sebastian Schunert; Yousry Y. Azmy; Damien Fournier

2011-05-01

294

caGrid 1.0 : an enterprise Grid infrastructure for biomedical research.

To develop software infrastructure that will provide support for discovery, characterization, integrated access, and management of diverse and disparate collections of information sources, analysis methods, and applications in biomedical research. Design: An enterprise Grid software infrastructure, called caGrid version 1.0 (caGrid 1.0), has been developed as the core Grid architecture of the NCI-sponsored cancer Biomedical Informatics Grid (caBIG{trademark}) program. It is designed to support a wide range of use cases in basic, translational, and clinical research, including (1) discovery, (2) integrated and large-scale data analysis, and (3) coordinated study. Measurements: The caGrid is built as a Grid software infrastructure and leverages Grid computing technologies and the Web Services Resource Framework standards. It provides a set of core services, toolkits for the development and deployment of new community provided services, and application programming interfaces for building client applications. Results: The caGrid 1.0 was released to the caBIG community in December 2006. It is built on open source components and caGrid source code is publicly and freely available under a liberal open source license. The core software, associated tools, and documentation can be downloaded from the following URL:

Oster, S.; Langella, S.; Hastings, S.; Ervin, D.; Madduri, R.; Phillips, J.; Kurc, T.; Siebenlist, F.; Covitz, P.; Shanbhag, K.; Foster, I.; Saltz, J.; Mathematics and Computer Science; The Ohio State Univ.; National Cancer Inst. Centerfor Bioinformatics; SemanticBits

2008-03-01

295

NSDL National Science Digital Library

Commodity Grid (CoG) Kits allow Grid users, Grid application developers, and Grid administrators to use, program, and administer Grids from a higher-level framework. The Java and Python CoG Kits are good examples. These kits allow for easy and rapid Grid application development. They encourage collaborative code reuse and avoid the duplication of effort among problem solving environments, science portals, Grid middleware, and collaboratory pilots.

Gregor von Laszewski

296

NASA Technical Reports Server (NTRS)

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

297

A Moving Grid Capability for NPARC

NASA Technical Reports Server (NTRS)

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.

Slater, John W.

1998-01-01

298

Random subspaces for encryption based on a private shared Cartesian frame

A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities.

Bartlett, Stephen D. [School of Physics, University of Sydney, New South Wales 2006 (Australia); Hayden, Patrick [School of Computer Science, McGill University, Montreal (Canada); Spekkens, Robert W. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada)

2005-11-15

299

GridMan: A grid manipulation system

NASA Technical Reports Server (NTRS)

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.

Eiseman, Peter R.; Wang, Zhu

1992-01-01

300

An analysis of a collision situation in polar coordinates

NASA Astrophysics Data System (ADS)

Avoiding collisions with other vessels and natural or artificial navigational obstructions is an important element of navigation safety. This problem is automatically solved in anti-collision ARPA systems, or geometrically as radar plots. In both cases we use radar measurements: bearing (or relative bearing) on the target position and distance, both naturally localized in the polar coordinates system with the origin at the radar antenna. We convert original measurements to an ortho-Cartesian coordinate system. Then we solve a collision avoiding problem in the new system, and then transform the results to the polar coordinate system. This article presents a method for an analysis of a collision situation performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation.

Wolski, Adam; Banachowicz, Andrzej

2014-05-01

301

ERIC Educational Resources Information Center

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…

CLEAVES, PAUL C.; AND OTHERS

302

Numerical simulations of acoustic fields on boundary-fitted grids

In this paper we propose a numerical method for the simulation of acoustic fields, in presence of an obstacle in the physical domain, by finite difference solution of a two-dimensional differential model on boundary-fitted grids. The computational process gathers the elliptic grid generation, the linear Euler equations in curvilinear coordinates, the associated bicharacteristic equation and a fully explicit finite difference

Maria M. Cerimele; Francesca Pistella; Rosa Maria Spitaleri

2008-01-01

303

Metadata for Managing Grid Resources in Data Mining Applications

The Grid is an infrastructure for resource sharing and coordinated use of those resources in dynamic heteroge- neous distributed environments. The effective use of a Grid requires the definition of metadata for managing the heterogeneity of involved resources that include computers, data, network facilities, and software tools provided by different organizations. Metadata management becomes a key issue when complex applications,

Carlo Mastroianni; Domenico Talia; Paolo Trunfio

2004-01-01

304

A review on distributed energy resources and MicroGrid

The distributed energy resources (DER) comprise several technologies, such as diesel engines, micro turbines, fuel cells, photovoltaic, small wind turbines, etc. The coordinated operation and control of DER together with controllable loads and storage devices, such as flywheels, energy capacitors and batteries are central to the concept of MicroGrid (MG). MG can operate interconnected to the main distribution grid, or

Huang Jiayi; Jiang Chuanwen; Xu Rong

2008-01-01

305

Automatic Structured Grid Generation by an Approximate Factorisation Algorithm

Abstract A procedure for automatic numerical generation of a static structured grid system with coordinate lines coincident with all boundaries of a general two-dimensional region containing a body of arbitrary shape is presented. Solving a system of two nonlinear elliptic partial differential equations in the computational domain, using a finite difference method, generates the grid. The solution procedure incorporates the

Eddie Ly; Daniel Norrison

2006-01-01

306

NSDL National Science Digital Library

* Overview of grid computing, * Basic Internet technologies: IP, HTTP, UDP, TCP, * Security, * Web Services and Enabling technologies, * Grid service concepts,* Resource Management, * Discovery and Information Services, * Parallel programming techniques suitable for a Grid, * Cluster computing and basic message passing techniques

Amy Apon

307

New approach to gridding using regularization and estimation theory.

When sampling under time-varying gradients, data is acquired over a non-equally spaced grid in k-space. The most computationally efficient method of reconstruction is first to interpolate the data onto a Cartesian grid, enabling the subsequent use of the inverse fast Fourier transform (IFFT). The most commonly used interpolation technique is called gridding, and is comprised of four steps: precompensation, convolution with a Kaiser-Bessel window, IFFT, and postcompensation. Recently, the author introduced a new gridding method called Block Uniform ReSampling (BURS), which is both optimal and efficient. The interpolation coefficients are computed by solving a set of linear equations using singular value decomposition (SVD). BURS requires neither the pre- nor the postcompensation steps, and resamples onto an n x n grid rather than the 2n x 2n matrix required by conventional gridding. This significantly decreases the computational complexity. Several authors have reported that although the BURS algorithm is very accurate, it is also sensitive to noise. As a consequence, even in the presence of a low level of measurement noise, the resulting image is often highly contaminated with noise. In this work, the origin of the noise sensitivity is traced back to the potentially ill-posed matrix inversion performed by BURS. Two approaches to the solution are presented. The first uses regularization theory to stabilize the inversion process. The second formulates the interpolation as an estimation problem, and employs estimation theory for the solution. The new algorithm, called rBURS, contains a regularization parameter, which is used to trade off the accuracy of the result against the signal-to-noise ratio (SNR). The results of the new method are compared with those obtained using conventional gridding via simulations. For the SNR performance of conventional gridding, it is shown that the rBURS algorithm exhibits equal or better accuracy. This is achieved at a decreased computational cost compared to conventional gridding. PMID:12111946

Rosenfeld, Daniel

2002-07-01

308

A Multi-chromosome Approach to Standard and Embedded Cartesian Genetic Programming

A Multi-chromosome Approach to Standard and Embedded Cartesian Genetic Programming Genetic in the form of modules. In this paper, we introduce for the first time a new multi-chromosome approach to CGP also propose a multi-chromosome evolutionary strategy which selects the best chromosomes from

Fernandez, Thomas

309

Self Modifying Cartesian Genetic Programming (SMCGP) aims to be a general purpose form of developmental genetic programming. The evolved programs are iterated thus allowing an infinite sequence of phenotypes (programs) to be obtained from a single evolved genotype. In previous work this approach has already shown that it is possible to obtain mathematically provable general solutions to certain problems. We

Simon Harding; Julian F. Miller; Wolfgang Banzhaf

2010-01-01

310

Investigating the Effects of Density and Volume of a Cartesian Diver

NSDL National Science Digital Library

This activity is an inquiry investigation where students gather data on why the Cartesian diver sinks or floats. They then develop a new question and then conduct a new investigation by changing one variable and repeat the altered experiment and record their conclusions.

Lee Anne Garhofer Ames Elementary School St. Paul, MN 55106

311

A Cartesian Robot for RFID Signal Distribution Model Verification Aliasgar Kutiyanawala instrumentation cost, i.e., a minimum number of surface-embedded passive RFID transponders. Our previous results were based on the assumption that the signal distribution model of an individual RFID transponder can

Kulyukin, Vladimir

312

An accurate cartesian method for incompress-ible flows with moving boundaries

are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method the advantage of being sharp, as opposed to the first one. The Ghost Cell method is inspired by this last approach since ghost-cell values are introduced based on an interpolation of neighboring fluid cells

Boyer, Edmond

313

Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion

ERIC Educational Resources Information Center

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…

Lelwica, Michelle Mary

2009-01-01

314

Juan Huarte de San Juan in cartesian and modern psycholinguistics: an encounter with Noam Chomsky

This article presents Noam Chomsky's standpoint on the relevance of Juan Huarte de San Juan's work Examen de ingenios para las ciencias (The Examination of Men's Wits, 1575-1594) for Cartesian lin- guistics and cognitive science. Huartian conceptions relevant to psycholinguistics and to Chomskian generativism include: (a) the generative quality of human understanding, (b) qualitative differences between human and animal capacity,

Javier Virués Ortega

2005-01-01

315

PHYSICS OF FLUIDS 25, 044105 (2013) Onset of buoyancy-driven convection in Cartesian

PHYSICS OF FLUIDS 25, 044105 (2013) Onset of buoyancy-driven convection in Cartesian the onset of buoyancy-driven convection relevant to subsurface carbon dioxide sequestration in confined and may help with understanding the onset of buoyancy-driven convection in real systems where lateral

Firoozabadi, Abbas

2013-01-01

316

NSDL National Science Digital Library

5th Grade Math State core Standard 3, Objective 2a: Locate points defined by ordered pairs of integers. Congratulations for earning a game day in the computer lab! Remember that even though it is game day I expect you to stay on task and follow directions. We have been talking in math about graphing integers on the coordinate plane. The games for today require that ...

Miss Zilles

2007-10-31

317

Embedding planar graphs on the grid

We show that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-2 grid. This embedding is computable in time O(n). A nice feature of the vertex-coordinates is that they have a purely combinatorial meaning.

Walter Schnyder

1990-01-01

318

A policy-driven multi-agent system for OGSA-compliant grid control

The emergence and the development of OGSA compliant grid provide powerful means for the integration and interaction of applications (grid services) within a virtual organization (VO). However, it is still a challenge to control the composition, transaction, and coordination, of grid services, according to the dynamic business requirements of a VO. Based on the policy-based management and autonomous intelligent agents,

Bei-shui Liao; Ji Gao; Jun Hu; Jiu-jun Chen

2004-01-01

319

Evaluation of geometric conservation law using pressure-based fluid solver and moving grid technique

The geometric conservation law (GCL) is an important concept for moving grid techniques because it directly regulates the treatments of the fluid flow and grid movement. With the grid movement at every time instant, the Jacobian, associated with the volume of each element in curvilinear co-ordinates, needs to be updated in a conservative manner. In this study, alternative GCL schemes

Ramji Kamakoti; Wei Shyy

2004-01-01

320

On constructing three-dimensional overlapping grids with CMPGRD

NASA Technical Reports Server (NTRS)

Techniques for the construction of three-dimensional composite overlapping grids, using the grid construction program CMPGRD, are described. The overlapping approach can be used to generate grids for regions of complicated geometry. The grids can be constructed to be smooth and free from coordinate singularities. The ability to create smooth grids for complicated regions is an important first step towards the accurate numerical solution of partial differential equations. The creation of grids for surfaces defined by cross-sections such as an airplane wing is described. A method for integrating the patched surfaces generated by a computer aided design (CAD) package with the CMPGRD program is described. Additionally, the creation of grids in regions where surfaces intersect is described.

Henshaw, William D.; Chesshire, Geoffrey; Henderson, Michael E.

1992-01-01

321

Parallel Grid Manipulations in Earth Science Calculations

NASA Technical Reports Server (NTRS)

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 sparse interpolation with little data locality between the physical lat-lon grid and a pole rotated computational grid- can be solved efficiently and at the GFlop/s rates needed to solve tomorrow's high resolution earth science models. In the subsequent presentation we will discuss the design and implementation of PILGRIM as well as a number of the problems it is required to solve. Some conclusions will be drawn about the potential performance of the overall earth science models on the supercomputer platforms foreseen for these problems.

Sawyer, W.; Lucchesi, R.; daSilva, A.; Takacs, L. L.

1999-01-01

322

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 model 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 optimizat...

Blanc, Emilie; Lombard, Bruno

2015-01-01

323

Wavelets in curvilinear coordinate quantum calculations: H2+ electronic states

NASA Astrophysics Data System (ADS)

Multiscale wavelets are used to solve the quantum eigenvalue equations for the hydrogen molecular ion H2+ in the Born-Oppenheimer approximation. Normally restricted to Cartesian systems, "wavelets on the interval" (a normal wavelet family augmented by special edge functions) have recently been applied to such boundary value problems as the hydrogen atom in spherical polar coordinates [J. Mackey, J. L. Kinsey, and B. R. Johnson, J. Comp. Phys. 168, 356 (2001)]. These methods are extended here to ground and excited electronic states of the simplest molecule, for which the electronic Hamiltonian is separable in confocal elliptic coordinates. The set of curvilinear coordinate quantum systems for which wavelet bases have been applied is thus enlarged.

Maloney, A.; Kinsey, James L.; Johnson, Bruce R.

2002-08-01

324

Computer coordination of limb motion for a three-legged walking robot

NASA Technical Reports Server (NTRS)

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.

Klein, C. A.; Patterson, M. R.

1980-01-01

325

NASA Technical Reports Server (NTRS)

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.

Kumar, D.

1980-01-01

326

Third-order superintegrable systems separable in parabolic coordinates

In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that all such systems are multi-separable and so admit two second-order integrals. The third-order integral is their Lie or Poisson commutator. We discuss how this situation is different from the Cartesian and polar cases where new potentials were discovered which are not multi-separable and which are expressed in terms of Painlev\\'e transcendents or elliptic functions.

I. Popper; S. Post; P. Winternitz

2012-04-08

327

Advancing Smart Grid Interoperability and Implementing NIST's Interoperability Roadmap

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.

Basso,T.; DeBlasio, R.

2010-04-01

328

NASA Astrophysics Data System (ADS)

Among the many areas of research that Professor Kawahara has been active in is the subject of open boundaries in which linear time-dependent dispersive waves are considered in an unbounded domain. The infinite domain is truncated via an artificial boundary B on which an open boundary condition (OBC) is imposed. In this paper, Higdon OBCs and Hagstrom-Hariharan (HH) OBCs are considered. Higdon-type conditions, originally implemented as low-order OBCs, are made accessible for any desired order via a new scheme. The higher-order Higdon OBC is then reformulated using auxiliary variables and made compatible for use with finite element (FE) methods. Methodologies for selecting Higdon parameters are also proposed. The performances of these schemes are demonstrated in two numerical examples. This is followed by a discussion of the HH OBC, which is applicable to non-dispersive media on cylindrical and spherical geometries. The paper extends this OBC to the "slightly dispersive" case.

van Joolen*, Vince; Givoli, Dan; Neta, Beny

2003-07-01

329

Mathematical model of coordinate transformations for 3D Depth-of-field collection system

Calculating the Cartesian coordinate is the first step of image reconstruct based on primitive information from laser scanner. A novel 3D Depth-of-field information collection system in this article is consisted of tow 2D laser scanners and a servo-actuates rotating mirror assembly. The system has a much higher detecting precision than others which drive 2D laser scanner to rotate to get

Lixia Rong; Weihai Chen; Shouqian Yu; Weiyang Song

2008-01-01

330

Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction

NASA Astrophysics Data System (ADS)

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 multidimensional 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 the previous designs [1] 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.

Yang, Zhili; Jacob, Mathews

2014-05-01

331

On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design

NASA Technical Reports Server (NTRS)

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.

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2004-01-01

332

Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry

NASA Technical Reports Server (NTRS)

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.

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2003-01-01

333

Making a fun Cartesian diver: a simple project to engage kinaesthetic learners

NASA Astrophysics Data System (ADS)

Students in the normal technical stream are generally less academically inclined. Teaching physics to them can be a challenge. A possible way to engage such kinaesthetic learners is to encourage them to fabricate physics-based toys. The activity described in this article shows how a group of three students were able to come up with a creative version of a Cartesian diver that incorporates game elements and physics principles, as well as uses only recyclable materials.

Amir, Nazir; Subramaniam, R.

2007-09-01

334

Surface mesh generation for dirty geometries by the Cartesian shrink-wrapping technique

A Cartesian shrink-wrapping technique has been investigated in this study to automatically generate triangular surface meshes\\u000a for 3D dirty geometries. The geometries dealt in this paper are defined by a faceted representation and have flaws such as\\u000a non-conforming edges, gaps, and overlaps. The proposed technique addresses a way of constructing triangular surface meshes\\u000a for upstream fluid simulations in design processes

Y. K. Lee; Chin K. Lim; Hamid Ghazialam; Harsh Vardhan; Erling Eklund

2010-01-01

335

Cartesian path control of a two-degree-of-freedom robot manipulator

NASA Technical Reports Server (NTRS)

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.

Nguyen, Charles C.; Pooran, Farhad J.

1988-01-01

336

A Cartesian feedback-trained digital predistortion system for RF power amplifier linearization offers many advantages with its combination of two different linearization techniques. This thesis describes such a system, ...

Huang, Jeffrey B

2006-01-01

337

Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method

This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel algorithm for accurate evaluation of the many-particle friction matrix in this system--no such algorithm has been available so far. Our approach involves expanding the fluid velocity field into spherical and Cartesian fundamental sets of Stokes flows. The interaction of the fluid with the particles is described using the spherical basis fields; the flow scattered with the walls is expressed in terms of the Cartesian fundamental solutions. At the core of our method are transformation relations between the spherical and Cartesian basis sets. These transformations allow us to describe the flow field in a system that involves both the walls and particles. We used our accurate numerical results to test the single-wall superposition approximation for the hydrodynamic friction matrix. The approximation yields fair results for quantities dominated by single particle contributions, but it fails to describe collective phenomena, such as a large transverse resistance coefficient for linear arrays of spheres.

S. Bhattacharya; J. Blawzdziewicz; E. Wajnryb

2005-04-27

338

NASA Astrophysics Data System (ADS)

Large-eddy simulation (LES) is a popular technique for studying the atmospheric boundary layer (ABL) on small domains. ABL simulations often use structured nested grids to scale the solution from the mesoscale to local scales, but using LES on non-uniform grids generates additional errors. The grid refinement interfaces in nested grids can reflect resolved energy and create interpolation errors. This study investigates the use of explicit filtering and reconstruction to mitigate grid interface errors in LES of a neutral boundary layer. The domain is split in the streamwise direction into two equally sized structured grids, one fine and one coarse, with periodic boundaries in the streamwise and spanwise directions. This simply nested, idealized test case allows observation of the effects of the grid interfaces. Explicit filtering is found to reduce accumulation of resolved energy at the fine-to-coarse interface and improve the shape of coherent structures, compared to basic LES. Additional reconstruction of the subfilter velocity is shown to further the improvements of explicit filtering. These results inform the use of LES to simulate the ABL on block-structured non-uniform grids, from typical nested grids to more complex cartesian AMR grids for urban boundary layers.

Goodfriend, L.; Chow, F. K.; Vanella, M.; Balaras, E.

2013-12-01

339

Visual SLAM Using Variance Grid Maps

NASA Technical Reports Server (NTRS)

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 maps are much better for representing the structure of vegetated or rocky terrain.

Howard, Andrew B.; Marks, Tim K.

2011-01-01

340

NASA Astrophysics Data System (ADS)

In the absence of symmetry assumptions most numerical relativity simulations adopt Cartesian coordinates. While Cartesian coordinates have some desirable properties, spherical polar coordinates appear better suited for certain applications, including gravitational collapse and supernova simulations. Development of numerical relativity codes in spherical polar coordinates has been hampered by the need to handle the coordinate singularities at the origin and on the axis, for example by careful regularization of the appropriate variables. Assuming spherical symmetry and adopting a covariant version of the Baumgarte-Shapiro-Shibata-Nakamura equations, Montero and Cordero-Carrión recently demonstrated that such a regularization is not necessary when a partially implicit Runge-Kutta method is used for the time evolution of the gravitational fields. Here we report on an implementation of the Baumgarte-Shapiro-Shibata-Nakamura equations in spherical polar coordinates without any symmetry assumptions. Using a partially implicit Runge-Kutta method we obtain stable simulations in three spatial dimensions without the need to regularize the origin or the axis. We perform and discuss a number of tests to assess the stability, accuracy and convergence of the code, namely weak gravitational waves, “hydro-without-hydro” evolutions of spherical and rotating relativistic stars in equilibrium, and single black holes.

Baumgarte, Thomas W.; Montero, Pedro J.; Cordero-Carrión, Isabel; Müller, Ewald

2013-02-01

341

NSDL National Science Digital Library

Students learn and discuss the advantages and disadvantages of renewable and non-renewable energy sources. They also learn about our nation's electric power grid and what it means for a residential home to be "off the grid."

Integrated Teaching and Learning Program,

342

Grid Computing Portals Lecture

NSDL National Science Digital Library

Grid Computing Lecture~~Grid portals: purpose, application-based portals, historical examples, GPDK, Gridport, etc., OGCE2/gridsphere portal, portal implementation, portlets, JSR 168, portlet source and deployment files.

Dr. Clayton Ferner

2011-07-05

343

NASA Astrophysics Data System (ADS)

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 Ż . 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 (? and ?) 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 mechanical energy equation indicate correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associated with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates greater isotropy than regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

Hamilton, Nicholas; Cal, Raúl Bayoán

2015-01-01

344

NASA Technical Reports Server (NTRS)

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.

Hinke, Thomas

2003-01-01

345

Grid2003 and Open Science Grid Ruth Pordes

: "Our" Experiments, Physics Grid Projects, Open Science Grid mid2004->2005: Plans: Grid with Europe Partnership with Condor Project in many dimensions Outline #12;Grid2003 - Project, Grid3 and Condor Week A Joint Project to Build a Significantly Scaled Shared Grid giving Science Benefit across

Wisconsin at Madison, University of

346

Grid Computing Lecture - Globus 4.0 grid services

NSDL National Science Digital Library

Grid Computing Lecture~~Globus 4.0 grid services: Using Web services for grid computing, stateful web services, Grid computing standards, Open Grid Services Architecture (OGSA), Web Services Resource Framework (WSRF), programming GT 4.0 grid services, GT 4.0 container.

Dr. Clayton Ferner

2011-07-05

347

NASA Technical Reports Server (NTRS)

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.

Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert

2005-01-01

348

This article describes a recently proposed standard, ISEA discrete global grids, for gridding information on the surface of the earth. The acronym ISEA stands for icosahedral Snyder equal area. The grid cells not only have equal areas, they are hexagons when projected onto an icosahedron! Being an advocate of hexagon binning, and corresponding graphics, my (Dan) enthu-siasm is such that

Dan Carr; Ralph Kahn; Kevin Sahr; Tony Olsen

349

Grid welding fixture for a spacer grid

A modular grid welding fixture for a spacer grid that facilitates full grid laser welding of a spacer grid in one setup is disclosed. The modular design allows for partial implementation of each weld type. A base plate is used for mounting to the positioning/rotational plate of the welding system. A removable sub-plate received in the base plate is used to position the grid strips for proper location for welding. A top fixture plate is aligned with the base plate and provides for mounting of a second sub-plate if required. Side plates with spring loaded pressure pads that are hinged to the top fixture plate apply uniform pressure to the outer grid strips during processing. The base plate, top plate, side plate, and pressure pads are provided with a plurality of through holes to allow access of the laser beam for welding. Corner clips are used to insure contact of the overlapping sections of the outer grid strips for proper corner welding. 4 figs.

Anderson, M.W.; Whitt, J.S.

1995-03-14

350

Characterising a grid site's traffic

Grid computing has been widely adopted for intensive high performance computing. Since grid resources are distributed over complex large-scale infrastructures, understanding grid site data traffic behaviour is important for efficient resource utilisation, performance optimisation, and the design of future grid sites as well as traffic-aware grid applications. In this paper, we study and analyse the traffic generated at a grid

Tiejun Ma; Yehia El-khatib; Michael Mackay; Christopher Edwards

2010-01-01

351

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.

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

352

Users manual for coordinate generation code CRDSRA

NASA Technical Reports Server (NTRS)

Generation of a viable coordinate system represents an important component of an isolated airfoil Navier-Stokes calculation. The manual describes a computer code for generation of such a coordinate system. The coordinate system is a general nonorthogonal one in which high resolution normal to the airfoil is obtained in the vicinity of the airfoil surface, and high resolution along the airfoil surface is obtained in the vicinity of the airfoil leading edge. The method of generation is a constructive technique which leads to a C type coordinate grid. The method of construction as well as input and output definitions are contained herein. The computer code itself as well as a sample output is being submitted to COSMIC.

Shamroth, S. J.

1985-01-01

353

Navigation in Grid Space with the NAS Grid Benchmarks

NASA Technical Reports Server (NTRS)

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.

Frumkin, Michael; Hood, Robert; Biegel, Bryan A. (Technical Monitor)

2002-01-01

354

A complete grid G/sub m,n/ is a graph having m x n pertices that are connected to form a rectangular lattice in the plane, i.e., all edges of G/sub m,n/ connect vertices along horizontal or vertical lines. A grid is a subgraph of a complete grid. As an illustration, complete grids describe the basic pattern of streets in most cities. This paper examines the existence of Hamiltonian cycles in complete grids and complete grids with one or two vertices removed. It is determined for most values of m,n greater than or equal to 1, which grids G/sub m,n/ - (u) and G/sub m,n/ - (u,v) are Hamiltonian. 12 figures. (RWR)

Hedetniemi, S. M.; Hedetniemi, S. T.; Slater, P. J.

1980-01-01

355

Collaboration in a Wireless Grid Innovation Testbed by Virtual Consortium

NASA Astrophysics Data System (ADS)

This paper describes the formation of the Wireless Grid Innovation Testbed (WGiT) coordinated by a virtual consortium involving academic and non-academic entities. Syracuse University and Virginia Tech are primary university partners with several other academic, government, and corporate partners. Objectives include: 1) coordinating knowledge sharing, 2) defining key parameters for wireless grids network applications, 3) dynamically connecting wired and wireless devices, content and users, 4) linking to VT-CORNET, Virginia Tech Cognitive Radio Network Testbed, 5) forming ad hoc networks or grids of mobile and fixed devices without a dedicated server, 6) deepening understanding of wireless grid application, device, network, user and market behavior through academic, trade and popular publications including online media, 7) identifying policy that may enable evaluated innovations to enter US and international markets and 8) implementation and evaluation of the international virtual collaborative process.

Treglia, Joseph; Ramnarine-Rieks, Angela; McKnight, Lee

356

Relationship between Astrometric and Theoretical Coordinates of Planetary Satellites

NASA Astrophysics Data System (ADS)

A step of calculations is considered at which the astrometric angular coordinates of planetary satellites are determined from their Cartesian coordinates with the aim of computing the efemerides or refining the parameters of motion of natural planetary satellites on the basis of observations. Usually, approximate formulas derived many years ago are used at this stage. These formulas are not adequate for the precision of modern observations. Accurate formulas based on geometrical analyses are proposed in this paper. The process of formation of satellite images in the photoreceivers of telescopes is considered. Time differences in light propagation from different satellites of the planet to the observer are taken into account. Estimates are given for the errors of similar approximate formulas used in previous papers aimed at refining the parameters of motion of natural planetary satellites from observations.

Emel'Yanov, N. V.

357

Trends in life science grid: from computing grid to knowledge grid

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

Akihiko Konagaya

2006-01-01

358

NASA Astrophysics Data System (ADS)

A numerical algorithm for computing the runup of a solitary tsunami wave in the case of complex shoreline topography is proposed. The algorithm involves the construction of coordinate mappings that transform a uniform rectangular grid over a reference computational domain into a grid over a physical domain with mesh refinement near the shoreline. The application of such coordinate mappings makes it possible to substantially reduce the number of grid points and save computation time. The mathematical model is based on the shallow water equations, and the problem is solved using the large particle method. An actual example is used to illustrate the computation of a curvilinear grid and the inundation area configuration.

Kofanov, A. V.; Liseikin, V. D.; Rychkov, A. D.

2015-01-01

359

Density- and wavefunction-normalized Cartesian spherical harmonics for l ? 20.

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] 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 [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ? 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ? 7 (Paturle & Coppens, 1988). 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 (Paturle & Coppens, 1988) method in the Wolfram Mathematica software 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. PMID:25727874

Michael, J Robert; Volkov, Anatoliy

2015-03-01

360

NASA Astrophysics Data System (ADS)

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.

Kemp, Martin

1998-08-01

361

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. PMID:18986706

Fara, Patricia

2008-12-01

362

NSDL National Science Digital Library

This activity gives students a hands-on look at the effects of increased water pressure and shows them how submarines work. Using a balloon and plastic water bottle, students create a neutrally buoyant diver. Then they squeeze the bottle to see how increased pressure compresses the balloon, making it heavier and causing it to sink. The activity includes an extension that has students further explore how animals use their swim bladders to dive and rise. Students can find out with a balloon and a bottle of water how a submarine, which is buoyant to start with, becomes heavier and dives down into the water.

363

NSDL National Science Digital Library

In this demonstration, learners observe the effects of density and pressure. A "diver" constructed out of a piece of straw and Blu-Tack will bob inside a bottle filled with water. This highly visual demonstration works best when learners can try moving the diver up and down themselves. This activity can also be related to how animals, like whales, dive in deep waters. This activity guide includes a helpful video that demonstrates each step of the demonstration.

2012-06-26

364

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 with 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 amount to 36! ? 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 are presented. 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

365

NASA Astrophysics Data System (ADS)

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.

Zimmerman, Paul M.

2013-05-01

366

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. PMID:23676024

Zimmerman, Paul M

2013-05-14

367

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

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

Omar, Mohamed A.

2014-01-01

368

System Wide Joint Position Sensor Fault Tolerance in Robot Systems Using Cartesian Accelerometers

NASA Technical Reports Server (NTRS)

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.

Aldridge, Hal A.; Juang, Jer-Nan

1997-01-01

369

Parallel adaptive Cartesian upwind methods for shock-driven multiphysics simulation

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.

Deiterding, Ralf [ORNL] [ORNL

2011-01-01

370

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

NASA Technical Reports Server (NTRS)

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. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian; Aftosmis,Michael J.

2006-01-01

371

The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges

In this paper using the apparatus of the Clifford bundle formalism we show how straightforwardly solve in Minkowski spacetime the Dirac-Hestenes equation -- which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation -- by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that contrary to what is expected at a first sight, the solution of the DHE in both gauges has exactly the same mathematical difficulty.

Roldao da Rocha; Waldyr A. Rodrigues Jr

2006-07-04

372

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2003-01-01

373

Securing smart grid technology

NASA Astrophysics Data System (ADS)

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.

Chaitanya Krishna, E.; Kosaleswara Reddy, T.; Reddy, M. YogaTeja; Reddy G. M., Sreerama; Madhusudhan, E.; AlMuhteb, Sulaiman

2013-03-01

374

Grid enabled Service Support Environment - SSE Grid

NASA Astrophysics Data System (ADS)

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 efficiently. A workflow can be built and submitted for execution on multiple loosely coupled Grids (e.g. at VITO and at ESRIN). It is ensured that the data are processed where they are located. For this purpose the project aims to upgrade the Service Support Environment (SSE) to integrate multi-Grid processing services to be used by the PI for the systematic processing or reprocessing of EO data. For both scenarios described above, two processing modes will be available. In near real-time (NRT), or 'subscription mode', processing, the execution of a workflow is started but suspended a certain step where the workflow waits until certain data are present on the Grid. As soon as the data become available from the sensors, the execution is resumed automatically. In 'historical mode' it is assumed that the data are already present. An other main objective of the SSEGrid project is to propose new or amended versions of 'Web Processing Service' protocols that may be able to bridge geo-spatial Service Oriented Architectures and Open Grid Services Architectures. In this context we will propose the Grid Web Processing Service as an extension of the OGC WPS service to allow for the dynamic deployment of user processes (workflows or Grid processes) and auxiliary data, for the discovery of user auxiliary data, for the query of process status and process audit (execution trace, log file) and for the notification of process completion or failure.

Goor, Erwin; Paepen, Martine

2010-05-01

375

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. PMID:23126691

Hollman, David S; Schaefer, Henry F

2012-10-28

376

SAGE - MULTIDIMENSIONAL SELF-ADAPTIVE GRID CODE

NASA Technical Reports Server (NTRS)

SAGE, Self Adaptive Grid codE, is a flexible tool for adapting and restructuring both 2D and 3D grids. Solution-adaptive grid methods are useful tools for efficient and accurate flow predictions. In supersonic and hypersonic flows, strong gradient regions such as shocks, contact discontinuities, shear layers, etc., require careful distribution of grid points to minimize grid error and produce accurate flow-field predictions. SAGE helps the user obtain more accurate solutions by intelligently redistributing (i.e. adapting) the original grid points based on an initial or interim flow-field solution. The user then computes a new solution using the adapted grid as input to the flow solver. The adaptive-grid methodology poses the problem in an algebraic, unidirectional manner for multi-dimensional adaptations. The procedure is analogous to applying tension and torsion spring forces proportional to the local flow gradient at every grid point and finding the equilibrium position of the resulting system of grid points. The multi-dimensional problem of grid adaption is split into a series of one-dimensional problems along the computational coordinate lines. The reduced one dimensional problem then requires a tridiagonal solver to find the location of grid points along a coordinate line. Multi-directional adaption is achieved by the sequential application of the method in each coordinate direction. The tension forces direct the redistribution of points to the strong gradient region. To maintain smoothness and a measure of orthogonality of grid lines, torsional forces are introduced that relate information between the family of lines adjacent to one another. The smoothness and orthogonality constraints are direction-dependent, since they relate only the coordinate lines that are being adapted to the neighboring lines that have already been adapted. Therefore the solutions are non-unique and depend on the order and direction of adaption. Non-uniqueness of the adapted grid is acceptable since it makes possible an overall and local error reduction through grid redistribution. SAGE includes the ability to modify the adaption techniques in boundary regions, which substantially improves the flexibility of the adaptive scheme. The vectorial approach used in the analysis also provides flexibility. The user has complete choice of adaption direction and order of sequential adaptions without concern for the computational data structure. Multiple passes are available with no restraint on stepping directions; for each adaptive pass the user can choose a completely new set of adaptive parameters. This facility, combined with the capability of edge boundary control, enables the code to individually adapt multi-dimensional multiple grids. Zonal grids can be adapted while maintaining continuity along the common boundaries. For patched grids, the multiple-pass capability enables complete adaption. SAGE is written in FORTRAN 77 and is intended to be machine independent; however, it requires a FORTRAN compiler which supports NAMELIST input. It has been successfully implemented on Sun series computers, SGI IRIS's, DEC MicroVAX computers, HP series computers, the Cray YMP, and IBM PC compatibles. Source code is provided, but no sample input and output files are provided. The code reads three datafiles: one that contains the initial grid coordinates (x,y,z), one that contains corresponding flow-field variables, and one that contains the user control parameters. It is assumed that the first two datasets are formatted as defined in the plotting software package PLOT3D. Several machine versions of PLOT3D are available from COSMIC. The amount of main memory is dependent on the size of the matrix. The standard distribution medium for SAGE is a 5.25 inch 360K MS-DOS format diskette. It is also available on a .25 inch streaming magnetic tape cartridge in UNIX tar format or on a 9-track 1600 BPI ASCII CARD IMAGE format magnetic tape. SAGE was developed in 1989, first released as a 2D version in 1991 and updated to 3D in 1993.

Davies, C. B.

1994-01-01

377

NASA Astrophysics Data System (ADS)

Historically, cellular automata (CA) is a discrete dynamical mathematical structure defined on spatial grid. Research on cellular automata system (CAS) has focused on rule sets and initial condition and has not discussed its adjacency. Thus, the main focus of our study is the effect of adjacency on CA behavior. This paper is to compare rectangular grids with hexagonal grids on their characteristics, strengths and weaknesses. They have great influence on modeling effects and other applications including the role of nearest neighborhood in experimental design. Our researches present that rectangular and hexagonal grids have different characteristics. They are adapted to distinct aspects, and the regular rectangular or square grid is used more often than the hexagonal grid. But their relative merits have not been widely discussed. The rectangular grid is generally preferred because of its symmetry, especially in orthogonal co-ordinate system and the frequent use of raster from Geographic Information System (GIS). However, in terms of complex terrain, uncertain and multidirectional region, we have preferred hexagonal grids and methods to facilitate and simplify the problem. Hexagonal grids can overcome directional warp and have some unique characteristics. For example, hexagonal grids have a simpler and more symmetric nearest neighborhood, which avoids the ambiguities of the rectangular grids. Movement paths or connectivity, the most compact arrangement of pixels, make hexagonal appear great dominance in the process of modeling and analysis. The selection of an appropriate grid should be based on the requirements and objectives of the application. We use rectangular and hexagonal grids respectively for developing city model. At the same time we make use of remote sensing images and acquire 2002 and 2005 land state of Wuhan. On the base of city land state in 2002, we make use of CA to simulate reasonable form of city in 2005. Hereby, these results provide a proof of concept for hexagonal which has great dominance.

Zhai, Xiaofang; Zhu, Xinyan; Xiao, Zhifeng; Weng, Jie

2009-10-01

378

NSDL National Science Digital Library

Hosted by IBM, the World Community Grid is an ambitious public-computing network developed to bolster humanitarian research around the world. The Grid gains its power through a vast network of computers, all contributing small pieces to large research projects while they are idle. At present the Grid is supporting the Institute for Systems Biology's Human Proteome Folding Project, which will ultimately contribute to disease prevention by developing a greater understanding of the shapes of human proteins. In addition to information about this ongoing project, the Grid website contains downloadable Request for Proposals documents, and a section for Project Archives. The site also provides simple instructions for joining the Grid; several online forums; and Grid statistics including current member totals.

379

Algebraic grid generation about wing-fuselage bodies

NASA Technical Reports Server (NTRS)

An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated. Each grid has six exterior surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Single-valued functions relating approximate arc lengths along the grid curves to a computational coordinate define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grid.

Smith, R. E.

1986-01-01

380

The time-dependent, three-dimensional incompressible Navier-Stokes equations are presently solved in generalized coordinate systems by means of a fractional-step method whose primitive variable formulation uses as dependent variables, in place of the Cartesian components of the velocity: (1) pressure (defined at the center of the computational cell), and (2) volume fluxes across the faces of the cells. The momentum equations are

Moshe Rosenfeld; Dochan Kwak; Marcel Vinokur

1991-01-01

381

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

M. Kim; J. J. Rosenberg; R. P. Smith; J. B. Hacker; M. P. DeLisio; D. B. Rutledge

1991-01-01

382

Benchmarking Grid Information Systems

\\u000a Grid information systems play a central role in today’s production Grid infrastructures, enabling the discovery of a range\\u000a of information about the Grid services that exist in an infrastructure. As the number of services within these infrastructures\\u000a continues to grow, it must be understood whether the current implementations are able to scale to meet the future requirements.\\u000a Existing approaches for

Laurence Field; Rizos Sakellariou

383

NSDL National Science Digital Library

Locate the Aliens or Help the Robot by understanding the four quadrants and the coordinates. Locate the Aliens By understanding the coordinates and quadrants, find the aliens. Direct the Robot Through the Maze Use your quadrant and coordinate knowledge to guide the Robot. Billy Bug s Quest for Grub Help Billy get to the right coordinates to feed. ...

Mr Clark

2012-10-31

384

Reflections on Statewide Coordination.

ERIC Educational Resources Information Center

Coordinating boards, no matter how carefully constructed, are super bureaucracies. Battles inevitably ensue between a coordinating board and the institutions that it proports to coordinate. Strong coordinating boards work best in large industrialized states, states with populations running into the many millions and spending hundreds of millions…

Sample, Steven B.

385

Challenges facing production grids

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.

Pordes, Ruth; /Fermilab

2007-06-01

386

Grid Computing Security Lecture

NSDL National Science Digital Library

Grid Computing Lecture~~Security: secure connection, authentication and authorization, password authentication, symmetric (secret) and asymmetric (public/private) key cyptography, RSA algorithm.

Dr. Clayton Ferner

2011-07-05

387

NASA Technical Reports Server (NTRS)

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.

Kim, Moonil; Weikle, Robert M., II; Hacker, Jonathan B.; Delisio, Michael P.; Rutledge, David B.; Rosenberg, James J.; Smith, R. P.

1991-01-01

388

A nonhydrostatic model with a generalized vertical coordinate

NASA Astrophysics Data System (ADS)

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.

He, Zuwen

389

Flexible Residential Smart Grid Simulation Framework

NASA Astrophysics Data System (ADS)

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.

Xiang, Wang

390

Coordinated Variable Structure Switching Attacks for Smart Grid

The effective modeling and analysis of large-scale power system disturbances especially those stemming from intentional attack represents an open engineering and research problem. Challenges stem from the need to develop intelligent models of cyber...

Liu, Shan

2013-02-11

391

Generation of Surface Coordinates by Elliptic Partial Differential Equations

NASA Technical Reports Server (NTRS)

The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.

Warsi, Z. U. A.

1985-01-01

392

A parallel 3D Poisson solver for space charge simulation in cylindrical coordinates

NASA Astrophysics Data System (ADS)

This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the ( r,?) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.

Xu, J.; Ostroumov, P. N.; Nolen, J.

2008-02-01

393

NASA Technical Reports Server (NTRS)

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.

Ives, David

1995-01-01

394

NASA Astrophysics Data System (ADS)

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.

Schäfer, Benjamin; Matthiae, Moritz; Timme, Marc; Witthaut, Dirk

2015-01-01

395

Grid Database Service Specification

Data management systems are central to many applications across multiple domains, and play a significant role in many others. Web services provide implementation neutral facilities for describing, invoking and orchestrating collections of networked resources. The Open Grid Services Architecture (OGSA) extends Web Services with consistent interfaces for creating, managing and exchanging information among Grid Services, which are dynamic computational artefacts

James Clerk Maxwell; Susan Malaika; Gavin McCance; James Magowan; Norman W. Paton; Greg Riccardi

2002-01-01

396

NSDL National Science Digital Library

This video segment, adapted from NOVA scienceNOW, addresses how new technology can help monitor and modernize the infrastructure of the U.S. power grid, which is ill-equipped to handle our increasing demand for electricity. Video provides a great overview of how electricity is generated and how the grid works.

WGBH Educational Foundation NOVA scienceNOW

397

NSDL National Science Digital Library

This lesson begins with a basic visual used in many textbooks: a 10 × 10 grid as a model for demonstrating percent as "parts per hundred" with a worksheet of these grids to print for each student. The lesson goes on to extend the model to solve various percentage problems. Especially valuable is the illustration of each problem and the thorough explanation that accompanies it.

2010-07-19

398

Grid Aware Parallelizing Algorithms

Running tightly coupled parallel MPI applications in a real grid environment using distributed MPI implementations (1, 2) can, in principle, make better and more fle xible use of computational resources, but for most parallel applications it has a major downside: The performance of such codes tends to be very poor. Most often the natural characteristics of realworld grids are responsible

Thomas Dramlitsch; Gabrielle Allen; Ed Seidel

399

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.

Humphrey, Marty; Thompson, Mary R.; Jackson, Keith R.

2005-08-14

400

Wireless Grids for Cultural Self-Preservation: Assessing E-Readiness in a Native American Nation

The role of wireless grids for distributed coordination and their suitability for sustainable cultural self preservation was assessed through a series of focus groups conducted in cooperation with a Native American Nation. After providing contextual information and definitions for key concepts in our research (wireless grid technologies, indigenous knowledge and the right to culture preservation in indigenous cultures) we discuss

Angela U. Ramnarine-Rieks; Lee W. McKnight; Gail Riina; Carlos Gardeazabal

2012-01-01

401

ORNL/TM-2008/085 A Vertical Grid Module for Baroclinic

ORNL/TM-2008/085 A Vertical Grid Module for Baroclinic Models of the Atmosphere June 2008 John B thereof. #12;ORNL/TM-2008/085 A VERTICAL GRID MODULE FOR BAROCLINIC MODELS OF THE ATMOSPHERE John B. Drake Generalized Meteorological Vertical Coordinates 2 2.1 Variables

Pennycook, Steve

402

Optimization Of A Computational Grid

NASA Technical Reports Server (NTRS)

In improved method of generation of computational grid, grid-generation process decoupled from definition of geometry. Not necessary to redefine boundary. Instead, continuous boundaries in physical domain specified, and then grid points in computational domain mapped onto continuous boundaries.

Pearce, Daniel G.

1993-01-01

403

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.

Moore, Reagan W.; Studham, Ronald S.; Rajasekar, Arcot; Watson, Chip; Stockinger, Heinz; Kunszt, Peter; Charlie Catlett and Ian Foster

2002-02-27

404

Transforming Power Grid Operations

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 research, development and demonstration of next-generation tools and technologies for enhanced energy infrastructure operations (EIOC sidebar).

Huang, Zhenyu; Guttromson, Ross T.; Nieplocha, Jarek; Pratt, Robert G.

2007-04-15

405

An implicit multi-dimensional particle-in-cell (PIC) code is developed to study the interaction of ultrashort pulse lasers with matter. The algorithm is based on current density decomposition and is only marginally more complicated compared to explicit PIC codes, but it completely eliminates grid heating and possesses good energy conserving properties with relaxed time step and grid resolution. This is demonstrated in a test case study, in which high-energy protons are generated from a thin carbon foil at solid density using linear and circular polarizations. The grid heating rate is estimated to be 1-10 eV/ps.

Petrov, G. M.; Davis, J. [Naval Research Laboratory, Plasma Physics Division, 4555 Overlook Ave. SW, Washington, DC 20375 (United States)

2011-07-15

406

Finite-surface method for the Maxwell equations in generalized coordinates

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. 12 refs.

Vinokur, M.; Yarrow, M. (NASA, Ames Research Center, Moffett Field, CA (United States))

1993-01-01

407

Finite-surface method for the Maxwell equations in generalized coordinates

NASA Technical Reports Server (NTRS)

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.

Vinokur, Marcel; Yarrow, Maurice

1993-01-01

408

Trends in life science grid: from computing grid to knowledge grid

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

Konagaya, Akihiko

2006-01-01

409

Numerical Simulation of Rolling-Airframes Using a Multi-Level Cartesian Method

NASA Technical Reports Server (NTRS)

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.

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)

2002-01-01

410

NASA Astrophysics Data System (ADS)

In this thesis, I present the results of studies of the structural properties and phase transition of a charge neutral FCC Lattice Gas with Yukawa Interaction and discuss a novel fast calculation algorithm---Accelerated Cartesian Expansion (ACE) method. In the first part of my thesis, I discuss the results of Monte Carlo simulations carried out to understand the finite temperature (phase transition) properties and the ground state structure of a Yukawa Lattice Gas (YLG) model. In this model the ions interact via the potential q iqjexp(-kappar> ij)/rij where qi,j are the charges of the ions located at the lattice sites i and j with position vectors R i and Rj; rij = Ri-Rj, kappa is a measure of the range of the interaction and is called the screening parameter. This model approximates an interesting quaternary system of great current thermoelectric interest called LAST-m, AgSbPbmTem+2. I have also developed rapid calculation methods for the potential energy calculation in a lattice gas system with periodic boundary condition bases on the Ewald summation method and coded the algorithm to compute the energies in MC simulation. Some of the interesting results of the MC simulations are: (i) how the nature and strength of the phase transition depend on the range of interaction (Yukawa screening parameter kappa) (ii) what is the degeneracy of the ground state for different values of the concentration of charges, and (iii) what is the nature of two-stage disordering transition seen for certain values of x. In addition, based on the analysis of the surface energy of different nano-clusters formed near the transition temperature, the solidification process and the rate of production of these nano-clusters have been studied. In the second part of my thesis, we have developed two methods for rapidly computing potentials of the form R-nu. Both these methods are founded on addition theorems based on Taylor expansions. Taylor's series has a couple of inherent advantages: (i) it forms a natural framework for developing addition theorem based computational schemes for a range of potentials; (ii) only Cartesian tensors (or products of Cartesian quantities) are used as opposed to special functions. This makes creating a fast scheme possible for potential of the form R-nu . Indeed, it is also possible to generalize the proposed methods to several potentials that are important in mathematical physics. An interesting consequence of the approach has been the demonstration of the equivalence of FMMs that are based on traceless Cartesian tensors to those based on spherical expansions for nu = 1. Two methods are introduced; the first relies on exact translation of the origin of the multipole whereas the second relies on cascaded Taylor's approximations. Finally, we have shown the application of this methodology to computing Coulombic, Lennard-Jones, Yukawa potentials and etc. We have also demonstrated the efficacy of this scheme for other (non-integer) potential functions.

Huang, He

411

In this paper a novel approach to the Cartesian Impedance Control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent motor

Christian Ott; Alin Albu-Sch; Andreas Kugiy; Stefano Stramigioliz; Gerd Hirzinger

412

ERIC Educational Resources Information Center

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…

Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao

2012-01-01

413

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

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.

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2001-01-01

414

This paper describes a simple method of converting visual coordinates to arm coordinates which does not require knowledge of the position of the camera(s). Comparisons are made to other methods and two camera, three ...

Speckert, Glen

415

Developmental coordination disorder

Physical education and perceptual motor training are the best ways to treat coordination disorder. Using a computer to take notes may help children who have trouble writing. Children with developmental coordination disorder are three times more likely to ...

416

Federal Register 2010, 2011, 2012, 2013, 2014

...OF ENERGY Federal Energy Regulatory Commission [Docket No. EL11-13-000] Atlantic Grid Operations A LLC, Atlantic Grid Operations B LLC, Atlantic Grid Operations C LLC, Atlantic Grid Operations D LLC and Atlantic Grid Operations E...

2011-01-07

417

NASA Astrophysics Data System (ADS)

DESY is one of the world-wide leading centers for research with particle accelerators, synchrotron light and astroparticles. DESY participates in LHC as a Tier-2 center, supports on-going analyzes of HERA data, is a leading partner for ILC, and runs the National Analysis Facility (NAF) for LHC and ILC in the framework of the Helmholtz Alliance, Physics at the Terascale. For the research with synchrotron light major new facilities are operated and built (FLASH, PETRA-III, and XFEL). DESY furthermore acts as Data-Tier1 centre for the Neutrino detector IceCube. Established within the EGI-project DESY operates a grid infrastructure which supports a number of virtual Organizations (VO), incl. ATLAS, CMS, and LHCb. Furthermore, DESY hosts some of HEP and non-HEP VOs, such as the HERA experiments and ILC as well as photon science communities. The support of the new astroparticle physics VOs IceCube and CTA is currently set up. As the global structure of the grid offers huge resources which are perfect for batch-like computing, DESY has set up the National Analysis Facility (NAF) which complements the grid to allow German HEP users for efficient data analysis. The grid infrastructure and the NAF use the same physics data which is distributed via the grid. We call the conjunction of grid and NAF the DESY Grid Centre. In the contribution to CHEP2012 we will in depth discuss the conceptional and operational aspects of our multi-VO and multi-community Grid Centre and present the system setup. We will in particular focus on the interplay of Grid and NAF and present experiences of the operations.

Haupt, A.; Gellrich, A.; Kemp, Y.; Leffhalm, K.; Ozerov, D.; Wegner, P.

2012-12-01

418

NSDL National Science Digital Library

Become familiar with the coordinate plane. Learn the quadrants and how to graph points and read points on a coordinate plane. You are required to do the assignment and take the quiz. The other resources are to help prepare you for the quiz and book assignment. This is a quick review of the lesson.The Coordinate Plane This is a game to practice plotting and reading points.coordinates game *Assignment: Watch Powerpoint 3.3 and fill in your ...

Miss Cook

2010-10-12

419

NASA Astrophysics Data System (ADS)

Die vorgestellte Architektur erleichtert wissenschaftlichen Benutzern den Zugriff auf Rechenkapazitäten innerhalb eines Grid ohne Vorkenntnisse der zugrundeliegenden Techniken. GridIJ ist eine Referenzimplementierung für die Bildverarbeitung. Dem Benutzer wird eine grafische Oberfläche bereitgestellt, die einen einfachen Zugriff auf Bildverarbeitungsalgorithmen in einem Grid erlaubt. Mit einem Java Interface kann die Funktionalität erweitert werden. Um die Architektur einzurichten sind zwei zusätzliche Web-Services in einem GT4 Container notwendig. Tests zeigen, dass die Architektur einen hohen Leistungsgewinn im Vergleich zur Ausführung auf einem Einzelplatzrechner ermöglicht.

Frank, Alexander; Stotzka, Rainer; Jejkal, Thomas; Hartmann, Volker; Sutter, Michael; Ruiter, Nicole; Zapf, Michael

420

MISCELLANEA Spherical Coordinates

and to denote polar coordinates. Most American calculus texts also utilize in spherical coordinates coordinate. There is however a much more serious problem. Several of the most commonly used calculus texts overnight from driving on the left to driving on the right! We argue that the conflict between the different

421

Digital Grid: Communicative Electrical Grids of the Future

To support a high penetration of intermittent solar and wind power generation, many regions are planning to add new high capacity transmission lines. These additional transmis- sion lines strengthen grid synchronization, but will also increase the grid's short circuit capacity, and furthermore will be very costly. With a highly interconnected grid and variable renewable generation, a small grid failure can

Rikiya Abe; Hisao Taoka; David McQuilkin

2011-01-01

422

myGrid: personalised bioinformatics on the information grid

Motivation: The my Grid project aims to exploit Grid technology, with an emphasis on the Information Grid, and provide middleware layers that make it appropriate for the needs of bioinformatics. my Grid is building high level services for data and application integration such as resource discovery, workflow enactment and distributed query processing. Additional services are provided to support the scientific

Robert D. Stevens; Alan J. Robinson; Carole A. Goble

2003-01-01

423

Surface grid generation for multi-block structured grids

NASA Astrophysics Data System (ADS)

A new grid generation technique for the computation of a structured grid on a generally curved surface in 3D is discussed. The starting assumption is that the parameterization of the surface exists, i.e. a smooth geometrical shape function exists which maps the parametric space (the unit square) one-to-one on the surface. The grid generation system computes a grid on the surface with as boundary conditions the following data specified along the four edges of the surface: (1) the position of the boundary grid points, (2) the grid line slopes at the boundary grid points, (3) the first grid cell lengths at the boundary grid points. The fourth-order elliptic biharmonic equations are used to compute the two families of grid lines in the parametric space. After that, each grid point in the parametric space is found as the intersection point between two individual grid lines, one from each family. The grid points on the surface are finally found by mapping the grid points in the parametric space on the surface via the geometrical shape function. Results are shown for an O-type 2D Euler grid, a C-type 2D Navier-Stokes grid and on some curved surfaces in 3D space.

Spekreijse, S. P.; Boerstoel, J. W.; Kuyvenhoven, J. L.; van der Marel, M. J.

424

The charging of batteries of plug-in hybrid electric vehicles at home at standard outlets has an impact on the distribution grid which may require serious investments in grid expansion. The coordination of the charging gives an improvement of the grid exploitation in terms of reduced power losses and voltage deviations with respect to uncoordinated charging. The vehicles must be dispatchable

Kristien Clement-Nyns; Edwin Haesen; Johan Driesen; QUADRATIC PROGRAMMING

2009-01-01

425

Coordinated Co-allocation Scheduling on Heterogeneous Clusters of SMPs

Job scheduling research for parallel systems has been widely exploited in recent years, especially in centers with high performance computing facilities. In the recent past we presented the eNANOS execution environment which is based on a coordinated architecture, from the CPU allocation to the grid scheduling, providing a good low level support to perform an efficient high level scheduling. In

Ivan Rodero; Julita Corbalan

2008-01-01

426

Using Grid Benchmarks for Dynamic Scheduling of Grid Applications

NASA Technical Reports Server (NTRS)

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.

Frumkin, Michael; Hood, Robert

2003-01-01

427

NASA Astrophysics Data System (ADS)

A domain is invariant under the eight-element D4 symmetry group if it is unchanged by reflection with respect to the x and y axes and also the diagonal line x=y. Previous treatments of group theory for spectral methods have generally demanded a semester's worth of group theory. We show this is unnecessary by providing explicit recipes for creating grids, etc. We show how to decompose an arbitrary function into six symmetry-invariant components, and thereby split the interpolation problem into six independent subproblems. We also show how to make symmetry-invariant basis functions from products of Chebyshev polynomials, from Zernike polynomials and from radial basis functions (RBFs) of any species. These recipes are completely general, and apply to any domain that is invariant under the dihedral group D4. These concepts are illustrated by RBF pseudospectral solutions of the Poisson equation in a domain bounded by a squircle, the square-with-rounded corners defined by x2?+y2?-1=0 where here ?=2. We also apply Chebyshev polynomials to compute eigenmodes of the Helmholtz equation on the square and show each mode belongs to one and only one of the six D4 classes.

Li, Shan; Boyd, John P.

2014-02-01

428

GRIDS: Grid-Scale Rampable Intermittent Dispatchable Storage

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.

None

2010-09-01

429

Arc Length Based Grid Distribution For Surface and Volume Grids

NASA Technical Reports Server (NTRS)

Techniques are presented for distributing grid points on parametric surfaces and in volumes according to a specified distribution of arc length. Interpolation techniques are introduced which permit a given distribution of grid points on the edges of a three-dimensional grid block to be propagated through the surface and volume grids. Examples demonstrate how these methods can be used to improve the quality of grids generated by transfinite interpolation.

Mastin, C. Wayne

1996-01-01

430

Grid Computing Education Support

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.

Steven Crumb

2008-01-15

431

NASA Technical Reports Server (NTRS)

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.

Vaziri, Arsi

2004-01-01

432

The gridded electromagnet probe

We attempted to measure the anisotropy in the electron distribution function in magnetized plasma by exploiting the adiabatic invariance of the electron's magnetic moment with a probe comprising a grid, a collector, and ...

Shadman, K. (Khashayar), 1972-

2003-01-01

433

Distributed Adaptive Grid Hierarchy

NSDL National Science Digital Library

DAGH (which stands for Distributed Adaptive Grid Hierarchy) was developed as a computational toolkit for the Binary Black Hole NSF Grand Challenge Project. It provides the framework to solve systems of partial differential equations using adaptive finite difference methods.

434

NASA Technical Reports Server (NTRS)

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.

Johnston, William E.; Ziobarth, John (Technical Monitor)

2002-01-01

435

NASA Astrophysics Data System (ADS)

Image Data Language is a software for data analysis, visualization and cross-platform application development. The potentiality of IDL is well-known in the academic scientific world, especially in the astronomical environment where thousands of procedures are developed by using IDL. The typical use of IDL is the interactive mode but it is also possible to run IDL programs that do not require any interaction with the user, submitting them in batch or background modality. Through the interactive mode the user immediately receives images or other data produced in the running phase of the program; in batch or background mode, the user will have to wait for the end of the program, sometime for many hours or days to obtain images or data that IDL produced as output: in fact in Grid environment it is possible to access to or retrieve data only after completion of the program. The work that we present gives flexibility to IDL procedures submitted to the Grid computer infrastructure. For this purpose we have developed an IDL Grid Web Portal to allow the user to access the Grid and to submit IDL programs granting a full job control and the access to images and data generated during the running phase, without waiting for their completion. We have used the PHP technology and we have given the same level of security that Grid normally offers to its users. In this way, when the user notices that the intermediate program results are not those expected, he can stop the job, change the parameters to better satisfy the computational algorithm and resubmit the program, without consuming the CPU time and other Grid resources. The IDL Grid Web Portal allows you to obtain IDL generated images, graphics and data tables by using a normal browser. All conversations from the user and the Grid resources occur via Web, as well as authentication phases. The IDL user has not to change the program source much because the Portal will automatically introduce the appropriate modification before submitting the IDL program to the Grid. When the user wishes, he will be able to check the status of his program and outputs, if any, because the Portal will assign the users a specific and univocal session identification number. This Web portal runs in the Trinacria Grid Virtual Laboratory and fully exploits the power of this grid in terms of CPU and data storage.

Massimino, P.; Costa, A.

2008-08-01

436

On the use of a high order overlapping grid method for coupling in CFD/CAA

NASA Astrophysics Data System (ADS)

This paper presents a theoretical analysis and two applications of a high-order overlapping grid method for coupling Cartesian and curvilinear grids, developed in order to simulate aerodynamic noise. First, the overlapping grid method based on Lagrange interpolating polynomials is described and a theoretical analysis of the interpolation operator is then carried out. It shows that the interpolation generates spurious modes that depend on the wavenumbers of the signal. Besides it also gives the optimal conditions in which interpolation can be applied. Then an application to the simulation of the aeroacoustic noise generated by the vortex shedding behind a cylinder is presented. During this simulation, it appears that interpolation can create some spurious acoustic modes in regions where hydrodynamic fluctuations are significant, as predicted by the theoretical analysis. It is shown that these spurious modes disappear when a refined Cartesian grid is used (26 points per wavelength of the vortex shedding were found to be adequate in this study). At last, the simulation of the aerodynamic noise of a three element high-lift wing profile has then been carried out. For this application, the main acoustic source at the slat trailing edge is represented analytically. The propagation of the generated acoustic wave is simulated with a mean flow at rest and with a steady turbulent mean flow computed by RANS. The first application allows us to assess the method by comparing the results to a reference solution. The second one shows that the influence of a non-uniform mean flow on the directivity of an acoustic source can be observed in complex geometries. This application therefore shows that the proposed coupling method is well adapted to complex geometries that are usually met in industrial applications.

Desquesnes, G.; Terracol, M.; Manoha, E.; Sagaut, P.

2006-12-01

437

In this paper we report on the features of the Java Commodity Grid Kit. The Java CoG Kit provides middleware for accessing Grid functionality from the Java framework. Java CoG Kit middleware is general enough to design a variety of advanced Grid applications with quite different user requirements. Access to the Grid is established via Globus protocols, allowing the Java

Gregor Von Laszewski; Ian T. Foster; Jarek Gawor

2001-01-01

438

ERIC Educational Resources Information Center

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.

Tennant, Roy

2005-01-01

439

Numerical methods for solid mechanics on overlapping grids: Linear elasticity

NASA Astrophysics Data System (ADS)

This paper presents a new computational framework for the simulation of solid mechanics on general overlapping grids with adaptive mesh refinement (AMR). The approach, described here for time-dependent linear elasticity in two and three space dimensions, is motivated by considerations of accuracy, efficiency and flexibility. We consider two approaches for the numerical solution of the equations of linear elasticity on overlapping grids. In the first approach we solve the governing equations numerically as a second-order system (SOS) using a conservative finite-difference approximation. The second approach considers the equations written as a first-order system (FOS) and approximates them using a second-order characteristic-based (Godunov) finite-volume method. A principal aim of the paper is to present the first careful assessment of the accuracy and stability of these two representative schemes for the equations of linear elasticity on overlapping grids. This is done by first performing a stability analysis of analogous schemes for the first-order and second-order scalar wave equations on an overlapping grid. The analysis shows that non-dissipative approximations can have unstable modes with growth rates proportional to the inverse of the mesh spacing. This new result, which is relevant for the numerical solution of any type of wave propagation problem on overlapping grids, dictates the form of dissipation that is needed to stabilize the scheme. Numerical experiments show that the addition of the indicated form of dissipation and/or a separate filter step can be used to stabilize the SOS scheme. They also demonstrate that the upwinding inherent in the Godunov scheme, which provides dissipation of the appropriate form, stabilizes the FOS scheme. We then verify and compare the accuracy of the two schemes using the method of analytic solutions and using problems with known solutions. These latter problems provide useful benchmark solutions for time dependent elasticity. We also consider two problems in which exact solutions are not available, and use a posterior error estimates to assess the accuracy of the schemes. One of these two problems is additionally employed to demonstrate the use of dynamic AMR and its effectiveness for resolving elastic “shock” waves. Finally, results are presented that compare the computational performance of the two schemes. These demonstrate the speed and memory efficiency achieved by the use of structured overlapping grids and optimizations for Cartesian grids.

Appelö, Daniel; Banks, Jeffrey W.; Henshaw, William D.; Schwendeman, Donald W.

2012-07-01

440

A hexagonally shaped quasi-random no-two-holes touching grid collimator. The quasi-random array grid collimator eliminates contamination from small angle off-axis rays by using a no-two-holes-touching pattern which simultaneously provides for a self-supporting array increasng throughput by elimination of a substrate. The presentation invention also provides maximum throughput using hexagonally shaped holes in a hexagonal lattice pattern for diffraction limited applications. Mosaicking is also disclosed for reducing fabrication effort.

Fenimore, E.E.

1980-08-22

441

Movement coordination during conversation.

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

Latif, Nida; Barbosa, Adriano V; Vatiokiotis-Bateson, Eric; Castelhano, Monica S; Munhall, K G

2014-01-01

442

Movement Coordination during Conversation

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

Latif, Nida; Barbosa, Adriano V.; Vatiokiotis-Bateson, Eric; Castelhano, Monica S.; Munhall, K. G.

2014-01-01

443

Grid Data Management and Customer Demands at MeteoSwiss

NASA Astrophysics Data System (ADS)

Data grids constitute the required input form for a variety of applications. Therefore, customers increasingly expect climate services to not only provide measured data, but also grids of these with the required configurations on an operational basis. Currently, MeteoSwiss is establishing a production chain for delivering data grids by subscription directly from the data warehouse in order to meet the demand for precipitation data grids by governmental, business and science customers. The MeteoSwiss data warehouse runs on an Oracle database linked with an ArcGIS Standard edition geodatabase. The grids are produced by Unix-based software written in R called GRIDMCH which extracts the station data from the data warehouse and stores the files in the file system. By scripts, the netcdf-v4 files are imported via an FME interface into the database. Currently daily and monthly deliveries of daily precipitation grids are available from MeteoSwiss with a spatial resolution of 2.2km x 2.2km. These daily delivered grids are a preliminary based on 100 measuring sites whilst the grid of the monthly delivery of daily sums is calculated out of about 430 stations. Crucial for the absorption by the customers is the understanding of and the trust into the new grid product. Clearly stating needs which can be covered by grid products, the customers require a certain lead time to develop applications making use of the particular grid. Therefore, early contacts and a continuous attendance as well as flexibility in adjusting the production process to fulfill emerging customer needs are important during the introduction period. Gridding over complex terrain can lead to temporally elevated uncertainties in certain areas depending on the weather situation and coverage of measurements. Therefore, careful instructions on the quality and use and the possibility to communicate the uncertainties of gridded data proofed to be essential especially to the business and science customers who require 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.

Rigo, G.; Lukasczyk, Ch.

2010-09-01

444

An arbitrary curvilinear coordinate particle in cell method

NASA Astrophysics Data System (ADS)

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in-Cell (PIC) simulation method, is explored. In this method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out on a uniform, unitary square logical domain and mapped to a nonuniform, boundary fitted physical domain. We utilize an elliptic grid generation technique known as Winslow's method to generate boundary-fitted physical domains. We have derived the logical grid macroparticle equations of motion based on a canonical transformation of Hamilton's equations from the physical domain to the logical. These equations of motion are not seperable, and therefore unable to be integrated using the standard Leapfrog method. We have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. We constructed a proof to show that the ML integrator is symplectic for systems of arbitrary dimension. We have constructed a generalized, curvilinear coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid. By our formulation, we supply the plasma charge density on the logical grid as a source term. By the formulations of the logical grid particle mover and the field equations, the plasma particles are weighted to the uniform logical grid and the self-consistent mean fields obtained from the solution of the Poisson equation are interpolated to the particle position on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid. In this work, we explore the feasibility of the ACC-PIC method as a first step towards building a production level, time-adaptive-grid, 3d electromagnetic ACC-PIC code. We begin by combining the individual components to construct a 1d, electrostatic ACC-PIC code on a stationary nonuniform grid. Several standard physics tests were used to validate the accuracy of our method in comparison with a standard uniform grid PIC code. We then extend the code to two spatial dimensions and repeat the physics tests on a rectangular domain with both orthogonal and nonorthogonal meshing in comparison with a standard 2d uniform grid PIC code. As a proof of principle, we then show the time evolution of an electrostatic plasma oscillation on an annular domain obtained using Winslow's method.

Fichtl, Christopher A.

445

Smart Grid Integration Laboratory

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 â?? 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 CSUâ??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 Laboratoryâ??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 electrical power distribution system that integrates significant quantities of renewable and distributed energy resources; (4) System dynamic modeling that considers end-user behavior, economics, security and regulatory frameworks; (5) Best practices for energy management IT control solutions for effective distributed energy integration (including security with the underlying physical power systems); (6) Experimental verification of effects of various arrangements of renewable generation, distributed generation and user load types along with conventional generation and transmission. Understanding the core technologies for enabling them to be used in an integrated fashion within a distribution network remains is a benefit to the future energy paradigm and future and present energy engineers.

Wade Troxell

2011-09-30

446

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

NASA Technical Reports Server (NTRS)

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 variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Nemec, Marian; Aftosmis, Michael J.

2006-01-01

447

The BioGRID interaction database: 2015 update

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

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

448

Marshall Space Flight Center surface modeling and grid generation applications

NASA Technical Reports Server (NTRS)

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.

Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.

1995-01-01

449

The BioGRID interaction database: 2015 update.

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

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

450

Marshall Space Flight Center surface modeling and grid generation applications

NASA Astrophysics Data System (ADS)

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.

Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.

1995-03-01

451

Complex Volume Grid Generation Through the Use of Grid Reusability

NASA Technical Reports Server (NTRS)

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.

Alter, Stephen J.

1997-01-01

452

Tax Coordination and Unemployment

This paper analyses the implications of unemployment for fiscal competition and tax coordination among small open economies.\\u000a Unemployment is modeled as resulting from wage bargaining. The analysis focuses on the effect of labour and capital tax coordination\\u000a on welfare. We show that, while coordinated capital and labour tax increases unambiguously raise welfare if labour markets\\u000a are competitive, different results emerge

Clemens Fuest; Bernd Huber

1999-01-01

453

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.

Hambrick, J.

2012-01-01

454

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 metaphor of "finding the walking path in a cloudy or foggy day". This is meant by stating "The Nebulous Cartesian System" (NCS). Descartes, at his time undertaking his genius step, did not possess the knowledge of today's physiology and modern physics; we think that the time has come to consider such a New Cartesian System. To deal with this, we propose the utilization of the Heisenberg S-Matrix and a modified version of the Feynman Diagrams which we call "Brain Feynman Diagrams". Another metaphor to consider within the oscillatory approach of the NCS is the "string theory". We also emphasize that fundamental steps should be undertaken in order to create the own dynamical framework of the brain-body-mind incorporation; suggestions or metaphors from physics and mathematics are useful; however, the grammar of the brains intrinsic language must be understood with the help of a new biologically founded, adaptive-probabilistic Carte