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Sample records for cartesian coordinate grid

  1. Hybrid C-H grids for turbomachinery cascades. [parabolic and Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Ghia, U.; Ghia, K. N.; Ramamurti, R.

    1983-01-01

    The three basic types of grids available for two-dimensional cascade configurations are examined with respect to their relative advantages and disadvantages. Subsequently, a hybrid coordinate system is proposed such that it combines the major advantages of the C-type and the H-type meshes. The development of the hybrid grid system employs the patching of appropriate regions of these two basic mesh systems such that the transformed domain has a multi-block structure. Viewing the transformed domain as a three-dimensional surface enables the coordinates to be continuous across the boundaries of the patches in a natural manner.

  2. Transonic airfoil flowfield analysis using Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Carlson, L. A.

    1975-01-01

    A numerical technique for analyzing transonic airfoils is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that Cartesian coordinates are used rather than a grid which fits the airfoil, such as the conformal circle-plane or 'sheared parabolic' coordinates which were used previously. Comparison with previous results shows that it is not necessary to match the computational grid to the airfoil surface, and that accurate results can be obtained with a Cartesian grid for lifting supercritical airfoils.

  3. Grid refinement in Cartesian coordinates for groundwater flow models using the divergence theorem and Taylor's series.

    PubMed

    Mansour, M M; Spink, A E F

    2013-01-01

    Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.

  4. Stable boundary conditions for Cartesian grid calculations

    NASA Technical Reports Server (NTRS)

    Berger, M. J.; Leveque, R. J.

    1990-01-01

    The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.

  5. Euler calculations for wings using Cartesian grids

    NASA Technical Reports Server (NTRS)

    Gaffney, R. L., Jr.; Hassan, H. A.; Salas, M. D.

    1987-01-01

    A method is presented for the calculation of transonic flows past wings using Cartesian grids. The calculations are based on a finite volume formulation of the Euler equations. Results are presented for a rectangular wing with a flat tip and the ONERA M6 wing. In general, the results are in good agreement with other computations and available experiment. However, Cartesian grids require a greater number of points than body fitted grids in order to resolve the flow properties near the leading edge of a swept wing.

  6. The 3D Euler solutions using automated Cartesian grid generation

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

    Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.

  7. Cartesian-coordinate dimensioning for plumbing systems

    NASA Technical Reports Server (NTRS)

    Buirgy, P. A.

    1971-01-01

    Nonprogressive dimensioning method specifies Cartesian coordinates for each critical point in detail drawings of precision plumbing and ducting components to avoid tolerance accumulation. Method permits direct fabrication of tubing shapes without necessitating generation of a preproduction tubing mockup.

  8. pySeismicFMM: Python based travel time calculation in regular 2D and 3D grids in Cartesian and geographic coordinates using Fast Marching Method

    NASA Astrophysics Data System (ADS)

    Polkowski, Marcin

    2016-04-01

    Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.

  9. Cartesian Grid Methods for Moving Geometries

    DTIC Science & Technology

    2006-07-27

    Technology transfer is facilitated by our Cart3D code, which is used by over 100 groups around the country. Introduction Cartesian grids have proven themselves...efforts are summarized below. Limiters for Finite Volume Schemes The Cart3D steady state flow solver has some stalling of convergence due to cut... Cart3D by my collaborator Scott Murman. One-dimensional Model Problem The simplest setting to study the accuracy and stability of flow with a moving

  10. Transonic airfoil analysis and design using Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Carlson, L. A.

    1975-01-01

    An inverse numerical technique for designing transonic airfoils having a prescribed pressure distribution is presented. The method uses the full potential equation, inverse boundary conditions, and Cartesian coordinates. It includes simultaneous airfoil update and utilizes a direct-inverse approach that permits a logical method for controlling trailing edge closure. The method can also be used for the analysis of flowfields about specified airfoils. Comparison with previous results shows that accurate results can be obtained with a Cartesian grid. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

  11. Transonic airfoil design using Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Carlson, L. A.

    1976-01-01

    A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

  12. Cartesian-cell based grid generation and adaptive mesh refinement

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1993-01-01

    Viewgraphs on Cartesian-cell based grid generation and adaptive mesh refinement are presented. Topics covered include: grid generation; cell cutting; data structures; flow solver formulation; adaptive mesh refinement; and viscous flow.

  13. Beamtracking in cylindrical and cartesian coordinates

    SciTech Connect

    Schillinger, B.; Weiland, T.

    1997-02-01

    For the design of devices with circular optical axes, e.g. bending magnets or spectrometers, the use of cylindrical coordinates for field calculations could be favourable. Additionally, in case of applications like bending systems with nonorthogonal entry and exit faces, the coupling of cylindrical and cartesian coordinates improves the simulation of fringe fields. In this context we have implemented a consistent coupling between the two coordinate systems and have extended the tracking code of the electromagnetic simulator MAFIA to cylindrical coordinates. This extensions could be of interest for the calculation of transfer maps of ionoptical devices using the tracked particle orbit as reference trajectory and including fringe field effects in a more general manner. We will give a short introduction to the extensions and show some examples for bending systems with nonorthogonal entries.

  14. Conversion of Cartesian coordinates from and to Generalized Balanced Ternary addresses

    USGS Publications Warehouse

    van Roessel, Jan W.

    1988-01-01

    Hexagonal grids have several advantages over square grids, such as a greater angular resolution and unambiguous connectivity. The Generalized Balanced Ternary (GBT) system is a spatial addressing method for hexagonal grids in which the hexagons are arranged in hierarchical aggregates, and which accommodates vector operations in GBT space. Efficient algorithms for converting Cartesian coordinates from and to GBT addresses are based on the dual representation of the hexagonal tessellation. The GBT-to-Cartesian algorithm is an order of magnitude faster than the Cartesian-to-GBT algorithm, the latter requiring interpolation and GBT addition for each digit of the generated GBT address.

  15. Unstructured Cartesian/prismatic grid generation for complex geometries

    NASA Technical Reports Server (NTRS)

    Karman, Steve L., Jr.

    1995-01-01

    The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.

  16. A Cartesian grid-based unified gas kinetic scheme

    NASA Astrophysics Data System (ADS)

    Chen, Songze; Xu, Kun

    2014-12-01

    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.

  17. 3D automatic Cartesian grid generation for Euler flows

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

    We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.

  18. A Cartesian grid approach with hierarchical refinement for compressible flows

    NASA Technical Reports Server (NTRS)

    Quirk, James J.

    1994-01-01

    Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

  19. Efficient Fluid Dynamic Design Optimization Using Cartesian Grids

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

    This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.

  20. On differential transformations between Cartesian and curvilinear (geodetic) coordinates

    NASA Technical Reports Server (NTRS)

    Soler, T.

    1976-01-01

    Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

  1. Cartesian grid method for gas kinetic scheme on irregular geometries

    NASA Astrophysics Data System (ADS)

    Chen, Songze; Xu, Kun; Li, Zhihui

    2016-12-01

    A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the boundaries are represented by a set of direction-oriented boundary points, and the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We adopt a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux solver. The reconstruction scheme for recovering the boundary conditions of compressible viscous and heat conducting flow with a Cartesian mesh can provide a smooth distribution of physical quantities at solid boundary, and present an accurate solution for the flow study with complex geometry.

  2. Zernike expansion of separable functions of cartesian coordinates.

    PubMed

    Sheppard, Colin J R; Campbell, Sam; Hirschhorn, Michael D

    2004-07-10

    A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.

  3. A general time element using Cartesian coordinates: Eccentric orbit integration

    NASA Technical Reports Server (NTRS)

    Janin, G.

    1980-01-01

    A general time element, valid with any arbitrary independent variables, and used with Cartesian coordinates for the integration of the elliptic motion in orbits, is examined. The derivation of the time element from a set of canonical elements of the Delaunay type, developed in the extended phase space, is presented. The application of the method using an example of a transfer orbit for a geosynchronous mission is presented. The eccentric and elliptic anomaly are utilized as the independent variable. The reduction of the in track error resulting from using Cartesian coordinates with the time element is reported.

  4. Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

  5. Triangle geometry processing for surface modeling and cartesian grid generation

    DOEpatents

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

    2002-09-03

    Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

  6. An adaptive Cartesian grid generation method for Dirty geometry

    NASA Astrophysics Data System (ADS)

    Wang, Z. J.; Srinivasan, Kumar

    2002-07-01

    Traditional structured and unstructured grid generation methods need a water-tight boundary surface grid to start. Therefore, these methods are named boundary to interior (B2I) approaches. Although these methods have achieved great success in fluid flow simulations, the grid generation process can still be very time consuming if non-water-tight geometries are given. Significant user time can be taken to repair or clean a dirty geometry with cracks, overlaps or invalid manifolds before grid generation can take place. In this paper, we advocate a different approach in grid generation, namely the interior to boundary (I2B) approach. With an I2B approach, the computational grid is first generated inside the computational domain. Then this grid is intelligently connected to the boundary, and the boundary grid is a result of this connection. A significant advantage of the I2B approach is that dirty geometries can be handled without cleaning or repairing, dramatically reducing grid generation time. An I2B adaptive Cartesian grid generation method is developed in this paper to handle dirty geometries without geometry repair. Comparing with a B2I approach, the grid generation time with the I2B approach for a complex automotive engine can be reduced by three orders of magnitude. Copyright

  7. Parallel Cartesian grid refinement for 3D complex flow simulations

    NASA Astrophysics Data System (ADS)

    Angelidis, Dionysios; Sotiropoulos, Fotis

    2013-11-01

    A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

  8. The approach to steady state using homogeneous and Cartesian coordinates.

    PubMed

    Gochberg, D F; Ding, Z

    2013-01-01

    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.

  9. Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm

    NASA Astrophysics Data System (ADS)

    Civicioglu, Pinar

    2012-09-01

    In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into geodetic coordinates or vice versa. It is very easy to solve the problem of transforming geodetic coordinates into geocentric cartesian coordinates. On the other hand, it is rather difficult to solve the problem of transforming geocentric cartesian coordinates into geodetic coordinates as it is very hard to define a mathematical relationship between the geodetic latitude (φ) and the geocentric cartesian coordinates (X, Y, Z). In this paper, a new algorithm, the Differential Search Algorithm (DS), is presented to solve the problem of transforming the geocentric cartesian coordinates into geodetic coordinates and its performance is compared with the performances of the classical methods (i.e., Borkowski, 1989; Bowring, 1976; Fukushima, 2006; Heikkinen, 1982; Jones, 2002; Zhang, 2005; Borkowski, 1987; Shu, 2010 and Lin, 1995) and Computational-Intelligence algorithms (i.e., ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES). The statistical tests realized for the comparison of performances indicate that the problem-solving success of DS algorithm in transforming the geocentric cartesian coordinates into geodetic coordinates is higher than those of all classical methods and Computational-Intelligence algorithms used in this paper.

  10. Hamiltonian formalism for semiflexible molecules in Cartesian coordinates.

    PubMed

    Kneller, G R

    2006-09-21

    The article gives a concise description of Hamiltonian dynamics and thermal averages of semiflexible molecules in Cartesian coordinates. Using the concept of constrained inverse matrices introduced by Bott and Duffin [Trans. Am. Math. Soc. 74, 99 (1953)] explicit expressions are derived for the constrained Hamiltonian, the corresponding equations of motion, and the momentum partition function. In this context Fixman-type corrections of constrained configurational averages are derived for different forms of the constraints. It is shown that the use of mass-weighted coordinates leads to a nonbiased sampling of constrained configurational averages in Cartesian coordinates. The formalism allows moreover to define and to calculate effective masses arising in thermal velocity averages of atoms in semiflexible molecules. These effective masses are identical to the corresponding Sachs-Teller recoil masses, which are here generalized to the case of only partially rigid molecules.

  11. Averaged initial Cartesian coordinates for long lifetime satellite studies

    NASA Technical Reports Server (NTRS)

    Pines, S.

    1975-01-01

    A set of initial Cartesian coordinates, which are free of ambiguities and resonance singularities, is developed to study satellite mission requirements and dispersions over long lifetimes. The method outlined herein possesses two distinct advantages over most other averaging procedures. First, the averaging is carried out numerically using Gaussian quadratures, thus avoiding tedious expansions and the resulting resonances for critical inclinations, etc. Secondly, by using the initial rectangular Cartesian coordinates, conventional, existing acceleration perturbation routines can be absorbed into the program without further modifications, thus making the method easily adaptable to the addition of new perturbation effects. The averaged nonlinear differential equations are integrated by means of a Runge Kutta method. A typical step size of several orbits permits rapid integration of long lifetime orbits in a short computing time.

  12. A cartesian grid embedded boundary method for hyperbolic conservation laws

    SciTech Connect

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

    2004-10-03

    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.

  13. An immersed boundary method for non-uniform Cartesian grids

    NASA Astrophysics Data System (ADS)

    Jang, Juwon; Lee, Changhoon

    2016-11-01

    Many kinds of immersed boundary method have been developed, but most of them have been used in uniform grids with discrete Dirac delta functions. Therefore, the distribution of Lagrangian points over the immersed surface is usually made uniformly. However, when any immersed boundary method is to be applied to non-uniform grids, uniform distribution might not be optimum for good performance. Recently, Akiki and Balachandar (2016) proposed a method to distribute the Lagrangian points nonuniformly over the surface of a sphere near the wall, but it cannot not be extended to more general shape of immersed surface. We propose a method that is capable for properly distributing the Lagrangian points over any kind of surface by considering the size of nearby Eulerian grids. Present method first finds intersection points between immersed surface and nonuniform Cartesian grids. Then, the centroid of the intersection points is projected on the immersed surface to be designated by Lagrangian point. This procedure guarantees one Lagrangian point per the Eulerian grid cell. This method is validated for various problems such as flows around a settling sphere, a moving sphere in the near-wall region and a tilted ellipsoid near the wall.

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

    NASA Technical Reports Server (NTRS)

    2003-01-01

    With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.

  15. Extending the functionalities of Cartesian grid solvers: Viscous effects modeling and MPI parallelization

    NASA Astrophysics Data System (ADS)

    Marshall, David D.

    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.

  16. Adaptive Cartesian coordinate control of space based robot manipulators

    NASA Technical Reports Server (NTRS)

    Walker, Michael W.; Wee, Liang-Boon

    1991-01-01

    A Cartesian coordinate robot controller is presented for use when the mass properties of a load are unknown. The mass, center of mass, and moments of inertia of the end-effector are assumed unknown. All other inertial properties of the robot are assumed known. This knowledge of the parameters allows the control of the end-effector in a way similar to the use of reaction wheels to control the orientation of a satellite. This is the primary result of the controller. The basic method of the controller is similar to that used for terrestrial-based robot manipulators. The controller is demonstrated using a new simulation algorithm which is based on Hamilton's form of the equations of motion.

  17. A general time element for orbit integration in Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Janin, G.; Bond, V. R.

    1981-01-01

    Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.

  18. Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates.

    PubMed

    Hikiri, Simon; Yoshidome, Takashi; Ikeguchi, Mitsunori

    2016-12-13

    The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to establish an efficient quantitative computational method to calculate configurational entropy as accurately as possible. In the present paper, we investigate the quantitative performance of the quasi-harmonic and related computational methods, including widely used methods implemented in popular molecular dynamics (MD) software packages, compared with the Clausius method, which is capable of accurately computing the change of the configurational entropy upon temperature change. Notably, we focused on the choice of the coordinate systems (i.e., internal or Cartesian coordinates). The Boltzmann-quasi-harmonic (BQH) method using internal coordinates outperformed all the six methods examined here. The introduction of improper torsions in the BQH method improves its performance, and anharmonicity of proper torsions in proteins is identified to be the origin of the superior performance of the BQH method. In contrast, widely used methods implemented in MD packages show rather poor performance. In addition, the enhanced sampling of replica-exchange MD simulations was found to be efficient for the convergent behavior of entropy calculations. Also in folding/unfolding transitions of a small protein, Chignolin, the BQH method was reasonably accurate. However, the independent term without the correlation term in the BQH method was most accurate for the folding entropy among the methods considered in this study, because the QH approximation of the correlation term in the BQH method was no longer valid for the divergent unfolded structures.

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

    NASA Astrophysics Data System (ADS)

    Liu, Jianming; Zhao, Ning; Hu, Ou

    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.

  20. An Investigation of Two-Dimensional CAD Generated Models with Body Decoupled Cartesian Grids for DSMC

    SciTech Connect

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

    2000-06-27

    This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.

  1. A Parallel Code for Solving the Molecular Time Dependent Schroedinger Equation in Cartesian Coordinates

    SciTech Connect

    Suarez, J.; Stamatiadis, S.; Farantos, S. C.; Lathouwers, L.

    2009-08-13

    Reproducing molecular dynamics is at the root of the basic principles of chemical change and physical properties of the matter. New insight on molecular encounters can be gained by solving the Schroedinger equation in cartesian coordinates, provided one can overcome the massive calculations that it implies. We have developed a parallel code for solving the molecular Time Dependent Schroedinger Equation (TDSE) in cartesian coordinates. Variable order Finite Difference methods result in sparse Hamiltonian matrices which can make the large scale problem solving feasible.

  2. Moment-of-fluid analytic reconstruction on 2D Cartesian grids

    NASA Astrophysics Data System (ADS)

    Lemoine, Antoine; Glockner, Stéphane; Breil, Jérôme

    2017-01-01

    Moment-of-Fluid (MoF) is a piecewise linear interface reconstruction method that tracks fluid through its volume fraction and centroid, which are deduced from the zeroth and first moments. We present a method that replaces the original minimization stage by an analytic reconstruction algorithm on bi-dimensional Cartesian grids. This algorithm provides accurate results for a lower computational cost than the original minimization algorithm. When more than two fluids are involved, this algorithm can be used coupled with the minimization algorithm. Although this paper deals with Cartesian grids, everything remains valid for any meshes that are made of rectangular cells.

  3. Time-Dependent Lattice Methods for Ion-Atom Collisions in Cartesian and Cylindrical Coordinate Systems

    SciTech Connect

    Pindzola, Michael S; Schultz, David Robert

    2008-01-01

    Time-dependent lattice methods in both Cartesian and cylindrical coordinates are applied to calculate excitation cross sections for p+H collisions at 40 keV incident energy. The time-dependent Schroedinger equation is solved using a previously formulated Cartesian coordinate single-channel method on a full 3D lattice and a newly formulated cylindrical coordinate multichannel method on a set of coupled 2D lattices. Cartesian coordinate single-channel and cylindrical coordinate five-channel calculations are found to be in reasonable agreement for excitation cross sections from the 1s ground state to the 2s, 2p, 3s, 3p, and 3d excited states. For extension of the time-dependent lattice method to handle the two electron dynamics found in p+He collisions, the cylindrical coordinate multichannel method appears promising due to the reduced dimensionality of its lattice.

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

    NASA Technical Reports Server (NTRS)

    Buning, Pieter G.; Pulliam, Thomas H.

    2011-01-01

    An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.

  5. Development and application of a 3D Cartesian grid Euler method

    NASA Technical Reports Server (NTRS)

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

    1995-01-01

    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.

  6. An improved method for rebinning kernels from cylindrical to Cartesian coordinates.

    PubMed

    Rathee, S; McClean, B A; Field, C

    1993-01-01

    This paper describes the errors in rebinning photon dose point spread functions and pencil beam kernels (PBKs) from cylindrical to Cartesian coordinates. An area overlap method, which assumes that the fractional energy deposited per unit volume remains constant within cylindrical voxels, provides large deviations (up to 20%) in rebinned Cartesian voxels while conserving the total energy. A modified area overlap method is presented that allows the fractional energy deposited per unit volume within cylindrical voxels to vary according to an interpolating function. This method rebins the kernels accurately in each Cartesian voxel while conserving the total energy. The dose distributions were computed for a partially blocked beam of uniform fluence using the Cartesian coordinate kernel and the kernels rebinned by both methods. The kernel rebinned by the modified area overlap method provided errors less than 1.7%, while the kernel rebinned by the area overlap method gave errors up to 4.4%.

  7. Direct determination of multipole moments of Cartesian Gaussian functions in spherical polar coordinates.

    PubMed

    Choi, Cheol Ho

    2004-02-22

    A new way of generating the multipole moments of Cartesian Gaussian functions in spherical polar coordinates has been established, bypassing the intermediary of Cartesian moment tensors. A new set of recurrence relations have also been derived for the resulting analytic integral values. The new method furnishes a conceptually simple and numerically efficient evaluation procedure for the multipole moments. The advantages over existing methods are documented. The results are relevant for the linear scaling quantum theories based on the fast multipole method.

  8. An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

    NASA Astrophysics Data System (ADS)

    Qiu, Linhai; Lu, Wenlong; Fedkiw, Ronald

    2016-01-01

    We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.

  9. Euler calculations with embedded Cartesian grids and small-perturbation boundary conditions

    NASA Astrophysics Data System (ADS)

    Liao, W.; Koh, E. P. C.; Tsai, H. M.; Liu, F.

    2010-05-01

    This study examines the use of stationary Cartesian mesh for steady and unsteady flow computations. The surface boundary conditions are imposed by reflected points. A cloud of nodes in the vicinity of the surface is used to get a weighted average of the flow properties via a gridless least-squares technique. If the displacement of the moving surface from the original position is typically small, a small-perturbation boundary condition method can be used. To ensure computational efficiency, multigrid solution is made via a framework of embedded grids for local grid refinement. Computations of airfoil wing and wing-body test cases show the practical usefulness of the embedded Cartesian grids with the small-perturbation boundary conditions approach.

  10. A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity

    NASA Astrophysics Data System (ADS)

    Thornburg, Jonathan

    2003-10-01

    In 3 + 1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder, AHFINDERDIRECT, which is very fast and accurate, typically taking only a few seconds to find an AH to ~ 10-5m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkörper (``star-shaped region'') with respect to some local origin, and so parameterize the AH shape by r = h(angle) for some single-valued function h: S2 --> R+. The AH equation then becomes a nonlinear elliptic PDE in h on S2, whose coefficients are algebraic functions of gij, Kij, and the Cartesian-coordinate spatial derivatives of gij. I discretize S2 using 6 angular patches (one each in the neighborhood of the +/-x, +/-y, and +/-z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using 4th order finite differencing. I solve the resulting system of nonlinear algebraic equations (for h at the angular grid points) by Newton's method, using a ``symbolic differentiation'' technique to compute the Jacobian matrix. AHFINDERDIRECT is implemented as a thorn in the CACTUS computational toolkit, and will be made freely available starting in fall 2003.

  11. Euler Technology Assessment program for preliminary aircraft design employing SPLITFLOW code with Cartesian unstructured grid method

    NASA Technical Reports Server (NTRS)

    Finley, Dennis B.

    1995-01-01

    This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

  12. Dynamical calculation of crystal truncation rods for surfaces and interfaces using a Cartesian coordinate transformation technique.

    PubMed

    Chien; Gau; Chang; Stetsko

    1999-07-01

    A dynamical calculation scheme that employs Cartesian coordinates with a z axis normal to the crystal surface to define polarization unit vectors and wavefields is applied to interpret the intensity distribution of crystal truncation rods for surfaces and interfaces. A comparison between this calculation scheme and the asymptotic iteration approach using the conventional presentation of the polarization components of the wavefields, with the sigma and pi components perpendicular to the wavevectors, is presented. It is found that the use of Cartesian coordinate systems can provide correct boundary conditions in determining the wavefield amplitudes, thus leading to a rigorous and general calculation scheme for dynamical diffraction from surfaces and interfaces.

  13. Transformation from angle-action variables to Cartesian coordinates for polyatomic reactions.

    PubMed

    González-Martínez, M L; Bonnet, L; Larrégaray, P; Rayez, J-C; Rubayo-Soneira, J

    2009-03-21

    The transformation from angle-action variables to Cartesian coordinates is an important step of the semiclassical description of bimolecular collisions and photofragmentations. The basic reason is that dynamical conditions corresponding to molecular beam experiments are ideally generated in angle-action variables, whereas the classical equations of motion are ideally solved in Cartesian coordinates by standard numerical approaches. To our knowledge, this transformation is available in the literature only for atom-diatom arrangements. The goal of the present work is to derive it for diatom-polyatom ones. The analogous transformation for any type of arrangement may then be straightforwardly deduced from that presented here.

  14. Fully Isotropic Fast Marching Methods on Cartesian Grids.

    PubMed

    Appia, Vikram; Yezzi, Anthony

    2010-01-01

    The existing Fast Marching methods which are used to solve the Eikonal equation use a locally continuous model to estimate the accumulated cost, but a discontinuous (discretized) model for the traveling cost around each grid point. Because the accumulated cost and the traveling (local) cost are treated differently, the estimate of the accumulated cost at any point will vary based on the direction of the arriving front. Instead we propose to estimate the traveling cost at each grid point based on a locally continuous model, where we will interpolate the traveling cost along the direction of the propagating front. We further choose an interpolation scheme that is not biased by the direction of the front. Thus making the fast marching process truly isotropic. We show the significance of removing the directional bias in the computation of the cost in certain applications of fast marching method. We also compare the accuracy and computation times of our proposed methods with the existing state of the art fast marching techniques to demonstrate the superiority of our method.

  15. Parallel Unsteady Overset Mesh Methodology for a Multi-Solver Paradigm with Adaptive Cartesian Grids

    DTIC Science & Technology

    2008-08-21

    a multi-stage Runge - Kutta time-stepping framework and is capable of up to fifth-order accurate spatial discretizations. Further, the Cartesian grids...cutting methodology such that no user inter- vention or explicit hole-map specification is necessary. The capabilities and performance of the package are...application to rotorcraft aerodynamics. Several Domain-Connectivity approaches have been investigated in the past by various research groups . The

  16. Geometry optimization for peptides and proteins: comparison of Cartesian and internal coordinates.

    PubMed

    Koslover, Elena F; Wales, David J

    2007-12-21

    We present the results of several benchmarks comparing the relative efficiency of different coordinate systems in optimizing polypeptide geometries. Cartesian, natural internal, and primitive internal coordinates are employed in quasi-Newton minimization for a variety of biomolecules. The peptides and proteins used in these benchmarks range in size from 16 to 999 residues. They vary in complexity from polyalanine helices to a beta-barrel enzyme. We find that the relative performance of the different coordinate systems depends on the parameters of the optimization method, the starting point for the optimization, and the size of the system studied. In general, internal coordinates were found to be advantageous for small peptides. For larger structures, Cartesians appear to be more efficient for empirical potentials where the energy and gradient can be evaluated relatively quickly compared to the cost of the coordinate transformations.

  17. Grid-coordinate generation program

    USGS Publications Warehouse

    Cosner, Oliver J.; Horwich, Esther

    1974-01-01

    This program description of the grid-coordinate generation program is written for computer users who are familiar with digital aquifer models. The program computes the coordinates for a variable grid -used in the 'Pinder Model' (a finite-difference aquifer simulator), for input to the CalComp GPCP (general purpose contouring program). The program adjusts the y-value by a user-supplied constant in order to transpose the origin of the model grid from the upper left-hand corner to the lower left-hand corner of the grid. The user has the options of, (1.) choosing the boundaries of the plot; (2.) adjusting the z-values (altitudes) by a constant; (3.) deleting superfluous z-values and (4.) subtracting the simulated surfaces from each other to obtain the decline. Output of this program includes the fixed format CNTL data cards and the other data cards required for input to GPCP. The output from GPCP then is used to produce a potentiometric map or a decline map by means of the CalComp plotter.

  18. Large-eddy simulation of wind turbine wake interactions on locally refined Cartesian grids

    NASA Astrophysics Data System (ADS)

    Angelidis, Dionysios; Sotiropoulos, Fotis

    2014-11-01

    Performing high-fidelity numerical simulations of turbulent flow in wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the turbine wakes and turbine/turbine interactions. The discretization of the governing equations on structured grids for mesoscale calculations may not be the most efficient approach for resolving the large disparity of spatial scales. A 3D Cartesian grid refinement method enabling the efficient coupling of the Actuator Line Model (ALM) with locally refined unstructured Cartesian grids adapted to accurately resolve tip vortices and multi-turbine interactions, is presented. Second order schemes are employed for the discretization of the incompressible Navier-Stokes equations in a hybrid staggered/non-staggered formulation coupled with a fractional step method that ensures the satisfaction of local mass conservation to machine zero. The current approach enables multi-resolution LES of turbulent flow in multi-turbine wind farms. The numerical simulations are in good agreement with experimental measurements and are able to resolve the rich dynamics of turbine wakes on grids containing only a small fraction of the grid nodes that would be required in simulations without local mesh refinement. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the National Science Foundation under Award number NSF PFI:BIC 1318201.

  19. A Cartesian coordinate system for human cerebral cortex.

    PubMed

    Li, David F; Freeman, Alan W; Tran-Dinh, Hoang; Morris, John G

    2003-05-30

    The most commonly used method for specifying the locations of functional areas in the human cerebral cortex is the coordinate system of Talairach and Tournoux (Co-planar Stereotaxic Altas of The Human Brain (1988) Georg Thieme Verlag, Stuttgart). It was designed to locate subcortical nuclei by reference to an axis joining the anterior and posterior commissures. The coordinate system has difficulties, however, when applied to cortical locations: (1) it can be difficult to locate the posterior commissure (PC); (2) the fundamental axis is short, and errors in specifying the axis lead to large errors at the cortical surface; (3) there is no normalisation for brain size. We sought to rectify these problems with a new coordinate system, the Sydney system, in which the fundamental axis runs in the medial sagittal plane from the anterior edge of the corpus callosum to the posterior end of the parieto-occipital sulcus. Normalisation is achieved by dividing all distances by the length of the fundamental axis. Using functionally important points and anatomical landmarks on cadaveric specimens and magnetic resonance images (MRI), three-dimensional coordinates were measured in both the Talairach and Sydney systems. The Sydney system has the following advantages over the Talairach system: (1) the fundamental axis is more than four times longer and is easier to identify; (2) the Sydney system is more precise, in that it reduces the spread of points across the sample; (3) the normalised coordinates allow locations to be compared across individuals, regardless of brain size. We conclude that for the mapping of cortical areas, the Sydney system is potentially an improvement on Talairach's.

  20. A conservative finite volume method for incompressible Navier-Stokes equations on locally refined nested Cartesian grids

    NASA Astrophysics Data System (ADS)

    Sifounakis, Adamandios; Lee, Sangseung; You, Donghyun

    2016-12-01

    A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher-order conservation principles - i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms. Hanging nodes at the interface are virtually slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is straight-forward to implement and shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids.

  1. Contrast sensitivity functions to stimuli defined in Cartesian, polar and hyperbolic coordinates.

    PubMed

    Zana, Y; Cavalcanti, A C G T

    2005-01-01

    Recent electrophysiological studies indicate that cells in the LGN, V1, V2, and V4 areas in monkeys are specifically sensitive to Cartesian, polar and hyperbolic stimuli. We have characterized the contrast sensitivity functions (CSF) to stimuli defined in these coordinates with the two-alternatives forced-choice paradigm. CSFs to Cartesian, concentric, and hyperbolic stimuli have had similar shapes, with peak sensitivity at approximately 3 c/deg. However, the Cartesian CSF peak sensitivity has been at least 0.1 log units higher than that to stimuli in any other coordinate system. The concentric-Bessel CSF has a low-pass shape, peaking at 1.5 c/deg or below. The radial CSF has a bell shape with maximum sensitivity at 8 c/360 degrees. Only the concentric-Bessel CSF could be explained in terms of the components of maximum amplitude of the Fourier transform. Neural models, which in previous studies predicted the responses to Cartesian and polar Glass patterns, failed to account for the full CSFs data.

  2. Computing reaching dynamics in motor cortex with Cartesian spatial coordinates.

    PubMed

    Tanaka, Hirokazu; Sejnowski, Terrence J

    2013-02-01

    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.

  3. The von Neumann basis in non-Cartesian coordinates: application to floppy triatomic molecules.

    PubMed

    Shimshovitz, Asaf; Bačić, Zlatko; Tannor, David J

    2014-12-21

    We extend the periodic von Neumann basis to non-Cartesian coordinates. The bound states of two isomerizing triatomic molecules, LiCN/LiNC and HCN/HNC, are calculated using the vibrational Hamiltonian in Jacobi coordinates. The phase space localization of the basis functions leads to a flexible and accurate representation of the Hamiltonian. This results in significant savings compared to a basis localized just in coordinate space. The favorable scaling of the method with dimensionality makes it promising for applications to larger systems.

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

    PubMed

    Batu, Vedat

    2014-01-01

    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.

  5. Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates.

    PubMed

    Cámara, Alejandro; Alieva, Tatiana; Rodrigo, José A; Calvo, María L

    2009-06-01

    We propose a simple approach for the phase space tomography reconstruction of the Wigner distribution of paraxial optical beams separable in Cartesian coordinates. It is based on the measurements of the antisymmetric fractional Fourier transform power spectra, which can be taken using a flexible optical setup consisting of four cylindrical lenses. The numerical simulations and the experimental results clearly demonstrate the feasibility of the proposed scheme.

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

    SciTech Connect

    Johansen, H.; Colella, P.

    1997-01-31

    The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.

  7. Development of a Cartesian-grid finite-volume characteristic flux model for marine applications

    NASA Astrophysics Data System (ADS)

    Leroy, C.; Le Touzé, D.; Alessandrini, B.

    2010-06-01

    A Finite Volume method based on Characteristic Fluxes for compressible fluids is developed. An explicit cell-centered resolution is adopted, where second-order accuracy is provided by using a MUSCL scheme with Sweby or Superbee limiters for the hyperbolic part. Resolution is performed on a generic unstructured Cartesian grid, where solid boundaries are handled by a Cut-Cell method. Interfaces are explicitely advected in a non-diffusive way, ensuring local mass conservation of each fluid. An improved cell cutting has been developed to handle boundaries of arbitrary geometrical complexity. The mesh density is locally adapted to provide accuracy along these boundaries, which can be fixed or move inside the mesh. Instead of using a polygon clipping algorithm, we use the Voxel traversal algorithm coupled with a local floodfill scanline to intersect 2D or 3D boundary surface meshes with the fixed Cartesian grid. Small cells stability problem near the boundaries is solved using a fully conservative merging method. Inflow and outflow conditions are also implemented in the model. The solver is validated on 2D academic test cases, such as the flow past a cylinder. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the mesh. Extension to 3D is presently being implemented and first results will be presented at the conference.

  8. On the diffuse interface method using a dual-resolution Cartesian grid

    NASA Astrophysics Data System (ADS)

    Ding, Hang; Yuan, Cheng-jun

    2014-09-01

    We investigate the applicability and performance of diffuse interface methods on a dual-resolution grid in solving two-phase flows. In the diffuse interface methods, the interface thickness represents a cut-off length scale in resolving the interfacial dynamics, and it was found that an apparent loss of mass occurs when the interface thickness is comparable to the length scale of flows [24]. From the accuracy and mass conservation point of view, it is desirable to have a thin interface in simulations. We propose to use a dual-resolution Cartesian grid, on which a finer resolution is applied to the volume fraction C than that for the velocity and pressure fields. Because the computation of C field is rather inexpensive compared to that required by velocity and pressure fields, dual-resolution grids can significantly increase the resolution of the interface with only a slight increase of computational cost, as compared to the single-resolution grid. The solution couplings between the fine grid for C and the coarse grid (for velocity and pressure) are delicately designed, to make sure that the interpolated velocity is divergence-free at a discrete level and that the mass and surface tension force are conserved. A variety of numerical tests have been performed to validate the method and check its performance. The dual-resolution grid appears to save nearly 70% of the computational time in two-dimensional simulations and 80% in three-dimensional simulations, and produces nearly the same results as the single-resolution grid. Quantitative comparisons are made with previous studies, including Rayleigh Taylor instability, steadily rising bubble, and partial coalescence of a drop into a pool, and good agreement has been achieved. Finally, results are presented for the deformation and breakup of three-dimensional drops in simple shear flows.

  9. Linear transformation of anharmonic molecular force constants between normal and Cartesian coordinates.

    PubMed

    Mackie, Cameron J; Candian, Alessandra; Huang, Xinchuan; Lee, Timothy J; Tielens, Alexander G G M

    2015-06-28

    A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D(+).

  10. Linear transformation of anharmonic molecular force constants between normal and Cartesian coordinates

    NASA Astrophysics Data System (ADS)

    Mackie, Cameron J.; Candian, Alessandra; Huang, Xinchuan; Lee, Timothy J.; Tielens, Alexander G. G. M.

    2015-06-01

    A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D+.

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

    NASA Astrophysics Data System (ADS)

    Emblemsvag, Jo-Einar

    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.

  12. Cartesian-Grid Simulations of a Canard-Controlled Missile with a Free-Spinning Tail

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    The proposed paper presents a series of simulations of a geometrically complex, canard-controlled, supersonic missile with free-spinning tail fins. Time-dependent simulations were performed using an inviscid Cartesian-grid-based method with results compared to both experimental data and high-resolution Navier-Stokes computations. At fixed free stream conditions and canard deflections, the tail spin rate was iteratively determined such that the net rolling moment on the empennage is zero. This rate corresponds to the time-asymptotic rate of the free-to-spin fin system. After obtaining spin-averaged aerodynamic coefficients for the missile, the investigation seeks a fixed-tail approximation to the spin-averaged aerodynamic coefficients, and examines the validity of this approximation over a variety of freestream conditions.

  13. A Higher-Order Boundary Treatment for Cartesian-Grid Methods

    NASA Astrophysics Data System (ADS)

    Forrer, Hans; Jeltsch, Rolf

    1998-03-01

    The Euler equations describe the flow phenomena of compressible inviscid gas dynamics. We simulate such flows using a higher-order Cartesian-grid method, together with a special treatment for the cells cut by the boundary of an object. A new method for the treatment of the boundary is described where these cut boundary cells are maintained as whole cells rather than as cut cells, thus avoiding stability problems. The method is second-order accurate in one dimension and higher-order accurate in two dimensions but not strictly conservative; however, we show that this error in the conservation does not lead to spurious phenomena on some representative test calculations. The advantages of the new boundary treatment are that it is higher-order accurate, that it is independent of the applied method, and that it is simple.

  14. A Cartesian Grid Generation Method Considering a Complicated Cell Geometry at the Body Surface

    NASA Astrophysics Data System (ADS)

    Lahur, Paulus R.; Nakamura, Yoshiaki

    A cell-splitting method for Cartesian grid generation that has the capability of taking into account the cases of thin body and sharp edge is proposed in this paper. Such cases are frequently found when solving the flow around a very thin wing, such as that of a supersonic transport (SST). The method has also been extended to treat the problem of multiple solid regions within a cell, which is sometimes encountered at a highly curved body surface. Validation of the method proposed here is carried out on a sharp, thin double wedge in a supersonic flow, where significant improvements in accuracy are achieved at the cost of a small increase in the number of cells. Furthermore, application of the present method to a model of SST shows its effectiveness on a three-dimensional, realistic geometry. As a result of making a pseudo-planar approximation for body surface elements, the total number of body surface elements was reduced by a factor of about 3.2 in this application. Local grid refinement by relocating grid cells to a curved surface is also proposed, so that a more accurate solution is obtained with a reasonable number of cells.

  15. Principal component analysis of molecular dynamics: on the use of Cartesian vs. internal coordinates.

    PubMed

    Sittel, Florian; Jain, Abhinav; Stock, Gerhard

    2014-07-07

    Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail.

  16. Simulating hydrodynamics in a spring-fed estuary using a three-dimensional unstructured Cartesian grid model

    NASA Astrophysics Data System (ADS)

    Chen, XinJian

    2012-12-01

    This paper presents an application of a three-dimensional unstructured Cartesian grid model (Chen, 2011) to a real-world case, namely the Crystal River/Kings Bay system located on the Gulf coast of the Florida peninsula of the United States. Crystal River/Kings Bay is a spring-fed estuarine system which is believed to be the largest natural refuge in the United States for manatees during the coldest days in winter because of the existence of a large amount of discharge out of numerous spring vents at the bottom of Kings Bay. The unstructured Cartesian grid model was used to simulate hydrodynamics, including salinity transport processes and thermodynamics, in the estuary during a 34-month period from April 2007 to February 2010. Although there are some unidentified uncertainties in quantifying flow rates from the spring vents and salinity variations in spring flows, simulated water elevations, salinities, temperatures, and cross-sectional flux all match well or very well with measured real-time field data. This suggests that the unstructured Cartesian grid model can adequately simulate hydrodynamics in a complex shallow water system such as Crystal River/Kings Bay and the numerical theory for the unstructured Cartesian grid model works properly. The successful simulation of hydrodynamics in the estuarine system also suggests that an empirical formula that relates the spring discharge with the water level in Kings Bay and the groundwater level measured in a nearby well is reasonable.

  17. Cartesian beams.

    PubMed

    Bandres, Miguel A; Gutiérrez-Vega, Julio C

    2007-12-01

    A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integration are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.

  18. Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Myhill, Elizabeth A.; Boss, Alan P.

    1993-01-01

    In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

  19. Euler Technology Assessment for Preliminary Aircraft Design: Compressibility Predictions by Employing the Cartesian Unstructured Grid SPLITFLOW Code

    NASA Technical Reports Server (NTRS)

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

    1996-01-01

    The objective of the second phase of the Euler Technology Assessment program was to evaluate the ability of Euler computational fluid dynamics codes to predict compressible flow effects over a generic fighter wind tunnel model. This portion of the study was conducted by Lockheed Martin Tactical Aircraft Systems, using an in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaption of the volume grid during the solution to resolve high-gradient regions. The SPLITFLOW code predictions of configuration forces and moments are shown to be adequate for preliminary design, including predictions of sideslip effects and the effects of geometry variations at low and high angles-of-attack. The transonic pressure prediction capabilities of SPLITFLOW are shown to be improved over subsonic comparisons. The time required to generate the results from initial surface data is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

  20. A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

    Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

  1. A Domain-Decomposed Multi-Level Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

    NASA Technical Reports Server (NTRS)

    Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.; Nixon, David (Technical Monitor)

    1998-01-01

    The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.

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

    PubMed

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

    2015-02-05

    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 (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ 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 ϕ 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.

  3. Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates.

    PubMed

    Cerezo, Javier; Santoro, Fabrizio

    2016-10-11

    Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q1-frame, where Q1 are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q1-frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal

  4. A Computer Program To Increase Comprehension of the Cartesian Rectangular Coordinate System in High School Pre-Algebra Students.

    ERIC Educational Resources Information Center

    Exley, I. Sheck

    The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…

  5. X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates.

    PubMed

    Cao, Guohua; Hamilton, Theron J; Rose-Petruck, Christoph; Diebold, Gerald J

    2007-04-01

    In-line, x-ray phase-contrast imaging is responsive to both phase changes and absorption as the x radiation traverses a body. Expressions are derived for phase-contrast imaging of objects having transmission functions separable in Cartesian coordinates. Starting from the Fresnel-Kirchhoff integral formula for image formation, an expression is found for the phase-contrast image produced by an x-ray source with nonvanishing dimensions. This expression is evaluated in limiting cases where the source-to-object distance is large, where the source acts as a point source, and where the weak phase approximation is valid. The integral expression for the image is evaluated for objects with simple geometrical shapes, showing the influence of the source dimensions on the visibility of phase-contrast features. The expressions derived here are evaluated for cases where the magnification is substantially greater than one as would be employed in biological imaging. Experiments are reported using the in-line phase-contrast imaging method with a microfocus x-ray source and a CCD camera.

  6. Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

    NASA Astrophysics Data System (ADS)

    Hergarten, S.; Robl, J.

    2015-03-01

    We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application - an almost horizontal fluid table - is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open-source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. Testing the results against analytical solutions and the proprietary avalanche model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool for assisting regional-scale natural hazard studies.

  7. Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy.

    PubMed

    Issack, Bilkiss B; Roy, Pierre-Nicholas

    2005-08-22

    An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

  8. Cartesian Methods for the Shallow Water Equations on a Sphere

    SciTech Connect

    Drake, J.B.

    2000-02-14

    The shallow water equations in a spherical geometry are solved using a 3-dimensional Cartesian method. Spatial discretization of the 2-dimensional, horizontal differential operators is based on the Cartesian form of the spherical harmonics and an icosahedral (spherical) grid. Computational velocities are expressed in Cartesian coordinates so that a problem with a singularity at the pole is avoided. Solution of auxiliary elliptic equations is also not necessary. A comparison is made between the standard form of the Cartesian equations and a rotational form using a standard set of test problems. Error measures and conservation properties of the method are reported for the test problems.

  9. Development of multiphase Navier-Stokes simulation capability for turbulent gas flow over laminar liquid for Cartesian grids

    NASA Astrophysics Data System (ADS)

    Miao, Sha; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad

    2015-11-01

    This work presents a novel and efficient Cartesian-grid based simulation capability for the study of an incompressible, turbulent gas layer over a liquid flow with disparate Reynolds numbers in two phases. This capability couples a turbulent gas-flow solver and a liquid-layer based on a second-order accurate Boundary Data Immersion Method (BDIM) at the deformable interface. The turbulent gas flow solver solves the incompressible Navier-Stokes equations via direct numerical simulation or through turbulence closure (unsteady Reynolds-Averaged Navier-Stokes Models) for Reynolds numbers O(106). In this application, a laminar liquid layer solution is obtained from depth-integrated Navier-Stokes equations utilizing shallow water wave assumptions. The immersed boundary method (BDIM) enforces the coupling at the deformable interface, the boundary conditions to turbulence closure equations and defines the domain geometry on the Cartesian grid. Validations are made for the turbulent gas channel flow over high-viscosity liquid. This simulation capability can be applied to problems in the oil and industrial sector such as channel and pipe flows with heavy oils as well as wind wave generation in shallow waters. Sponsored by the Chevron Energy Technology Company.

  10. A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modeling

    NASA Astrophysics Data System (ADS)

    Qu, Yingming; Huang, Jianping; Li, Zhenchun; Li, Jinli

    2016-11-01

    Seismic wave propagation in a fluid-solid environment cannot be simulated with a single wave equation, but can be described by use of the acoustic and viscoelastic wave equations for their respective fluid and solid parts. Proper boundary conditions at the fluid-solid interface based on the relationship between pressure and stress are crucial when combining the two different wave equations. Traditional finite difference methods (FDM) have had difficulties in dealing with the irregular fluid-solid interface topography. The Cartesian grids discretization leads to artificial reflections and diffractions during the conversion between acoustic wave and elastic waves. We propose a variable coordinate transformation methodology to simulate seismic waves in a fluid-solid environment. An irregular fluid-solid interface can be transformed into a horizontal interface, so that pressure and stress can be well converted. We also introduce a multi-block coordinate transformation (MCT) method which meshes each layer with curvilinear grids to transform the interface topography into a horizontal one, thereby allocating vertical sampling points adaptively. The grid size is determined adaptively based on the shape and the parameters of the target area, which reduces in size in when the layers are thin or exhibit low velocities. A Lebedev-standard staggered grid (LSSG) scheme is applied to the MCT method to reduce both the computational cost associated with the Lebedev grid (LG) scheme and the instability in the auxiliary coordinate system when using a standard staggered grid scheme.

  11. A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modelling

    NASA Astrophysics Data System (ADS)

    Qu, Yingming; Huang, Jianping; Li, Zhenchun; Li, Jinli

    2017-03-01

    Seismic wave propagation in a fluid-solid environment cannot be simulated with a single wave equation, but can be described by use of the acoustic and viscoelastic wave equations for their respective fluid and solid parts. Proper boundary conditions at the fluid-solid interface based on the relationship between pressure and stress are crucial when combining the two different wave equations. Traditional finite difference methods have had difficulties in dealing with the irregular fluid-solid interface topography. The Cartesian grids discretization leads to artificial reflections and diffractions during the conversion between acoustic wave and elastic waves. We propose a variable coordinate transformation methodology to simulate seismic waves in a fluid-solid environment. An irregular fluid-solid interface can be transformed into a horizontal interface, so that pressure and stress can be well converted. We also introduce a multiblock coordinate transformation (MCT) method which meshes each layer with curvilinear grids to transform the interface topography into a horizontal one, thereby allocating vertical sampling points adaptively. The grid size is determined adaptively based on the shape and the parameters of the target area, which reduces in size in when the layers are thin or exhibit low velocities. A Lebedev-standard staggered grid scheme is applied to the MCT method to reduce both the computational cost associated with the Lebedev grid scheme and the instability in the auxiliary coordinate system when using a standard staggered grid scheme.

  12. Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell’s equations on Cartesian grids

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

    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.

  13. Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures.

    PubMed

    Cerezo, Javier; Zúñiga, José; Requena, Alberto; Ávila Ferrer, Francisco J; Santoro, Fabrizio

    2013-11-12

    When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.

  14. Quantum molecular dynamics of hydrogen bonded complexes of rigid molecules using the semiclassical initial value representation in Cartesian coordinates.

    PubMed

    Issack, Bilkiss B; Roy, Pierre-Nicholas

    2007-08-07

    Semiclassical initial value representation calculations are performed for the constrained water dimer in Cartesian coordinates. The study represents the first application of a previously reported method [Issak and Roy, J. Chem. Phys. 123, 084103 (2005); 126, 024111 (2007)] to a molecular cluster. Bound state energies are calculated for a dimer of rigid water molecules (H2O)2 as well as its deuterated form (D2O)2. The results show that the approach fares well with respect to accuracy in capturing quantum effects in intermolecular interactions.

  15. Wave simulation in 2D heterogeneous transversely isotropic porous media with fractional attenuation: A Cartesian grid approach

    NASA Astrophysics Data System (ADS)

    Blanc, Emilie; Chiavassa, Guillaume; Lombard, Bruno

    2014-10-01

    A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, these coefficients introduce shifted fractional derivatives of order 1/2, involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation) model. The properties of both the Biot-JKD and the Biot-DA models are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, two approaches are analyzed: Gaussian quadratures and optimization methods in the frequency range of interest. The nonlinear optimization is shown to be the better way of determination. A splitting strategy is then applied to approximate numerically the Biot-DA equations. The propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. An immersed interface method is implemented to take into account heterogeneous media on a Cartesian grid and to discretize the jump conditions at interfaces. Numerical experiments are presented. Comparisons with analytical solutions show the efficiency and the accuracy of the approach, and some numerical experiments are performed to investigate wave phenomena in complex media, such as multiple scattering across a set of random scatterers.

  16. Semiclassical initial value representation treatment of a hydrogen bonded complex of rigid water molecules from a single trajectory in Cartesian coordinates.

    PubMed

    Issack, Bilkiss B; Roy, Pierre-Nicholas

    2007-10-14

    A semiclassical initial value representation approach for molecular systems in Cartesian coordinates is combined with a recently proposed time averaging technique [J. Chem. Phys. 118, 7174 (2003)]. It is shown that a single trajectory can yield the zero-point energy of the water dimer with good accuracy for the model chosen when compared to fully constrained Cartesian semiclassical calculations. The convergence with respect to the number of averaging time origins is discussed.

  17. Applications of the Cartesian coordinate tensor transfer technique in the simulations of vibrational circular dichroism spectra of oligonucleotides.

    PubMed

    Andrushchenko, Valery; Bouř, Petr

    2010-01-01

    The application of the Cartesian coordinate tensor transfer (CCT) technique for simulations of the IR absorption and vibrational circular dichroism (VCD) spectra of relatively large nucleic acid fragments is demonstrated on several case studies. The approach is based on direct ab initio calculations of atomic tensors, determining molecular properties, for relatively small fragments, and subsequent transfer of these tensors to the larger systems in Cartesian coordinates. This procedure enables precise computations of vibrational spectra for large biomolecular systems, currently with up to several thousands of atoms. The versatile ability of the CCT methods is emphasized on the examples of VCD and IR absorption spectra calculations for B- and Z-forms of DNA, single-, double-, and triple-stranded RNA helices and DNA structures with different base content and sequences. The development and recent improvements of the methodology are followed, including utilization of the constrained normal mode optimization (NMO) strategy and combined quantum mechanics and molecular dynamics simulations. Advantages, drawbacks, and recommendations for future improvements of the CCT method as applied to nucleic acid spectra calculations are discussed.

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

    SciTech Connect

    Walters, W.F.

    1985-01-01

    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.

  19. A Fully Conservative and Entropy Preserving Cut-Cell Method for Incompressible Viscous Flows on Staggered Cartesian Grids

    NASA Astrophysics Data System (ADS)

    Le Chenadec, Vincent; Bay, Yong Yi

    2015-11-01

    The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods also introduce new challenges, in that the formulation of accurate and well-posed discrete operators is not trivial. A cut-cell method for the solution of the incompressible Navier-Stokes equation is proposed for staggered Cartesian grids. In both scalar and vector cases, the emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. This ensures mass, momentum and kinetic energy conservation. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The accuracy of method is finally assessed in standard test cases.

  20. Simulation of a prescribed fruitfly flapping motion by the ALE-GFD method on a hybrid Cartesian-meshfree grid

    NASA Astrophysics Data System (ADS)

    Trong, N. T.; Lim, T. T.; Yeo, K. S.

    2011-11-01

    The flapping-wing aerodynamics of insects has been a subject of immense interest for many years. The Arbitrary Lagrangian-Eulerian - Generalized Finite Difference (ALE-GFD) computational scheme on hybrid convecting Cartesian-meshfree grid systems represents a viable alternative to existing mesh-based and immersed boundary approaches for simulating the highly complex and unsteady flows generated by the flapping wings of insects. The three-dimensional flapping-wing flows of a fruitfly (Drosophila) are simulated in the present study. As the forces generated are very sensitive to the acceleration of the wings, a smoothing process was applied on the flapping kinematics to suppress non-physical fluctuations and spikes from the force outcome. The resulting lift and drag forces are then validated with the experimental results, obtained from a parallel experimental study conducted by the research group, measured on a fruitfly-like wing profile executing the identical motion. The excellent agreement between the results demonstrates the feasibility and efficacy of the ALE-GFD numerical approach.

  1. Balancing Area Coordination: Efficiently Integrating Renewable Energy Into the Grid, Greening the Grid

    SciTech Connect

    Katz, Jessica; Denholm, Paul; Cochran, Jaquelin

    2015-06-01

    Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. Coordinating balancing area operation can promote more cost and resource efficient integration of variable renewable energy, such as wind and solar, into power systems. This efficiency is achieved by sharing or coordinating balancing resources and operating reserves across larger geographic boundaries.

  2. Early and Late Inhibitions Elicited by a Peripheral Visual Cue on Manual Response to a Visual Target: Are They Based on Cartesian Coordinates?

    ERIC Educational Resources Information Center

    Gawryszewski, Luiz G.; Carreiro, Luiz Renato R.; Magalhaes, Fabio V.

    2005-01-01

    A non-informative cue (C) elicits an inhibition of manual reaction time (MRT) to a visual target (T). We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7[degrees]) positions, the C-T angular distances (in polar…

  3. The effect of object-centered instructions in Cartesian and polar coordinates on saccade vector.

    PubMed

    Edelman, Jay A; Mieses, Alexa M; Konnova, Kira; Shiu, David

    2017-03-01

    Express saccades (ES) are the most reflexive saccadic eye movements, with very short reaction times of 70-110 ms. It is likely that ES have the shortest saccade reaction times (SRTs) possible given the known physiological and anatomical delays present in sensory and motor systems. Nevertheless, it has been demonstrated that a vector displacement of ES to spatially extended stimuli can be influenced by spatial cognition. Edelman, Kristjansson, and Nakayama (2007) found that when two horizontally separated visual stimuli appear at a random location, the spatial vector, but not the reaction time, of human ES is strongly influenced by an instruction to make a saccade to one side (either left or right) of a visual stimulus array. Presently, we attempt to extend these findings of cognitive effects on saccades in three ways: (a) determining whether ES could be affected by other types of spatial instructions: vertical, polar amplitude, and polar direction; (b) determining whether these spatial effects increased with practice; and (c) determining how these effects depended on SRTs. The results demonstrate that both types of Cartesian as well as polar amplitude instructions strongly affect ES vector, but only modestly affect SRTs. Polar direction instructions had sizable effects only on nonreflexive saccades where the visual stimuli could be viewed for several hundred milliseconds prior to saccade execution. Short- (trial order within a block) and long-term (experience across several sessions) practice had little effect, though the effect of instruction increased with SRT. Such findings suggest a generalized, innate ability of cognition to affect the most reflexive saccadic eye movements.

  4. The effect of object-centered instructions in Cartesian and polar coordinates on saccade vector

    PubMed Central

    Edelman, Jay A.; Mieses, Alexa M.; Konnova, Kira; Shiu, David

    2017-01-01

    Express saccades (ES) are the most reflexive saccadic eye movements, with very short reaction times of 70–110 ms. It is likely that ES have the shortest saccade reaction times (SRTs) possible given the known physiological and anatomical delays present in sensory and motor systems. Nevertheless, it has been demonstrated that a vector displacement of ES to spatially extended stimuli can be influenced by spatial cognition. Edelman, Kristjansson, and Nakayama (2007) found that when two horizontally separated visual stimuli appear at a random location, the spatial vector, but not the reaction time, of human ES is strongly influenced by an instruction to make a saccade to one side (either left or right) of a visual stimulus array. Presently, we attempt to extend these findings of cognitive effects on saccades in three ways: (a) determining whether ES could be affected by other types of spatial instructions: vertical, polar amplitude, and polar direction; (b) determining whether these spatial effects increased with practice; and (c) determining how these effects depended on SRTs. The results demonstrate that both types of Cartesian as well as polar amplitude instructions strongly affect ES vector, but only modestly affect SRTs. Polar direction instructions had sizable effects only on nonreflexive saccades where the visual stimuli could be viewed for several hundred milliseconds prior to saccade execution. Short- (trial order within a block) and long-term (experience across several sessions) practice had little effect, though the effect of instruction increased with SRT. Such findings suggest a generalized, innate ability of cognition to affect the most reflexive saccadic eye movements. PMID:28265650

  5. Hybrid freeform TIR optics construction in Cartesian coordinate system: a new composite ray mapping method

    NASA Astrophysics Data System (ADS)

    Ma, Donglin; Feng, Zexin; Wang, Chengliang; Liang, Rongguang

    2015-09-01

    In this paper, we propose a new composite ray mapping method to design freeform total internal reflective (TIR) optics for LED illumination. We sample the ray intensity distribution into rectangular grids which have the best topological match to those rectangular grids on the target surface. With the multiple-to-one mapping relationships between the source intensity distribution and target irradiance distribution, we can construct the freeform TIR surfaces and freeform refractive surface using Snell's law. Compared to our previous design using uv-θϕ composite ray mapping method, this design approach is expected to have much less surface error and improve the illumination uniformity further because of the better topological match. In addition, due to the overlapping mechanism by multiple-to-one (composite) ray mapping, the method could lead to a more robust freeform optics compared to traditional freeform optics designs.

  6. Efficient generation of the cartesian coordinates of truncated icosahedron and related polyhedra.

    PubMed

    Hosoya, H; Maruyama, Y

    2001-01-01

    Efficient algorithms for deriving the analytical expressions of the rectangular coordinates of the vertices of regular polyhedra and truncated icosahedron inscribed in a cube is described and the results are exposed. Various characteristic quantities of the geometrical structure of truncated icosahedron are obtained. Kaleidoscopes for projecting the truncated icosahedron are discussed.

  7. Relationship between Students' Understanding of Functions in Cartesian and Polar Coordinate Systems

    ERIC Educational Resources Information Center

    Montiel, Mariana; Vidakovic, Draga; Kabael, Tangul

    2009-01-01

    The present study was implemented as a prelude to a study on the generalization of the single variable function concept to multivariate calculus. In the present study we analyze students' mental processes and adjustments, as they are being exposed to single variable calculus with polar coordinates. The results show that there appears to be a…

  8. A topological coordinate system for the diamond cubic grid.

    PubMed

    Čomić, Lidija; Nagy, Benedek

    2016-09-01

    Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.

  9. On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.

    PubMed

    Dagdug, Leonardo; García-Chung, Angel A; Chacón-Acosta, Guillermo

    2016-08-21

    We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.

  10. On the description of Brownian particles in confinement on a non-Cartesian coordinates basis

    NASA Astrophysics Data System (ADS)

    Dagdug, Leonardo; García-Chung, Angel A.; Chacón-Acosta, Guillermo

    2016-08-01

    We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.

  11. Robust multigrid for high-order discontinuous Galerkin methods: A fast Poisson solver suitable for high-aspect ratio Cartesian grids

    NASA Astrophysics Data System (ADS)

    Stiller, Jörg

    2016-12-01

    We present a polynomial multigrid method for nodal interior penalty and local discontinuous Galerkin formulations of the Poisson equation on Cartesian grids. For smoothing we propose two classes of overlapping Schwarz methods. The first class comprises element-centered and the second face-centered methods. Within both classes we identify methods that achieve superior convergence rates, prove robust with respect to the mesh spacing and the polynomial order, at least up to P = 32. Consequent structure exploitation yields a computational complexity of O (PN), where N is the number of unknowns. Further we demonstrate the suitability of the face-centered method for element aspect ratios up to 32.

  12. Computing UV/vis spectra from the adiabatic and vertical Franck-Condon schemes with the use of Cartesian and internal coordinates.

    PubMed

    Götze, Jan P; Karasulu, Bora; Thiel, Walter

    2013-12-21

    We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.

  13. Computing UV/vis spectra from the adiabatic and vertical Franck-Condon schemes with the use of Cartesian and internal coordinates

    SciTech Connect

    Götze, Jan P.; Karasulu, Bora; Thiel, Walter

    2013-12-21

    We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.

  14. An efficient game for vehicle-to-grid coordination problems in smart grids

    NASA Astrophysics Data System (ADS)

    Shi, Xingyu; Ma, Zhongjing

    2015-11-01

    Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey-Clarke-Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.

  15. A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

    SciTech Connect

    Crockett, Robert; Graves, Daniel; Colella, Phillip

    2009-10-23

    We present a method for solving Poisson and heat equations with discon- tinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materi- als, as described in Johansen& Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 106, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

  16. A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

    SciTech Connect

    Crockett, R.K.; Colella, P.; Graves, D.T.

    2011-04-01

    We present a method for solving Poisson and heat equations with discontinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in Johansen and Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10{sup 6}, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

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

    NASA Technical Reports Server (NTRS)

    Deane, Anil E.

    1996-01-01

    Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

  18. Concurrent negotiation and coordination for grid resource coallocation.

    PubMed

    Sim, Kwang Mong; Shi, Benyun

    2010-06-01

    Bolstering resource coallocation is essential for realizing the Grid vision, because computationally intensive applications often require multiple computing resources from different administrative domains. Given that resource providers and consumers may have different requirements, successfully obtaining commitments through concurrent negotiations with multiple resource providers to simultaneously access several resources is a very challenging task for consumers. The impetus of this paper is that it is one of the earliest works that consider a concurrent negotiation mechanism for Grid resource coallocation. The concurrent negotiation mechanism is designed for 1) managing (de)commitment of contracts through one-to-many negotiations and 2) coordination of multiple concurrent one-to-many negotiations between a consumer and multiple resource providers. The novel contributions of this paper are devising 1) a utility-oriented coordination (UOC) strategy, 2) three classes of commitment management strategies (CMSs) for concurrent negotiation, and 3) the negotiation protocols of consumers and providers. Implementing these ideas in a testbed, three series of experiments were carried out in a variety of settings to compare the following: 1) the CMSs in this paper with the work of others in a single one-to-many negotiation environment for one resource where decommitment is allowed for both provider and consumer agents; 2) the performance of the three classes of CMSs in different resource market types; and 3) the UOC strategy with the work of others [e.g., the patient coordination strategy (PCS )] for coordinating multiple concurrent negotiations. Empirical results show the following: 1) the UOC strategy achieved higher utility, faster negotiation speed, and higher success rates than PCS for different resource market types; and 2) the CMS in this paper achieved higher final utility than the CMS in other works. Additionally, the properties of the three classes of CMSs in

  19. Parallelization of TWOPORFLOW, a Cartesian Grid based Two-phase Porous Media Code for Transient Thermo-hydraulic Simulations

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

    TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.

  20. A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

    This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.

  1. A comparative study of molecular dynamics in Cartesian and in internal coordinates: dynamical instability in the latter caused by nonlinearity of the equations of motion.

    PubMed

    Lee, Sang-Ho; Palmo, Kim; Krimm, Samuel

    2007-04-30

    The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass-matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass-matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B-matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n-octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B-matrices for external rotations without imposing the Casimir-Eckart conditions.

  2. Recognizing Patterns In Log-Polar Coordinates

    NASA Technical Reports Server (NTRS)

    Weiman, Carl F. R.

    1992-01-01

    Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.

  3. The Evolution of the "Cartesian Connection"

    ERIC Educational Resources Information Center

    Anderson, Gail M.

    2008-01-01

    Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

  4. Agent Concept for Intelligent Distributed Coordination in the Electric Power Grid

    SciTech Connect

    SMATHERS, DOUGLAS C.; GOLDSMITH, STEVEN Y.

    2001-03-01

    Intelligent agents and multi-agent systems promise to take information management for real-time control of the power grid to a new level. This report presents our concept for intelligent agents to mediate and coordinate communications between Control Areas and Security Coordinators for real-time control of the power grid. An appendix describes the organizations and publications that deal with agent technologies.

  5. Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation

    NASA Astrophysics Data System (ADS)

    Manzhos, Sergei; Carrington, Tucker

    2016-12-01

    We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H2CO, we obtain a mean absolute error of less than 1 cm-1; with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm-1.

  6. Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation.

    PubMed

    Manzhos, Sergei; Carrington, Tucker

    2016-12-14

    We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H2CO, we obtain a mean absolute error of less than 1 cm(-1); with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm(-1).

  7. Electronic Absolute Cartesian Autocollimator

    NASA Technical Reports Server (NTRS)

    Leviton, Douglas B.

    2006-01-01

    An electronic absolute Cartesian autocollimator performs the same basic optical function as does a conventional all-optical or a conventional electronic autocollimator but differs in the nature of its optical target and the manner in which the position of the image of the target is measured. The term absolute in the name of this apparatus reflects the nature of the position measurement, which, unlike in a conventional electronic autocollimator, is based absolutely on the position of the image rather than on an assumed proportionality between the position and the levels of processed analog electronic signals. The term Cartesian in the name of this apparatus reflects the nature of its optical target. Figure 1 depicts the electronic functional blocks of an electronic absolute Cartesian autocollimator along with its basic optical layout, which is the same as that of a conventional autocollimator. Referring first to the optical layout and functions only, this or any autocollimator is used to measure the compound angular deviation of a flat datum mirror with respect to the optical axis of the autocollimator itself. The optical components include an illuminated target, a beam splitter, an objective or collimating lens, and a viewer or detector (described in more detail below) at a viewing plane. The target and the viewing planes are focal planes of the lens. Target light reflected by the datum mirror is imaged on the viewing plane at unit magnification by the collimating lens. If the normal to the datum mirror is parallel to the optical axis of the autocollimator, then the target image is centered on the viewing plane. Any angular deviation of the normal from the optical axis manifests itself as a lateral displacement of the target image from the center. The magnitude of the displacement is proportional to the focal length and to the magnitude (assumed to be small) of the angular deviation. The direction of the displacement is perpendicular to the axis about which the

  8. GRID3C: Computer program for generation of C type multilevel, three dimensional and boundary conforming periodic grids

    NASA Technical Reports Server (NTRS)

    Dulikravich, D. S.

    1982-01-01

    A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.

  9. Design and validation of a novel Cartesian biomechanical testing system with coordinated 6DOF real-time load control: application to the lumbar spine (L1-S, L4-L5).

    PubMed

    Kelly, Brian P; Bennett, Charles R

    2013-07-26

    Robotic methods applied to in-vitro biomechanical testing potentially offer more comprehensive evaluations however, standard position control algorithms make real-time load control problematic. This paper describes and evaluates a novel custom developed Cartesian force controlled biomechanical testing system with coordinated 6 degree of freedom (DOF) real-time load control. A custom developed 6-DOF serial manipulator with cascaded force over position control algorithms was designed, assembled, and programmed. Dial gauge tests assessed accuracy of custom linear axes. Standard test input and tuning procedures refined control performance. Two single motion segment units (L4-L5) and lumbar (L1-S) spine segments were tested under continuous pure moment application in flexion-extension, left-right lateral bending and axial rotation to 8Nm under full 6-DOF load control. Mean load control tracking errors between commanded and experimental loads were computed. Global spinal ranges of motion were compared to previously published values for standard non-robotic protocols. Individual linear and rotational axis position control accuracies were equal to or less than 6.35μm and 0.0167° respectively. Pilot pure bending tests demonstrated stable load control performance, as well as load rates, rotational velocities, and ranges of motion comparable to those for standard non-robotic in-vitro tests. Tracking errors for zero commanded forces and all moment controlled axes were less than 0.81±0.68N and 0.18±0.19Nm over all tests, respectively. The Cartesian based system simplified control application and demonstrated robust position and load control that was not limited to single axis or zero commanded loads. In addition to emulating standard biomechanical tests, the novel Cartesian force controlled testing system developed is a promising tool for biomechanical assessments with coordinated dynamic load application and coupled motion response in 6DOF.

  10. General curvilinear coordinate systems

    NASA Technical Reports Server (NTRS)

    Thompson, J. P.

    1982-01-01

    The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial differential equations are discussed. With such coordinate systems, all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries. A number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given. The material of this paper is applicable to all types of coordinate system generation.

  11. An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

    NASA Technical Reports Server (NTRS)

    Dagenhart, J. R; Saric, W. S.

    1983-01-01

    Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

  12. Hybrid optimal online-overnight charging coordination of plug-in electric vehicles in smart grid

    NASA Astrophysics Data System (ADS)

    Masoum, Mohammad A. S.; Nabavi, Seyed M. H.

    2016-10-01

    Optimal coordinated charging of plugged-in electric vehicles (PEVs) in smart grid (SG) can be beneficial for both consumers and utilities. This paper proposes a hybrid optimal online followed by overnight charging coordination of high and low priority PEVs using discrete particle swarm optimization (DPSO) that considers the benefits of both consumers and electric utilities. Objective functions are online minimization of total cost (associated with grid losses and energy generation) and overnight valley filling through minimization of the total load levels. The constraints include substation transformer loading, node voltage regulations and the requested final battery state of charge levels (SOCreq). The main challenge is optimal selection of the overnight starting time (toptimal-overnight,start) to guarantee charging of all vehicle batteries to the SOCreq levels before the requested plug-out times (treq) which is done by simultaneously solving the online and overnight objective functions. The online-overnight PEV coordination approach is implemented on a 449-node SG; results are compared for uncoordinated and coordinated battery charging as well as a modified strategy using cost minimizations for both online and overnight coordination. The impact of toptimal-overnight,start on performance of the proposed PEV coordination is investigated.

  13. Multi-agent coordination algorithms for control of distributed energy resources in smart grids

    NASA Astrophysics Data System (ADS)

    Cortes, Andres

    Sustainable energy is a top-priority for researchers these days, since electricity and transportation are pillars of modern society. Integration of clean energy technologies such as wind, solar, and plug-in electric vehicles (PEVs), is a major engineering challenge in operation and management of power systems. This is due to the uncertain nature of renewable energy technologies and the large amount of extra load that PEVs would add to the power grid. Given the networked structure of a power system, multi-agent control and optimization strategies are natural approaches to address the various problems of interest for the safe and reliable operation of the power grid. The distributed computation in multi-agent algorithms addresses three problems at the same time: i) it allows for the handling of problems with millions of variables that a single processor cannot compute, ii) it allows certain independence and privacy to electricity customers by not requiring any usage information, and iii) it is robust to localized failures in the communication network, being able to solve problems by simply neglecting the failing section of the system. We propose various algorithms to coordinate storage, generation, and demand resources in a power grid using multi-agent computation and decentralized decision making. First, we introduce a hierarchical vehicle-one-grid (V1G) algorithm for coordination of PEVs under usage constraints, where energy only flows from the grid in to the batteries of PEVs. We then present a hierarchical vehicle-to-grid (V2G) algorithm for PEV coordination that takes into consideration line capacity constraints in the distribution grid, and where energy flows both ways, from the grid in to the batteries, and from the batteries to the grid. Next, we develop a greedy-like hierarchical algorithm for management of demand response events with on/off loads. Finally, we introduce distributed algorithms for the optimal control of distributed energy resources, i

  14. Skeletal octahedral nanoframe with Cartesian coordinates via geometrically precise nanoscale phase segregation in a Pt@Ni core-shell nanocrystal.

    PubMed

    Oh, Aram; Baik, Hionsuck; Choi, Dong Shin; Cheon, Jae Yeong; Kim, Byeongyoon; Kim, Heejin; Kwon, Seong Jung; Joo, Sang Hoon; Jung, Yousung; Lee, Kwangyeol

    2015-03-24

    Catalytic properties of nanoparticles can be significantly enhanced by controlling nanoscale alloying and its structure. In this work, by using a facet-controlled Pt@Ni core-shell octahedron nanoparticle, we show that the nanoscale phase segregation can have directionality and be geometrically controlled to produce a Ni octahedron that is penetrated by Pt atoms along three orthogonal Cartesian axes and is coated by Pt atoms along its edges. This peculiar anisotropic diffusion of Pt core atoms along the ⟨100⟩ vertex, and then toward the ⟨110⟩ edges, is explained via the minimum strain energy for Ni-Ni pair interactions. The selective removal of the Ni-rich phase by etching then results in structurally fortified Pt-rich skeletal PtNi alloy framework nanostructures. Electrochemical evaluation of this hollow nanoframe suggests that the oxygen reduction reaction (ORR) activity is greatly improved compared to conventional Pt catalysts.

  15. More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs

    PubMed Central

    Gai, Jiading; Obeid, Nady; Holtrop, Joseph L.; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P.; Hwu, Wen-mei W.; Liang, Zhi-Pei; Sutton, Bradley P.

    2013-01-01

    Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code. PMID:23682203

  16. More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs.

    PubMed

    Gai, Jiading; Obeid, Nady; Holtrop, Joseph L; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P; Hwu, Wen-Mei W; Liang, Zhi-Pei; Sutton, Bradley P

    2013-05-01

    Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code.

  17. Molecular tectonics: heterometallic (Ir,Cu) grid-type coordination networks based on cyclometallated Ir(III) chiral metallatectons.

    PubMed

    Xu, Chaojie; Guenet, Aurélie; Kyritsakas, Nathalie; Planeix, Jean-Marc; Hosseini, Mir Wais

    2015-10-11

    A chiral-at-metal Ir(III) organometallic metallatecton was synthesised as a racemic mixture and as enantiopure complexes and combined with Cu(II) to afford a heterobimetallic (Ir,Cu) grid-type 2D coordination network.

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

    NASA Technical Reports Server (NTRS)

    Rubincam, D. P.

    1980-01-01

    The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations.

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

    NASA Astrophysics Data System (ADS)

    Péron, Stéphanie; Benoit, Christophe

    2013-01-01

    This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.

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

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

    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.

  1. A novel coordination polymer containing both interdigitated 1D chains and interpenetrated 2D grids.

    PubMed

    Ayyappan, Ponnaiyan; Evans, Owen R; Lin, Wenbin

    2002-07-01

    A hydro(solvo)thermal reaction between zinc perchlorate and ethyl ester of a new pyridinecarboxylate bridging ligand of approximately 17.6 A in length yields a unique coordination polymer which contains both interdigitated infinite 1D chains and interpenetrated 2D rhombohedral grids [Zn(2.5)(L)(4)(mu(3)-OH)] x (H(2)O)(5), 1, where L is 3-[[4-(4-pyridylethenyl)phenyl]ethenyl]benzoate. The 1D chains contain mu(3)-bridged hydroxy groups and have a [Zn(4)(mu(3)-OH)(2)(L)(6)] stoichiometry, while the 2D grids have a Zn(L)(2) formula and diagonal distances of 31.7 and 25.2 A. Crystal data for 1: monoclinic space group P2/c, a = 15.686(2) A, b = 12.6103(16) A, c = 38.999(5) A, beta = 98.397(2) degrees, and Z = 4.

  2. The adaptive, cut-cell Cartesian approach (warts and all)

    NASA Astrophysics Data System (ADS)

    Powell, Kenneth G.

    1995-10-01

    Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.

  3. The adaptive, cut-cell Cartesian approach (warts and all)

    NASA Technical Reports Server (NTRS)

    Powell, Kenneth G.

    1995-01-01

    Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.

  4. Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates

    NASA Astrophysics Data System (ADS)

    Milić, Ivan; Atanacković, Olga

    2014-10-01

    State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme.

  5. A nested grid, nonhydrostatic, elastic model using a terrain-following coordinate transformation - The radiative-nesting boundary conditions

    NASA Technical Reports Server (NTRS)

    Chen, Chaing

    1991-01-01

    This study presents a nested-grid nonhydrostatic and elastic model using a terrain-following coordinate transformation as well as a unique application of grid-nesting techniques to the time-splitting elastic model. A simulation of the 10-m-high Witch of Agnesi Mountain provides the control to test this new model. The results show that the model produces the same solution as that derived from a simple linear analytic model. It is demonstrated that the new nested-grid model improves model resolution without resorting to the costly method of placing a fine-resolution grid over the entire domain. Since the wave reflection from the boundaries of the fine-grid model is well controlled, the boundary of the nested fine-grid model can be located even at the wave-active region. The model can be used to simulate various weather systems in which scale interactions are important.

  6. Quasi-Cartesian Finite-Difference Computation of Seismic Wave Propagation for a Three-Dimensional Sub-global Earth Model

    NASA Astrophysics Data System (ADS)

    Takenaka, H.; Komatsu, M.; Toyokuni, G.; Nakamura, T.; Okamoto, T.

    2015-12-01

    A simple and efficient finite-difference scheme is developed to compute seismic wave propagation for a partial spherical shell model of a three-dimensionally (3-D) heterogeneous global earth structure. This new scheme solves the elastodynamic equations in the "quasi-Cartesian" coordinate system similar to a local Cartesian one, instead of the spherical coordinate system, with a staggered-grid finite-difference method in time domain (FDTD) which is one of the most popular numerical methods in seismic motion simulations for local to regional scale models. The proposed scheme may be useful for modeling seismic wave propagation in a very large region of sub-global scale beyond regional and less than global ones, where the effects of roundness of earth cannot be ignored. In "quasi-Cartesian" coordinates, x, y, and z are set to be locally in directions of latitude, longitude and depth, respectively. The stencil for each of the x-derivatives then depends on the depth coordinate at the evaluation point, while the stencil for each of the y-derivatives varies with both coordinates of the depth and latitude. In order to reduce lateral variations of the horizontal finite-difference stencils over the computational domain, we move the target area to a location around the equator of the computational spherical coordinate system using a way similar to the conversion from equatorial coordinates to ecliptic coordinates. The developed scheme can be easily implemented in 3-D Cartesian FDTD codes for local to regional scale modeling by changing a very small part of the codes. Our scheme may be able to open a window for multi-scale modeling of seismic wave propagation in scales from sub-global to local one.

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

    PubMed Central

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

    2010-01-01

    Coordination polymers (CPs) or metal-organic frameworks (MOFs) have attracted considerable attention because of the tunable diversity of structures and functions. A 4,4′-bipyridine molecule, which is a simple, linear, exobidentate, and rigid ligand molecule, can construct two-dimensional (2D) square grid type CPs. Only the 2D-CPs with appropriate metal cations and counter anions exhibit flexibility and adsorb gas with a gate mechanism and these 2D-CPs are called elastic layer-structured metal-organic frameworks (ELMs). Such a unique property can make it possible to overcome the dilemma of strong adsorption and easy desorption, which is one of the ideal properties for practical adsorbents. PMID:21152303

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

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

    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.

  9. Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

    PubMed Central

    Mathiowetz, A. M.; Goddard, W. A.

    1995-01-01

    Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better. PMID:7549885

  10. Development and Applications of 3D Cartesian CFD Technology

    NASA Technical Reports Server (NTRS)

    Melton, John E.; Berger, Marsha J.; VanDalsem, William (Technical Monitor)

    1994-01-01

    The urgent need for dramatic reductions in aircraft design cycle time is focusing scrutiny upon all aspects of computational fluid dynamics (CFD). These reductions will most likely come not from increased reliance upon user-interactive (and therefore time-expensive) methods, but instead from methods that can be fully automated and incorporated into 'black box' solutions. In comparison with tetrahedral methods, three-dimensional Cartesian grid approaches are in relative infancy, but initial experiences with automated Cartesian techniques are quite promising. Our research is targeted at furthering the development of Cartesian methods so that they can become key elements of a completely automatic grid generation/flow solution procedure applicable to the Euler analysis of complex aircraft geometries.

  11. Rapid Structured Volume Grid Smoothing and Adaption Technique

    NASA Technical Reports Server (NTRS)

    Alter, Stephen J.

    2006-01-01

    A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.

  12. Rapid Structured Volume Grid Smoothing and Adaption Technique

    NASA Technical Reports Server (NTRS)

    Alter, Stephen J.

    2004-01-01

    A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reduction 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.

  13. Numerical modeling of conjugate heat transfer on complex geometries with diagonal Cartesian method. Part 1: Methods

    SciTech Connect

    Lin, W.L.; Carlson, K.D.; Chen, C.J. |

    1999-05-01

    In this study, a diagonal Cartesian method for thermal analysis is developed for simulation of conjugate heat transfer over complex boundaries. This method uses diagonal line segments in addition to Cartesian coordinates. The velocity fields are also modeled using the diagonal Cartesian method. The transport equations are discretized with the finite analytic (FA) method. The current work is validated by simulating a rotated lid-driven cavity flow with conjugate heat transfer, and accurate results are obtained.

  14. Software for Automated Generation of Cartesian Meshes

    NASA Technical Reports Server (NTRS)

    Aftosmis, Michael J.; Melton, John E.; Berger, Marshal J.

    2006-01-01

    Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.

  15. Three-dimensional adaptive grid generation for body-fitted coordinate system

    NASA Technical Reports Server (NTRS)

    Chen, S. C.

    1988-01-01

    This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

  16. A Cartesian embedded boundary method for hyperbolic conservation laws

    SciTech Connect

    Sjogreen, B; Petersson, N A

    2006-12-04

    The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.

  17. Tweed Relaxation: a new multigrid smoother for stretched structured grids

    NASA Astrophysics Data System (ADS)

    Bewley, Thomas; Mashayekhi, Alireza

    2012-11-01

    In DNS/LES of the NSE using a fractional step method, one must accurately solve a Poisson equation for the pressure update at each timestep. This step often represents a significant fraction of the overall computational burden and, when Fourier methods are unavailable, geometric multigrid methods are a preferred choice. When working on an unstretched Cartesian grid, the red-black Gauss-Seidel method is the most efficient multigrid smoother available. When working on a Cartesian grid that is stretched in 1 coordinate direction to provide grid clustering near a wall, zebra relaxation, on sets of lines perpendicular to the wall, is most efficient. When working on a structured grid that is stretched in 2 or 3 coordinate directions, however, one is forced to alternate the directions that the zebra relaxation is applied in order to pass information quickly across all regions of grid clustering. A new relaxation method is introduced which is shown to significantly outperform such alternating direction line smoothers. This new method is implicit along sets of lines that branch and form 90° corners, like the stripes at the shoulder of a tweed shirt, to stay everywhere perpendicular to the nearest wall, thus passing information quickly across all regions of grid clustering.

  18. Interconversion between truncated Cartesian and polar expansions of images.

    PubMed

    Park, Wooram; Chirikjian, Gregory S

    2007-08-01

    In this paper, we propose an algorithm for lossless conversion of data between Cartesian and polar coordinates, when the data is sampled from a 2-D real-valued function (a mapping: R2 --> R) expressed as a particular kind of truncated expansion. We use Laguerre functions and the Fourier basis for the polar coordinate expression. Hermite functions are used for the Cartesian coordinate expression. A finite number of coefficients for the truncated expansion specifies the function in each coordinate system. We derive the relationship between the coefficients for the two coordinate systems. Based on this relationship, we propose an algorithm for lossless conversion between the two coordinate systems. Resampling can be used to evaluate a truncated expansion on the complementary coordinate system without computing a new set of coefficients. The resampled data is used to compute the new set of coefficients to avoid the numerical instability associated with direct conversion of the coefficients. In order to apply our algorithm to discrete image data, we propose a method to optimally fit a truncated expression to a given image. We also quantify the error that this filtering process can produce. Finally the algorithm is applied to solve the polar-Cartesian interpolation problem.

  19. 78 FR 7464 - Large Scale Networking (LSN)-Middleware And Grid Interagency Coordination (MAGIC) Team

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-02-01

    ... Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO.... Submitted by the National Science Foundation in support of the Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO) on January 29, 2013. Suzanne...

  20. Nursing research methodology: transcending Cartesianism.

    PubMed

    Walters, A J

    1996-06-01

    Nurses involved in research are concerned with methodological issues. This paper explores the Cartesian debate that has polarized the discourse on nursing research methodology. It is argued that methodologies exclusively based on objectivism, one pole of the Cartesian debate, or subjectivism, the other, do not provide nurses with adequate research foundations to understand the complexity of the lifeworld of nursing practice. This paper provides nurse researchers with an alternative methodological perspective, Gadamerian hermeneutics, which is in harmony with the clinical world of nursing practice.

  1. 78 FR 70076 - Large Scale Networking (LSN)-Middleware and Grid Interagency Coordination (MAGIC) Team

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-11-22

    ... Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO... of the Networking and Information Technology Research and Development (NITRD) National...

  2. 77 FR 58416 - Large Scale Networking (LSN); Middleware and Grid Interagency Coordination (MAGIC) Team

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-09-20

    ... Networking and Information Technology Research and Development (NITRD) National Coordination Office (NCO... National Science Foundation in support of the Networking and Information Technology Research...

  3. Two-Liquid Cartesian Diver

    ERIC Educational Resources Information Center

    Planinsic, G.; Kos, M.; Jerman, R.

    2004-01-01

    It is quite easy to make a version of the well known Cartesian diver experiment that uses two immiscible liquids. This allows students to test their knowledge of density and pressure in explaining the diver's behaviour. Construction details are presented here together with a mathematical model to explain the observations.

  4. Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing

    PubMed Central

    Si, Weijian; Qu, Xinggen; Qu, Zhiyu

    2015-01-01

    This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods. PMID:26343658

  5. Grid-based methods for diatomic quantum scattering problems: a finite-element, discrete variable representation in prolate spheroidal coordinates

    SciTech Connect

    Tao, Liang; McCurdy, C.W.; Rescigno, T.N.

    2008-11-25

    We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.

  6. NPSS on NASA's Information Power Grid: Using CORBA and Globus to Coordinate Multidisciplinary Aeroscience Applications

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

    This paper describes a project to evaluate the feasibility of combining Grid and Numerical Propulsion System Simulation (NPSS) technologies, with a view to leveraging the numerous advantages of commodity technologies in a high-performance Grid environment. A team from the NASA Glenn Research Center and Argonne National Laboratory has been studying three problems: a desktop-controlled parameter study using Excel (Microsoft Corporation); a multicomponent application using ADPAC, NPSS, and a controller program-, and an aviation safety application running about 100 jobs in near real time. The team has successfully demonstrated (1) a Common-Object- Request-Broker-Architecture- (CORBA-) to-Globus resource manager gateway that allows CORBA remote procedure calls to be used to control the submission and execution of programs on workstations and massively parallel computers, (2) a gateway from the CORBA Trader service to the Grid information service, and (3) a preliminary integration of CORBA and Grid security mechanisms. We have applied these technologies to two applications related to NPSS, namely a parameter study and a multicomponent simulation.

  7. An architecture for consolidating multidimensional time-series data onto a common coordinate grid

    SciTech Connect

    Shippert, Tim; Gaustad, Krista

    2016-12-16

    Consolidating measurement data for use by data models or in inter-comparison studies frequently requires transforming the data onto a common grid. Standard methods for interpolating multidimensional data are often not appropriate for data with non-homogenous dimensionality, and are hard to implement in a consistent manner for different datastreams. In addition, these challenges are increased when dealing with the automated procedures necessary for use with continuous, operational datastreams. In this paper we introduce a method of applying a series of one-dimensional transformations to merge data onto a common grid, examine the challenges of ensuring consistent application of data consolidation methods, present a framework for addressing those challenges, and describe the implementation of such a framework for the Atmospheric Radiation Measurement (ARM) program.

  8. An architecture for consolidating multidimensional time-series data onto a common coordinate grid

    DOE PAGES

    Shippert, Tim; Gaustad, Krista

    2016-12-16

    Consolidating measurement data for use by data models or in inter-comparison studies frequently requires transforming the data onto a common grid. Standard methods for interpolating multidimensional data are often not appropriate for data with non-homogenous dimensionality, and are hard to implement in a consistent manner for different datastreams. In addition, these challenges are increased when dealing with the automated procedures necessary for use with continuous, operational datastreams. In this paper we introduce a method of applying a series of one-dimensional transformations to merge data onto a common grid, examine the challenges of ensuring consistent application of data consolidation methods, presentmore » a framework for addressing those challenges, and describe the implementation of such a framework for the Atmospheric Radiation Measurement (ARM) program.« less

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

    SciTech Connect

    Michael Schmitt

    2008-05-01

    As the Department of Defense develops the Global Information Grid, the Department of Transportation develops the Next Generation 9-1-1 system. Close examinations of these initiatives show that the two are similar in architectures, applications, and communications interoperability. These similarities are extracted from the lowest user level to the highest commander rank that will be involved in each network. Once the similarities are brought into perspective, efforts should be made to collaborate between the two departments.

  10. Internal-to-Cartesian back transformation of molecular geometry steps using high-order geometric derivatives.

    PubMed

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

    2013-08-05

    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.

  11. Orthogonal grid generation in two dimensional space

    NASA Astrophysics Data System (ADS)

    Theodoropoulos, T.; Bergeles, G.; Athanassiadis, N.

    A generalization of a numerical technique for orthogonal mapping, used by Ryskin and Leal (1983) for the construction of boundary-fitted curvilinear coordinate systems in two-dimensional space, is proposed. The boundary-fitted orthogonal curvilinear coordinates are assumed to transform to Cartesian coordinates by Laplace equations. The scale factors involved in the Laplace equations are computed on boundaries and estimated on internal points by means of an interpolation formula. Three types of boundary conditions have been tested: Dirichlet, Cauchy-Riemann, and pseudo-Dirichlet. It is shown that, using this method, grids appropriate for the calculation of flow fields over sharp edges, complex boundary shapes, etc., can be easily constructed. Examples on various geometries are presented, together with a convenient method to check the orthogonality of the resulting meshes.

  12. Irreducible Cartesian tensors of highest weight, for arbitrary order

    NASA Astrophysics Data System (ADS)

    Mane, S. R.

    2016-03-01

    A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.

  13. 76 FR 72203 - Voltage Coordination on High Voltage Grids; Notice of Reliability Workshop Agenda

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-11-22

    ... improvements to dispatch and voltage control software could improve reliability and market efficiency. This... existing and emerging software to improve coordination and optimization of the Bulk-Power System from a... free 1-(866) 208- 3372 (voice) or (202) 208-1659 (TTY), or send a FAX to (202) 208-2106 with...

  14. 76 FR 70721 - Voltage Coordination on High Voltage Grids; Notice of Staff Workshop

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-11-15

    ... software could improve reliability and market efficiency. The workshop will address how entities currently coordinate economic dispatch and voltage control and the capability of existing and emerging software to... email to accessibility@ferc.gov or call toll free 1-(866) 208- 3372 (voice) or (202) 208-1659 (TTY),...

  15. The structure of integral dimensions: contrasting topological and Cartesian representations.

    PubMed

    Jones, Matt; Goldstone, Robert L

    2013-02-01

    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 coordinate system, just as with spaces defined by separable dimensions. This approach entails a rich geometrical structure that has never been questioned but may not be psychologically meaningful for integral dimensions. In particular, Cartesian models carry a notion of orthogonality of component dimensions, such that if 1 dimension is diagnostic for a classification or discrimination task, another can be selected as uniquely irrelevant. This article advances an alternative model in which integral dimensions are characterized as topological spaces. The Cartesian and topological models are tested in a series of experiments using the perceptual-learning phenomenon of dimension differentiation, whereby discrimination training with integral-dimension stimuli can induce an analytic representation of those stimuli. Under the present task design, the 2 models make contrasting predictions regarding the analytic representation that will be learned. Results consistently support the Cartesian model. These findings indicate that perceptual representations of integral dimensions are surprisingly structured, despite their holistic, unanalyzed nature.

  16. SACR ADVance 3-D Cartesian Cloud Cover (SACR-ADV-3D3C) product

    DOE Data Explorer

    Meng Wang, Tami Toto, Eugene Clothiaux, Katia Lamer, Mariko Oue

    2017-03-08

    SACR-ADV-3D3C remaps the outputs of SACRCORR for cross-wind range-height indicator (CW-RHI) scans to a Cartesian grid and reports reflectivity CFAD and best estimate domain averaged cloud fraction. The final output is a single NetCDF file containing all aforementioned corrected radar moments remapped on a 3-D Cartesian grid, the SACR reflectivity CFAD, a profile of best estimate cloud fraction, a profile of maximum observable x-domain size (xmax), a profile time to horizontal distance estimate and a profile of minimum observable reflectivity (dBZmin).

  17. A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID

    SciTech Connect

    Feng, Xueshang; Zhang, Man; Zhou, Yufen

    2014-09-01

    In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.

  18. Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

    NASA Technical Reports Server (NTRS)

    Smith, R. E.

    1981-01-01

    A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

  19. On automating domain connectivity for overset grids

    NASA Technical Reports Server (NTRS)

    Chiu, Ing-Tsau

    1994-01-01

    An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximated body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian Systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems.

  20. Velocity field calculation for non-orthogonal numerical grids

    SciTech Connect

    Flach, G. P.

    2015-03-01

    Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non

  1. A direct procedure for interpolation on a structured curvilinear two-dimensional grid

    NASA Technical Reports Server (NTRS)

    Zingg, David W.; Yarrow, Maurice

    1989-01-01

    A direct procedure is presented for locally bicubic interpolation on a structured, curvilinear, two-dimensional grid. The physical (Cartesian) space is transformed to a computational space in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. Required partial derivative information is obtained by finite differences in the computational space. The partial derivatives in physical space are determined by repeated application of the chain rule for partial differentiation. A bilinear transformation is used to analytically transform the individual quadrilateral cells in physical space into unit squares. The interpolation is performed within each unit square using a piecewise bicubic spline.

  2. Sink or Swim: The Cartesian Diver.

    ERIC Educational Resources Information Center

    Pinkerton, K. David

    2001-01-01

    Presents the activity of Cartesian divers which demonstrates the relationship between pressure, temperature, volume, and buoyancy. Includes both instructor information and student activity sheet. (YDS)

  3. Adjoint Formulation for an Embedded-Boundary Cartesian Method

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

    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

  4. Transient molecular electro-optics Cartesian rotation vector versus Eulerian angles.

    PubMed

    Evensen, Tom Richard; Elgsaeter, Arnljot; Naess, Stine Nalum

    2007-04-15

    Comparing the Euler angles, the classical choice of generalized coordinates describing the three rotational degrees of freedom of a rigid body, and the Cartesian rotation vector, we show that they both have their advantages and disadvantages in kinetic theory and Brownian dynamics analysis of molecular electro-optics. The Eulerian angles often yield relatively simple, yet singular, equations of motion, while their counterparts expressed in terms of Cartesian rotation vector are non-singular but more complex. In a special case, we show that the generalized force associated with the Cartesian rotation vector equals the torque. In addition, we introduce a new graphical approach to qualitatively track how changes in the Eulerian angles affect the Cartesian rotation vector.

  5. CUDA accelerated uniform re-sampling for non-Cartesian MR reconstruction.

    PubMed

    Feng, Chaolu; Zhao, Dazhe

    2015-01-01

    A grid-driven gridding (GDG) method is proposed to uniformly re-sample non-Cartesian raw data acquired in PROPELLER, in which a trajectory window for each Cartesian grid is first computed. The intensity of the reconstructed image at this grid is the weighted average of raw data in this window. Taking consider of the single instruction multiple data (SIMD) property of the proposed GDG, a CUDA accelerated method is then proposed to improve the performance of the proposed GDG. Two groups of raw data sampled by PROPELLER in two resolutions are reconstructed by the proposed method. To balance computation resources of the GPU and obtain the best performance improvement, four thread-block strategies are adopted. Experimental results demonstrate that although the proposed GDG is more time consuming than traditional DDG, the CUDA accelerated GDG is almost 10 times faster than traditional DDG.

  6. Creation operators for Cartesian and circular beams.

    PubMed

    Siguenza-Torres, Anibal; Gutiérrez-Vega, Julio C

    2016-05-01

    Creation operators of fractional order, to derive the general Cartesian beams and circular beams from the lowest-order Gaussian beam, are introduced and discussed. Finding the creation operator for these general cases is a way to find the creation operator of all the special cases of Cartesian and circular beams.

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

    SciTech Connect

    Passian, Ali; Koucheckian, Sherwin; Yakubovich, Semyon

    2011-01-01

    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.

  8. Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.

    PubMed

    Rabow, A A; Scheraga, H A

    1996-09-01

    We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints.

  9. A Cartesian cut cell method for rarefied flow simulations around moving obstacles

    SciTech Connect

    Dechristé, G.; Mieussens, L.

    2016-06-01

    For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including a 3D unsteady simulation of the Crookes radiometer.

  10. Minimization of deviations of gear real tooth surfaces determined by coordinate measurements

    NASA Technical Reports Server (NTRS)

    Litvin, F. L.; Kuan, C.; Wang, J.-C.; Handschuh, R. F.; Masseth, J.; Maruyama, N.

    1992-01-01

    The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

  11. Rms characterization of Bessel Gauss beams: Correspondence between polar and Cartesian representations

    NASA Astrophysics Data System (ADS)

    Rousseau, Guy; Gay, David; Piché, Michel

    2006-09-01

    A recent analysis [G. Rousseau, D. Gay and M. Piché, One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams, J. Opt. Soc. Am. A, 22 (2005) 1274] has shown that any cylindrically symmetric laser beam can be synthesized from a single wave called a constituent wave. This representation allows the introduction of one-dimensional Cartesian root-mean-square (rms) parameters to describe the conical structure of cylindrically symmetric laser beams. In this paper, we compare the rms characterization of Bessel-Gauss beams in polar coordinates with that of their respective constituent waves in Cartesian coordinates. Numerical results reveal an asymptotic correspondence between polar and Cartesian rms parameters of Bessel-Gauss beams propagating in a nondiffracting regime. Such a correspondence eliminates misleading interpretations about the propagation factor and the Rayleigh range of nondiffracting Bessel-type beams characterized in terms of polar rms parameters.

  12. Useful coordinate transformations for antenna applications

    NASA Technical Reports Server (NTRS)

    Rahmat-Samii, Y.

    1979-01-01

    General coordinate transformations which are commonly encountered in many antenna applications are presented. Neither the feed coordinates nor the far-field pattern coordinates in general coincide with the antenna coordinates. Transformations discussed allow one to relate the spherical and cartesian components of one system to the spherical and cartesian components of the other system. In particular, attempts are made to use unified notations to assist in a straightforward application of the transformations.

  13. Diverse assemblies of the (4,4) grid layers exemplified in Zn(II)/Co(II) coordination polymers with dual linear ligands

    NASA Astrophysics Data System (ADS)

    Liu, Guang-Zhen; Li, Xiao-Dong; Xin, Ling-Yun; Li, Xiao-Ling; Wang, Li-Ya

    2013-07-01

    Diverse (4,4) grid layers are exemplified in five two-dimensional coordination polymers with dual μ2-bridged ligands, namely, {[Zn(cbaa)(bpp)]·H2O}n (1), [Zn2(cbaa)2(bpy)]n (2), [Co2(cbaa)2(bpp)2]n (3), [Co(cbaa)(bpp)]n (4), and [Co(bdaa)(bpp)(H2O)2]n (5) (H2cbaa=4-carboxybenzeneacetic acid, bpp=1,3-di(4-pyridyl)propane, bpy=4,4‧-bipyridyl, and H2bdaa=1,4-benzenediacrylic acid). For 1, two (4,4) grid layers with [ZnN2O2] tetrahedron as the node are held together by lattice water forming a H-bonding bilayer. Individual (4,4) grid layer in 2 is based on {Zn2(OCO)4} paddlewheel unit as the node. Two (4,4) grid layers with {Co2O(OCO)2} dimer as the node are covalently interconnected by organic ligands affording a thick bilayer of 3 with new framework topology. The different entanglements between two coincident (4,4) grid layers with [CoN2O4] octahedron as the node leads to two 2D→2D interpenetrated structures for 4 and 5. Furthermore, fluorescent properties of 1 and 2 as well as magnetic properties of 3 are investigated.

  14. Near-Body Grid Adaption for Overset Grids

    NASA Technical Reports Server (NTRS)

    Buning, Pieter G.; Pulliam, Thomas H.

    2016-01-01

    A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.

  15. Quantum integrable systems in three-dimensional magnetic fields: the Cartesian case

    NASA Astrophysics Data System (ADS)

    Zhalij, Alexander

    2015-06-01

    In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems obtained are new and not related to the separation of variables in the corresponding Schrödinger equation.

  16. Dip and anisotropy effects on flow using a vertically skewed model grid.

    PubMed

    Hoaglund, John R; Pollard, David

    2003-01-01

    Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

  17. Moment Closures on Two-Dimensional Cartesian Grids

    SciTech Connect

    Garrett, Charles K.

    2015-07-31

    Some moment methods for kinetic equations are complicated and take time to develop. Over the course of a couple years, this software was developed to test different closures on standard test problems in the literature. With this software, researchers in the field of moment closures will be able to rapidly test new methods.

  18. Multi-stencils fast marching methods: a highly accurate solution to the eikonal equation on cartesian domains.

    PubMed

    Hassouna, M Sabry; Farag, A A

    2007-09-01

    A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.

  19. Turing instabilities on Cartesian product networks

    PubMed Central

    Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline

    2015-01-01

    The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory. PMID:26245138

  20. Grid-based methods for diatomic quantum scattering problems: A finite-element discrete-variable representation in prolate spheroidal coordinates

    NASA Astrophysics Data System (ADS)

    Tao, Liang; McCurdy, C. W.; Rescigno, T. N.

    2009-01-01

    We show how to combine finite elements and the discrete-variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+ , as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.

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

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher Lockwood

    1991-01-01

    A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.

  2. Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1996-01-01

    A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

  3. Maintain rigid structures in Verlet based cartesian molecular dynamics simulations.

    PubMed

    Tao, Peng; Wu, Xiongwu; Brooks, Bernard R

    2012-10-07

    An algorithm is presented to maintain rigid structures in Verlet based cartesian molecular dynamics (MD) simulations. After each unconstrained MD step, the coordinates of selected particles are corrected to maintain rigid structures through an iterative procedure of rotation matrix computation. This algorithm, named as SHAPE and implemented in CHARMM program suite, avoids the calculations of Lagrange multipliers, so that the complexity of computation does not increase with the number of particles in a rigid structure. The implementation of this algorithm does not require significant modification of propagation integrator, and can be plugged into any cartesian based MD integration scheme. A unique feature of the SHAPE method is that it is interchangeable with SHAKE for any object that can be constrained as a rigid structure using multiple SHAKE constraints. Unlike SHAKE, the SHAPE method can be applied to large linear (with three or more centers) and planar (with four or more centers) rigid bodies. Numerical tests with four model systems including two proteins demonstrate that the accuracy and reliability of the SHAPE method are comparable to the SHAKE method, but with much more applicability and efficiency.

  4. Data Grid Management Systems

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

    The "Grid" is an emerging infrastructure for coordinating access across autonomous organizations to distributed, heterogeneous computation and data resources. Data grids are being built around the world as the next generation data handling systems for sharing, publishing, and preserving data residing on storage systems located in multiple administrative domains. A data grid provides logical namespaces for users, digital entities and storage resources to create persistent identifiers for controlling access, enabling discovery, and managing wide area latencies. This paper introduces data grids and describes data grid use cases. The relevance of data grids to digital libraries and persistent archives is demonstrated, and research issues in data grids and grid dataflow management systems are discussed.

  5. Structured background grids for generation of unstructured grids by advancing front method

    NASA Technical Reports Server (NTRS)

    Pirzadeh, Shahyar

    1991-01-01

    A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

  6. A staggered overset grid method for resolved simulation of incompressible flow around moving spheres

    NASA Astrophysics Data System (ADS)

    Vreman, A. W.

    2017-03-01

    An overset grid method for resolved simulation of incompressible (turbulent) flows around moving spherical particles is presented. The Navier-Stokes equations in spherical coordinates are solved on body-fitted spherical polar grids attached to the moving spheres. These grids are overset on a fixed Cartesian background grid, where the Navier-Stokes equations in Cartesian coordinates are solved. The standard second-order staggered finite difference scheme is used on each grid. The velocities and pressures on different grids are coupled by third-order Lagrange interpolations. The method, implemented in the form of a Message Passing Interface parallel program, has been validated for a range of flows around spheres. In a first validation section, the results of simulations of four Stokes flows around a single moving sphere are compared with classical analytical results. The first three cases are the flows due to a translating, an oscillating sphere and a rotating sphere. The numerically produced velocity and pressure fields appear to converge to the corresponding (transient) analytical solutions in the maximum norm. The fourth Stokes case is the flow due to an instantaneously accelerated sphere. For this case, the results are compared with the corresponding numerical solution of the Basset-Boussinesq-Oseen equation. In a second validation section, results of three Navier-Stokes flows around one or more moving spheres are presented. These test configurations are a moving face-centered cubic array of spheres, laminar channel flow with a falling a sphere, and freely moving small spheres in a Taylor-Green flow. Results for the flow with the falling sphere are compared with the results from the literature on immersed boundary methods.

  7. Parallel Coordinate Axes.

    ERIC Educational Resources Information Center

    Friedlander, Alex; And Others

    1982-01-01

    Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

  8. Divergent Coordination Chemistry: Parallel Synthesis of [2×2] Iron(II) Grid-Complex Tauto-Conformers.

    PubMed

    Schäfer, Bernhard; Greisch, Jean-François; Faus, Isabelle; Bodenstein, Tilmann; Šalitroš, Ivan; Fuhr, Olaf; Fink, Karin; Schünemann, Volker; Kappes, Manfred M; Ruben, Mario

    2016-08-26

    The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism-driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe(II) 4 L4 ](8+) complexes were determined by X-ray diffraction, and the distinctness of the products was confirmed by ion-mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe(II) spin crossover vs. a blocked Fe(II) high-spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology.

  9. Fibonacci Grids

    NASA Technical Reports Server (NTRS)

    Swinbank, Richard; Purser, James

    2006-01-01

    Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.

  10. Arbitrary order permanent Cartesian multipolar electrostatic interactions

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

    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.

  11. Surface Generation and Cartesian Mesh Support

    NASA Technical Reports Server (NTRS)

    Haimes, Robert

    2004-01-01

    This document serves as the final report for the grant titled Surface Generation and Cartesian Mesh Support . This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cart3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.

  12. On automating domain connectivity for overset grids

    NASA Technical Reports Server (NTRS)

    Chiu, Ing-Tsau; Meakin, Robert L.

    1995-01-01

    An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.

  13. Grid-based methods for diatomic quantum scattering problems III: Double photoionization of molecular hydrogen in prolate spheroidal coordinates

    SciTech Connect

    Tao, Liang; McCurdy, Bill; Rescigno, Tom

    2010-06-10

    Our previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H$_2$ with fixed-nuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.

  14. Variable density sampling and non-Cartesian super-resolved reconstruction for spatiotemporally encoded single-shot MRI

    NASA Astrophysics Data System (ADS)

    Chen, Lin; Huang, Jianpan; Zhang, Ting; Li, Jing; Cai, Congbo; Cai, Shuhui

    2016-11-01

    Spatiotemporally encoded (SPEN) single-shot MRI is an emerging ultrafast technique, which is capable of spatially selective acquisition and reduced field-of-view imaging. Compared to uniform sampling, variable density sampling has great potential in reducing aliasing artifacts and improving sampling efficiency. In this study, variable density spiral trajectory and non-Cartesian super-resolved (SR) reconstruction method are developed for SPEN MRI. The gradient waveforms design of spiral trajectory is mathematically described as an optimization problem subjected to the limitations of hardware. Non-Cartesian SR reconstruction with specific gridding method is developed to retrieve a resolution enhanced image from raw SPEN data. The robustness and efficiency of the proposed methods are demonstrated by numerical simulation and various experiments. The results indicate that variable density SPEN MRI can provide better spatial resolution and fewer aliasing artifacts compared to Cartesian counterpart. The proposed methods will facilitate the development of variable density SPEN MRI.

  15. Variable density sampling and non-Cartesian super-resolved reconstruction for spatiotemporally encoded single-shot MRI.

    PubMed

    Chen, Lin; Huang, Jianpan; Zhang, Ting; Li, Jing; Cai, Congbo; Cai, Shuhui

    2016-11-01

    Spatiotemporally encoded (SPEN) single-shot MRI is an emerging ultrafast technique, which is capable of spatially selective acquisition and reduced field-of-view imaging. Compared to uniform sampling, variable density sampling has great potential in reducing aliasing artifacts and improving sampling efficiency. In this study, variable density spiral trajectory and non-Cartesian super-resolved (SR) reconstruction method are developed for SPEN MRI. The gradient waveforms design of spiral trajectory is mathematically described as an optimization problem subjected to the limitations of hardware. Non-Cartesian SR reconstruction with specific gridding method is developed to retrieve a resolution enhanced image from raw SPEN data. The robustness and efficiency of the proposed methods are demonstrated by numerical simulation and various experiments. The results indicate that variable density SPEN MRI can provide better spatial resolution and fewer aliasing artifacts compared to Cartesian counterpart. The proposed methods will facilitate the development of variable density SPEN MRI.

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.

  17. Guest inclusion and interpenetration tuning of Cd(II)/Mn(II) coordination grid networks assembled from a rigid linear diimidazole Schiff base ligand.

    PubMed

    Wang, Qing; Zhang, Jianyong; Zhuang, Chun-Feng; Tang, Yu; Su, Cheng-Yong

    2009-01-05

    Cd(II)/Mn(II) coordination grid networks containing large meshes have been assembled from a long rigid ligand, 2,5-bis(4'-(imidazol-1-yl)benzyl)-3,4-diaza-2,4-hexadiene (ImBNN), and M(CF(3)SO(3))(2) (M = Cd and Mn) salts, and their interpenetration change upon guest inclusion has been investigated with a series of aromatic molecules. Without guest molecules, the grid networks are triply interpenetrated to form closely packed layer structures [M(ImBNN)(2)(CF(3)SO(3))(2)](n) (M = Cd (1) and Mn (2)), but when guest molecules are introduced, the triply interpenetrated frameworks are changed to doubly interpenetrated ones with the inclusion of various aromatic molecules, namely, {[M(ImBNN)(2)(CF(3)SO(3))(2)] superset guest}(n) (M = Cd, guest = o-xylene (3), naphthalene (4), phenanthrene (5), and pyrene (6); M = Mn, guest = benzene (7), p-xylene (8), naphthalene (9), phenanthrene (10), and pyrene (11)). These complexes have been characterized by means of single-crystal X-ray diffraction, X-ray powder diffraction, and IR spectra. The guest-inclusion/desorption behaviors of representative complexes have been studied by thermogravimetric analyses and (1)H NMR measurements. The grid networks display strong preference for aromatic guest inclusion, but less selectivity toward shape and size difference. Tuning of network interpenetration from 3-fold to 2-fold has been successfully achieved through the introduction of guest molecules, when the network displays flexibility to change cavity size to match the guest molecules.

  18. A Cartesian Adaptive Level Set Method for Two-Phase Flows

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

  19. Body-oriented coordinates applied to the finite-element method

    SciTech Connect

    Cook, W.A.

    1986-10-01

    The objective of this research is to increase the accuracy of the finite-element method using coordinates intrinsic to the shape of the body being analyzed. We refer to these coordinates as body coordinates. Existing finite elements use Cartesian coordinates and are more accurate for solving rectangular-shaped problems than for solving nonrectangular-shaped problems. To check the feasibility of this research, we developed finite-element codes that used both cylindrical and Cartesian coordinates to solve problems in which the bodies were cylindrical-shaped. We obtained the most accurate solutions using the code that used cylindrical coordinates. Body coordinates become Cartesian coordinates for rectangular-shaped bodies and cylindrical coordinates for circular-shaped bodies. The body coordinate's finite-element formulation uses coordinate transformations from the body to the Cartesian coordinates. These transformations are developed using blending functions and boundary functions. Gradients of the Cartesian coordinates, with respect to body coordinates, are needed for stiffness calculations. Thus, the criterion for the blending function derivation is ''the nearest boundaries dominate,'' both for coordinate transformations and for gradient of coordinate transformations. For our studies, we developed two codes, one that uses body coordinates and one that uses Cartesian coordinates. These codes have been used to solve six example problems. 7 refs., 14 figs.

  20. Evaluation of gridded scanning ARM cloud radar reflectivity observations and vertical doppler velocity retrievals

    NASA Astrophysics Data System (ADS)

    Lamer, K.; Tatarevic, A.; Jo, I.; Kollias, P.

    2014-04-01

    The scanning Atmospheric Radiation Measurement (ARM) cloud radars (SACRs) provide continuous atmospheric observations aspiring to capture the 3-D cloud-scale structure. Sampling clouds in 3-D is challenging due to their temporal-spatial scales, the need to sample the sky at high elevations and cloud radar limitations. Thus, a suggested scan strategy is to repetitively slice the atmosphere from horizon to horizon as clouds advect over the radar (Cross-Wind Range-Height Indicator - CW-RHI). Here, the processing and gridding of the SACR CW-RHI scans are presented. First, the SACR sample observations from the ARM Southern Great Plains and Cape Cod sites are post-processed (detection mask, gaseous attenuation correction, insect filtering and velocity de-aliasing). The resulting radial Doppler moment fields are then mapped to Cartesian coordinates with time as one of the dimensions. Next the Cartesian-gridded Doppler velocity fields are decomposed into the horizontal wind velocity contribution and the vertical Doppler velocity component. For validation purposes, all gridded and retrieved fields are compared to collocated zenith-pointing ARM cloud radar measurements. We consider that the SACR sensitivity loss with range, the cloud type observed and the research purpose should be considered in determining the gridded domain size. Our results also demonstrate that the gridded SACR observations resolve the main features of low and high stratiform clouds. It is established that the CW-RHI observations complemented with processing techniques could lead to robust 3-D cloud dynamical representations up to 25-30 degrees off zenith. The proposed gridded products are expected to advance our understanding of 3-D cloud morphology, dynamics and anisotropy and lead to more realistic 3-D radiative transfer calculations.

  1. Material translations in the Cartesian brain.

    PubMed

    Bassiri, Nima

    2012-03-01

    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.

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

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1995-01-01

    A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

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

    NASA Technical Reports Server (NTRS)

    Hood, Caroline; Frendi, Abdelkader

    2006-01-01

    This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.

  4. A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1994-01-01

    A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

  5. A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1995-01-01

    A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

  6. Supramolecular assembly at interfaces: formation of an extended two-dimensional coordinate covalent square grid network at the air-water interface.

    PubMed

    Culp, Jeffrey T; Park, Ju-Hyun; Stratakis, Diktys; Meisel, Mark W; Talham, Daniel R

    2002-08-28

    Reaction of a Langmuir monolayer of an amphiphilic pentacyanoferrate(3+) complex with Ni(2+) ions from the subphase results in the formation of a two-dimensional iron-nickel cyanide-bridged network at the air-water interface. The network can be transferred to various supports to form monolayer or multilayer lamellar films by the Langmuir-Blodgett (LB) technique. The same network does not form from homogeneous reaction conditions. Therefore, the results demonstrate the potential utility of an interface as a structure director in the assembly of low dimensional coordinate covalent network solids. Characterization of the LB film extended networks by X-ray photoelectron spectroscopy (XPS), FT-IR spectroscopy, SQUID magnetometry, X-ray absorption fine structure (XAFS), and grazing incidence synchrotron X-ray diffraction (GIXD) revealed a face-centered square grid structure with an average domain size of 3600 A(2). Magnetic measurements indicated that the network undergoes a transition to a ferromagnetic state below a T(c) of 8 K.

  7. Visual Methods for Model and Grid Validation

    NASA Technical Reports Server (NTRS)

    Pang, Alex

    1998-01-01

    This joint research interchange proposal allowed us to contribute in two directions that are of interest to NASA. These are: (a) data level comparative visualization of experimental and computational fluid flow, and (b) visualization tools for analysis of adaptively refined Cartesian grids.

  8. A General-Coordinate Formulation For Boundary-Layer Flow

    NASA Technical Reports Server (NTRS)

    Steger, Joseph L.; Van Dalsem, William R.; Panaras, Argyris G.; Rao, K. V.

    1991-01-01

    Formulation for solution of equations of boundary-layer flow in general body-fitted curvilinear coordinates retains velocities in Cartesian coordinates. Increases stability of numerical simulations by avoiding coordinate source terms. In formulation, curvilinear coordinates do not have to be orthogonal, and much of software developed previously for use in numerical simulations of flow based on Navier-Stokes equations used.

  9. Inviscid transonic wing design using inverse methods in curvilinear coordinates

    NASA Technical Reports Server (NTRS)

    Gally, Thomas A.; Carlson, Leland A.

    1987-01-01

    An inverse wing design method has been developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.

  10. OVERGRID: A Unified Overset Grid Generation Graphical Interface

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

    This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.

  11. Umbrella integration in two or more reaction coordinates.

    PubMed

    Kästner, Johannes

    2009-07-21

    Umbrella integration is a method to analyze umbrella sampling simulations by calculating and integrating the mean force. Here, the method is extended to multidimensional reaction coordinates. Approximation of the probability distribution obtained from sampling by a multivariate normal distribution allows to calculate the mean force from the average and the covariance matrix of the reaction coordinate. Integration schemes of the free-energy gradient field are discussed. Integration on a real-space grid is compared to expansion of the gradient in a series of analytic functions (such as a Fourier analysis), which can be integrated, and the expansion of the gradient only at the window means in a series of analytic functions. The Fourier analysis was found particularly useful for periodic reaction coordinates, such as torsion angles. An expression is provided to calculate the Hessian of the free energy with respect to the reaction coordinates from sampling data. The utility of the method is demonstrated at the example of the free-energy surface of the alanine dipeptide in vacuum calculated with respect to the backbone torsion angles Phi and Psi. Relevance of the Jacobian term for non-Cartesian reaction coordinates is discussed.

  12. Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors

    NASA Astrophysics Data System (ADS)

    Lin, Dejun

    2015-09-01

    Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A

  13. Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors.

    PubMed

    Lin, Dejun

    2015-09-21

    Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A

  14. FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

    NASA Technical Reports Server (NTRS)

    Kaul, Upender K.

    2005-01-01

    A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

  15. Hybrid-CVFE method for flexible-grid reservoir simulation

    SciTech Connect

    Fung, L.S.K.; Buchanan, L.; Sharma, R. )

    1994-08-01

    Well flows and pressures are the most important boundary conditions in reservoir simulation. In a typical simulation, rapid changes and large pressure, temperature, saturation, and composition gradients occur in near-well regions. Treatment of these near-well phenomena significantly affects the accuracy of reservoir simulation results; therefore, extensive efforts have been devoted to the numerical treatment of wells and near-well flows. The flexible control-volume finite-element (CVFE) method is used to construct hybrid grids. The method involves use of a local cylindrical or elliptical grid to represent near-well flow accurately while honoring complex reservoir boundaries. The grid transition is smooth without any special discretization approximation, which eliminates the grid transition problem experienced with Cartesian local grid refinement and hybrid Cartesian gridding techniques.

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

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.

    2004-01-01

    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

  17. NonCartesian MR image reconstruction with integrated gradient nonlinearity correction

    PubMed Central

    Tao, Shengzhen; Trzasko, Joshua D.; Shu, Yunhong; Huston, John; Johnson, Kevin M.; Weavers, Paul T.; Gray, Erin M.; Bernstein, Matt A.

    2015-01-01

    Purpose: To derive a noniterative gridding-type reconstruction framework for nonCartesian magnetic resonance imaging (MRI) that prospectively accounts for gradient nonlinearity (GNL)-induced image geometrical distortion during MR image reconstruction, as opposed to the standard, image-domain based GNL correction that is applied after reconstruction; to demonstrate that such framework is able to reduce the image blurring introduced by the conventional GNL correction, while still offering effective correction of GNL-induced geometrical distortion and compatibility with off-resonance correction. Methods: After introducing the nonCartesian MRI signal model that explicitly accounts for the effects of GNL and off-resonance, a noniterative gridding-type reconstruction framework with integrated GNL correction based on the type-III nonuniform fast Fourier transform (NUFFT) is derived. A novel type-III NUFFT implementation is then proposed as a numerically efficient solution to the proposed framework. The incorporation of simultaneous B0 off-resonance correction to the proposed framework is then discussed. Several phantom and in vivo data acquired via various 2D and 3D nonCartesian acquisitions, including 2D Archimedean spiral, 3D shells with integrated radial and spiral, and 3D radial sampling, are used to compare the results of the proposed and the standard GNL correction methods. Results: Various phantom and in vivo data demonstrate that both the proposed and the standard GNL correction methods are able to correct the coarse-scale geometric distortion and blurring induced by GNL and off-resonance. However, the standard GNL correction method also introduces blurring effects to corrected images, causing blurring of resolution inserts in the phantom images and loss of small vessel clarity in the angiography examples. On the other hand, the results after the proposed GNL correction show better depiction of resolution inserts and higher clarity of small vessel. Conclusions

  18. A grid spacing control technique for algebraic grid generation methods

    NASA Technical Reports Server (NTRS)

    Smith, R. E.; Kudlinski, R. A.; Everton, E. L.

    1982-01-01

    A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.

  19. Grid Interaction Technical Team Roadmap

    SciTech Connect

    2013-06-01

    The mission of the Grid Interaction Technical Team (GITT) is to support a transition scenario to large scale grid-connected vehicle charging with transformational technology, proof of concept and information dissemination. The GITT facilitates technical coordination and collaboration between vehicle-grid connectivity and communication activities among U.S. DRIVE government and industry partners.

  20. Internal coordinate density of state from molecular dynamics simulation.

    PubMed

    Lai, Pin-Kuang; Lin, Shiang-Tai

    2015-03-30

    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.

  1. Biangular Coordinates Redux: Discovering a New Kind of Geometry

    ERIC Educational Resources Information Center

    Winkel, Brian; Naylor, Michael

    2010-01-01

    Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the…

  2. Semi-Supervised Learning of Cartesian Factors: A Top-Down Model of the Entorhinal Hippocampal Complex

    PubMed Central

    Lőrincz, András; Sárkány, András

    2017-01-01

    The existence of place cells (PCs), grid cells (GCs), border cells (BCs), and head direction cells (HCs) as well as the dependencies between them have been enigmatic. We make an effort to explain their nature by introducing the concept of Cartesian Factors. These factors have specific properties: (i) they assume and complement each other, like direction and position and (ii) they have localized discrete representations with predictive attractors enabling implicit metric-like computations. In our model, HCs make the distributed and local representation of direction. Predictive attractor dynamics on that network forms the Cartesian Factor “direction.” We embed these HCs and idiothetic visual information into a semi-supervised sparse autoencoding comparator structure that compresses its inputs and learns PCs, the distributed local and direction independent (allothetic) representation of the Cartesian Factor of global space. We use a supervised, information compressing predictive algorithm and form direction sensitive (oriented) GCs from the learned PCs by means of an attractor-like algorithm. Since the algorithm can continue the grid structure beyond the region of the PCs, i.e., beyond its learning domain, thus the GCs and the PCs together form our metric-like Cartesian Factors of space. We also stipulate that the same algorithm can produce BCs. Our algorithm applies (a) a bag representation that models the “what system” and (b) magnitude ordered place cell activities that model either the integrate-and-fire mechanism, or theta phase precession, or both. We relate the components of the algorithm to the entorhinal-hippocampal complex and to its working. The algorithm requires both spatial and lifetime sparsification that may gain support from the two-stage memory formation of this complex. PMID:28270783

  3. Semi-Supervised Learning of Cartesian Factors: A Top-Down Model of the Entorhinal Hippocampal Complex.

    PubMed

    Lőrincz, András; Sárkány, András

    2017-01-01

    The existence of place cells (PCs), grid cells (GCs), border cells (BCs), and head direction cells (HCs) as well as the dependencies between them have been enigmatic. We make an effort to explain their nature by introducing the concept of Cartesian Factors. These factors have specific properties: (i) they assume and complement each other, like direction and position and (ii) they have localized discrete representations with predictive attractors enabling implicit metric-like computations. In our model, HCs make the distributed and local representation of direction. Predictive attractor dynamics on that network forms the Cartesian Factor "direction." We embed these HCs and idiothetic visual information into a semi-supervised sparse autoencoding comparator structure that compresses its inputs and learns PCs, the distributed local and direction independent (allothetic) representation of the Cartesian Factor of global space. We use a supervised, information compressing predictive algorithm and form direction sensitive (oriented) GCs from the learned PCs by means of an attractor-like algorithm. Since the algorithm can continue the grid structure beyond the region of the PCs, i.e., beyond its learning domain, thus the GCs and the PCs together form our metric-like Cartesian Factors of space. We also stipulate that the same algorithm can produce BCs. Our algorithm applies (a) a bag representation that models the "what system" and (b) magnitude ordered place cell activities that model either the integrate-and-fire mechanism, or theta phase precession, or both. We relate the components of the algorithm to the entorhinal-hippocampal complex and to its working. The algorithm requires both spatial and lifetime sparsification that may gain support from the two-stage memory formation of this complex.

  4. Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations

    SciTech Connect

    Xia, Guoping . E-mail: xiag@purdue.edu; Li, Ding; Merkle, Charles L.

    2007-07-01

    An efficient reconstruction procedure for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Properties and their pertinent derivatives are evaluated by means of an adaptive Cartesian mesh in the thermodynamic plane that provides user-specified accuracy over any selected domain. The Cartesian grid produces a binary tree data structure whose search efficiency is competitive with that for an equally spaced table or with simple equations of state such as a perfect gas. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh that ensures function continuity across cell boundaries in equally and unequally spaced portions of the table to C {sup 0}, C {sup 1} or C {sup 2} levels. The C {sup 0} and C {sup 1} reconstructions fit the equation of state and enthalpy relations separately, while the C {sup 2} reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD solutions obtained to date. The efficiency of the method is demonstrated through storage and data retrieval examples for air, water and carbon dioxide. The time required for property evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations resulting in estimated 3D CFD savings of from 30 to 60. Storage requirements are modest for today's computers, with the C {sup 1} method requiring slightly less storage than those for the C {sup 0} and C {sup 2} reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C {sup 1} and C {sup 2} methods are approximately a factor of two slower than the C {sup 0} method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy

  5. Configuration space representation in parallel coordinates

    NASA Technical Reports Server (NTRS)

    Fiorini, Paolo; Inselberg, Alfred

    1989-01-01

    By means of a system of parallel coordinates, a nonprojective mapping from R exp N to R squared is obtained for any positive integer N. In this way multivariate data and relations can be represented in the Euclidean plane (embedded in the projective plane). Basically, R squared with Cartesian coordinates is augmented by N parallel axes, one for each variable. The N joint variables of a robotic device can be represented graphically by using parallel coordinates. It is pointed out that some properties of the relation are better perceived visually from the parallel coordinate representation, and that new algorithms and data structures can be obtained from this representation. The main features of parallel coordinates are described, and an example is presented of their use for configuration space representation of a mechanical arm (where Cartesian coordinates cannot be used).

  6. Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

    NASA Astrophysics Data System (ADS)

    Zhang, Z.; Zhu, G.; Chen, X.

    2011-12-01

    We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

  7. Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

    NASA Astrophysics Data System (ADS)

    Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

    2016-11-01

    A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates

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

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

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

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

  10. Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers

    PubMed Central

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

    2010-01-01

    A modified Cartesian feedback method called “frequency-offset Cartesian feedback” and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems. In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200–1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback. In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450

  11. Neutron-transport equation in a general curvelinear coordinate system

    SciTech Connect

    Takahashi, H

    1981-01-01

    Different from a fission reactor, a fusion reactor has complex geometry, such as toroidal geometry. Neutron transport equation for the toroidal coordinate system has been derived by using coordinate transformation from the cartesian coordinate. These methods require rather tedious calculations. Presented here is a simple method to formulate the neutron transport equation in the general curvelinear coordinate system. The equations for parabolic cylinder and toroidal coordinate systems are derived as an example.

  12. Visualizing Three-dimensional Volumetric Data with an Arbitrary Coordinate System

    NASA Astrophysics Data System (ADS)

    Taylor, R.

    2017-02-01

    Astronomical data does not always use Cartesian coordinates. Both all-sky observational data and simulations of rotationally symmetric systems, such as accretion and protoplanetary disks, may use spherical polar or other coordinate systems. Standard displays rely on Cartesian coordinates, but converting non-Cartesian data into Cartesian format causes distortion of the data and loss of detail. Here, I demonstrate a method using standard techniques from computer graphics that avoids these problems with three-dimensional data in arbitrary coordinate systems. The method adds minimum computational cost to the display process and is suitable for both realtime, interactive content, and producing fixed rendered images and videos. Proof-of-concept code is provided which works for data in spherical polar coordinates.

  13. String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems.

    PubMed

    Branduardi, Davide; Faraldo-Gómez, José D

    2013-09-10

    The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.

  14. String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems

    PubMed Central

    Branduardi, Davide; Faraldo-Gómez, José D.

    2014-01-01

    The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID

  15. A Cartesian parametrization for the numerical analysis of material instability

    SciTech Connect

    Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; Ostien, Jakob T.; Lai, Zhengshou

    2016-02-25

    We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, the performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.

  16. A Cartesian parametrization for the numerical analysis of material instability

    DOE PAGES

    Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

    2016-02-25

    We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

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

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    This work considers numerical simulation of three-dimensional flows with time-evolving boundaries. Such problems pose a variety of challenges for numerical schemes, and have received a substantial amount of attention in the recent literature. Since such simulations are unsteady, time-accurate solution of the governing equations is required. In special cases, the body motion can be treated by a uniform rigid motion of the computational domain. For the more general situation of relative-body motion, however, this simplification is unavailable and the simulations require a mechanism for ensuring that the mesh evolves with the moving boundaries. This involves a "remeshing" of the computational domain (either localized or global) at each physical timestep, and places a premium on both the speed and robustness of the remeshing algorithms. This work presents a method which includes unsteady flow simulation, rigid domain motion, and relative body motion using a time-evolving Cartesian grid system in three dimensions.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

    In this work, the fully compressible, nonhydrostatic 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. An implicit time integration scheme ensures numerical stability around small cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid scale model, a two-moment bulk microphysics scheme, precipitation and vertical surface fluxes by a constant flux layer or a more complex soil model are implemented. Results for three benchmark test cases from the literature are shown. A sensitivity study regarding the development of a convective boundary layer together with island effects at Barbados is carried out to show the capability to perform real case simulations with ASAM.

  19. Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4

    NASA Astrophysics Data System (ADS)

    Avila, Gustavo; Carrington, Tucker

    2011-08-01

    In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtμπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only ˜1.52 × 108 quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 1013 points.

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

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

    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.

  1. Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors

    PubMed Central

    Lin, Dejun

    2015-01-01

    Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A

  2. Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors

    SciTech Connect

    Lin, Dejun

    2015-09-21

    Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A

  3. Notes on a method to transform digitized coordinates to geographic coordinates

    USGS Publications Warehouse

    Evenden, Gerald I.

    1991-01-01

    The process of conversion of coordinates (typically carte- sian) obtained from digitizing devices into application de- ned coordinate systems is discussed. Application of a secondary function representing the transformation of the application coordinate system to and from cartesian space will greatly simplify conversion of highly non-linear sys- tems. Although emphasis is given to cartographic conver- sions the method will work with a wide variety of digitizing problems.

  4. Topological coordinates for deformed nanotubes

    NASA Astrophysics Data System (ADS)

    László, István; Rassat, André

    2003-10-01

    Starting from the topological arrangement of carbon atoms an algorithm is given for the construction of nanotube Cartesian coordinates. The final relaxed structures were obtained by a molecular mechanics calculation where the carbon-carbon interactions were supposed only between neighboring atoms of the initial tiling. In a given tiling we obtained toroidal or helical structures depending on the special position of the super cell parallelogram.

  5. A Lot of Good Physics in the Cartesian Diver

    ERIC Educational Resources Information Center

    De Luca, Roberto; Ganci, Salvatore

    2011-01-01

    The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…

  6. The Cartesian Diver, Surface Tension and the Cheerios Effect

    ERIC Educational Resources Information Center

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

    2014-01-01

    A Cartesian diver can be used to measure the surface tension of a liquid to a certain extent. The surface tension measurement is related to the two critical pressures at which the diver is about to sink and about to emerge. After sinking because of increasing pressure, the diver is repulsed to the centre of the vessel. After the pressure is…

  7. The Cartesian Diver as an Aid for Teaching Respiratory Physiology

    ERIC Educational Resources Information Center

    Fitch, Greg K.

    2004-01-01

    The mechanism by which air enters the mammalian lung is difficult for many students of physiology. In particular, some students have trouble seeing how pressure can be transmitted through a fluid such as the intrapleural fluid and how the magnitude of that pressure can change. A Cartesian diver, an old-time child's toy, may be used as a visual aid…

  8. Grid Connected Functionality

    DOE Data Explorer

    Baker, Kyri; Jin, Xin; Vaidynathan, Deepthi; Jones, Wesley; Christensen, Dane; Sparn, Bethany; Woods, Jason; Sorensen, Harry; Lunacek, Monte

    2016-08-04

    Dataset demonstrating the potential benefits that residential buildings can provide for frequency regulation services in the electric power grid. In a hardware-in-the-loop (HIL) implementation, simulated homes along with a physical laboratory home are coordinated via a grid aggregator, and it is shown that their aggregate response has the potential to follow the regulation signal on a timescale of seconds. Connected (communication-enabled), devices in the National Renewable Energy Laboratory's (NREL's) Energy Systems Integration Facility (ESIF) received demand response (DR) requests from a grid aggregator, and the devices responded accordingly to meet the signal while satisfying user comfort bounds and physical hardware limitations.

  9. Equipartition Principle for Internal Coordinate Molecular Dynamics.

    PubMed

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

    2012-08-14

    The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has ½kT 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.

  10. Plasticity of Intermediate Mechanics Students' Coordinate System Choice

    ERIC Educational Resources Information Center

    Sayre, Eleanor C.; Wittman, Michael C.

    2008-01-01

    We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their…

  11. Conservation equations of gasdynamics in curvilinear coordinate systems

    NASA Technical Reports Server (NTRS)

    Vinokur, M.

    1974-01-01

    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.

  12. A Cartesian quasi-classical model to nonequilibrium quantum transport: the Anderson impurity model.

    PubMed

    Li, Bin; Levy, Tal J; Swenson, David W H; Rabani, Eran; Miller, William H

    2013-03-14

    We apply the recently proposed quasi-classical approach for a second quantized many-electron Hamiltonian in Cartesian coordinates [B. Li and W. H. Miller, J. Chem. Phys. 137, 154107 (2012)] to correlated nonequilibrium quantum transport. The approach provides accurate results for the resonant level model for a wide range of temperatures, bias, and gate voltages, correcting the flaws of our recently proposed mapping using action-angle variables. When electron-electron interactions are included, a Gaussian function scheme is required to map the two-electron integrals, leading to quantitative results for the Anderson impurity model. In particular, we show that the current mapping is capable of capturing quantitatively the Coulomb blockade effect and the temperature dependence of the current below and above the blockade.

  13. Polar versus Cartesian velocity models for maneuvering target tracking with IMM

    NASA Astrophysics Data System (ADS)

    Laneuville, Dann

    This paper compares various model sets in different IMM filters for the maneuvering target tracking problem. The aim is to see whether we can improve the tracking performance of what is certainly the most widely used model set in the literature for the maneuvering target tracking problem: a Nearly Constant Velocity model and a Nearly Coordinated Turn model. Our new challenger set consists of a mixed Cartesian position and polar velocity state vector to describe the uniform motion segments and is augmented with the turn rate to obtain the second model for the maneuvering segments. This paper also gives a general procedure to discretize up to second order any non-linear continuous time model with linear diffusion. Comparative simulations on an air defence scenario with a 2D radar, show that this new approach improves significantly the tracking performance in this case.

  14. Calculation of steady and unsteady transonic flow using a Cartesian mesh and gridless boundary conditions with application to aeroelasticity

    NASA Astrophysics Data System (ADS)

    Kirshman, David

    A numerical method for the solution of inviscid compressible flow using an array of embedded Cartesian meshes in conjunction with gridless surface boundary conditions is developed. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the surface geometry. The method allows for accurate treatment of the surface boundary conditions using a grid resolution an order of magnitude coarser than required of typical Cartesian approaches. Additionally, the method does not suffer from issues associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, multi-grid acceleration can be effectively incorporated and issues associated with global conservation are alleviated. The "gridless" surface boundary condition provides for efficient and simple problem set up since definition of the body geometry is generated independently from the field mesh, and automatically incorporated into the field discretization of the domain. The applicability of the method is first demonstrated for steady flow of single and multi-element airfoil configurations. Using this method, comparisons with traditional body-fitted grid simulations reveal that steady flow solutions can be obtained accurately with minimal effort associated with grid generation. The method is then extended to unsteady flow predictions. In this application, flow field simulations for the prescribed oscillation of an airfoil indicate excellent agreement with experimental data. Furthermore, it is shown that the phase lag associated with shock oscillation is accurately predicted without the need for a deformable mesh. Lastly, the method is applied to the prediction of transonic flutter using a two-dimensional wing model, in which comparisons with moving mesh simulations yield nearly identical results. As a result

  15. Enhanced Elliptic Grid Generation

    NASA Technical Reports Server (NTRS)

    Kaul, Upender K.

    2007-01-01

    An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are

  16. Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

    PubMed

    Hornikx, Maarten; Dragna, Didier

    2015-07-01

    The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

  17. Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

    NASA Astrophysics Data System (ADS)

    Pathak, Harshavardhana S.; Shukla, Ratnesh K.

    2016-08-01

    A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of

  18. Simulations of 6-DOF Motion with a Cartesian Method

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    Coupled 6-DOF/CFD trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-32/JDAM store separating from an F-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed, and compared with flight-test telemetry and photographic-derived data. Simulation results obtained with a sequential-static series of flow solutions are contrasted with results using a time-dependent flow solver. Both numerical methods show good agreement with the flight-test data through the first half of the simulations. The sequential-static and time-dependent methods diverge over the last half of the trajectory prediction. after the store produces peak angular rates. A cost comparison for the Cartesian method is included, in terms of absolute cost and relative to computing uncoupled 6-DOF trajectories. A detailed description of the 6-DOF method, as well as a verification of its accuracy, is provided in an appendix.

  19. The Overgrid Interface for Computational Simulations on Overset Grids

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.

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

    SciTech Connect

    Tao, S; Trzasko, JD; Polley, TW; Shu, Y; Bernstein, MA

    2014-06-01

    Purpose: Nonlinearities in the spatial encoding gradients of MRI systems cause geometric distortion in images. Typically, this is retrospectively corrected via image-domain interpolation (a.k.a., “gradwarp”) albeit with a loss of spatial resolution. For non-Cartesian MRI, the latter problem is exaggerated by noise and undersampling artifact. In this study, we describe a novel correction strategy that accounts for gradient nonlinearities during — rather than after — non-Cartesian MRI reconstruction, and demonstrate that this approach mitigates the resolution loss that can occur with standard methods. Methods: To test the proposed method, the American College of Radiology (ACR) quality control phantom was scanned on at 1.5 T (General Electric, v16.0, “zoom” gradient) using a 1.6x undersampled 3D non- Cartesian Shells trajectory (GRE, FOV=24 cm3, 120 shells, 16552 shots, 512 readout, matrix=2403). Image reconstruction was first performed via standard k-space density-compensated gridding and retrospectively corrected via cubic spline interpolation. Image reconstruction was then separately performed using a k-space and image-domain densitycompensated type-3 non-uniform fast Fourier transform (NUFFT), which provides a direct mapping between non-Cartesian k-space samples and warped image space voxel locations. Thus, no separate distortion correction procedure is needed for the proposed approach. The gradient distortion field was determined using vendor provided calibration data. Results: Phantom scan results show that both processing approaches successfully correct geometric distortion. However, visual inspection of the ACR phantom spatial resolution inserts shows that the proposed strategy preserves the resolution of the nominal (uncorrected) reconstruction while “gradwarp” imparts marked spatial blurring (especially for the 1.0 and 1.1 mm inserts) and thus resolution loss. Conclusion: We've presented a novel reconstruction strategy for non-Cartesian MRI

  1. Cartesian positioning system for localization of blast and ballistic fragments: a phantom-based pilot study.

    PubMed

    Folio, Les; Fischer, Tatjana; Shogan, Paul J; Frew, Michael; Bunger, Rolf; Provenzale, James M

    2011-11-01

    Our purpose was to demonstrate the consistency of radiologists' three-dimensional measurements of simulated blast fragment locations in vitro in an effort to objectively localize retained fragments and wound paths. We designed a phantom consisting of 10 nail heads (simulating blast fragments) glued to wooden pegs that were randomly situated at distances from a reference point within a plastic tub. The x, y, and z coordinates of simulated fragments were recorded in Cartesian 3-space relative to the reference point. Computed tomography images of the phantom were acquired. Differences in x, y, and z positions as determined by three observers were summed for each fragment. Agreement between recordings of coordinates across readers was assessed using the intraclass correlation coefficient. Summed differences in coordinate positions as determined by readers ranged between 0.00 and 1.204 cm (mean: 0.732 cm). Across readers, the intraclass correlation coefficient for each dimension was >0.99. We found excellent agreement among readers with minimal discrepancy of measured locations of simulated fragments. Our results provide a foundation for trajectory analysis necessary to lead to automated organ damage reporting for immediate assessment in the emergency department and for forensic investigation and long-term epidemiological analysis.

  2. Conformal coordinates associated with uniformly accelerated motion

    NASA Technical Reports Server (NTRS)

    Jones, R. T.

    1976-01-01

    Specific problems in the theory of relativity are often simplified by an appropriate choice of the coordinate system. Restricted conformal coordinates provide an especially simple analysis of motion with uniform acceleration, known as hyperbolic motion. Conformal coordinates x', t' may be obtained from Cartesian coordinates x, t by the transformation x'+ct'=F(x+ct) and x'-ct'=G(x-ct), where c is the velocity of light. A variable motion of the x' system is determined by the choice of the functions F and G.

  3. Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.

    PubMed

    Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H

    2013-05-01

    In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.

  4. Frequency-Offset Cartesian Feedback for MRI Power Amplifier Linearization

    PubMed Central

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

    2011-01-01

    High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and DC offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called “frequency-offset Cartesian feedback” (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than DC, so that quadrature ghosts and DC errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system. PMID:20959264

  5. Constructing the ASCI computational grid

    SciTech Connect

    BEIRIGER,JUDY I.; BIVENS,HUGH P.; HUMPHREYS,STEVEN L.; JOHNSON,WILBUR R.; RHEA,RONALD E.

    2000-06-01

    The Accelerated Strategic Computing Initiative (ASCI) computational grid is being constructed to interconnect the high performance computing resources of the nuclear weapons complex. The grid will simplify access to the diverse computing, storage, network, and visualization resources, and will enable the coordinated use of shared resources regardless of location. To match existing hardware platforms, required security services, and current simulation practices, the Globus MetaComputing Toolkit was selected to provide core grid services. The ASCI grid extends Globus functionality by operating as an independent grid, incorporating Kerberos-based security, interfacing to Sandia's Cplant{trademark},and extending job monitoring services. To fully meet ASCI's needs, the architecture layers distributed work management and criteria-driven resource selection services on top of Globus. These services simplify the grid interface by allowing users to simply request ''run code X anywhere''. This paper describes the initial design and prototype of the ASCI grid.

  6. A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

    NASA Technical Reports Server (NTRS)

    Levy, R.; Mcdonald, H.; Briley, W. R.; Kreskovsky, J. P.

    1981-01-01

    An approximate analysis is presented which is applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline. The primary flow direction is taken to coincide with the local direction of the duct centerline and is hence normal to transverse coordinate planes. The formulation utilizes vector components (velocity, vorticity, transport equations) defined in terms of local Cartesian directions aligned with the centerline tangent, although the governing equations themselves are expressed in general nonorthogonal coordinates. For curved centerlines, these vector quantities are redefined in new local Cartesian directions at each streamwise location. The use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation, and this provides for the aforementioned ease in using constructed coordinates.

  7. Verification and validation of the Spalart-Allmaras turbulence model for strand grids

    NASA Astrophysics Data System (ADS)

    Tong, Oisin

    The strand-Cartesian grid approach provides many advantages for complex moving- body flow simulations, including fully-automatic volume grid generation, highly scalable domain connectivity, and high-order accuracy. In this work the Spalart-Allmaras model is implemented, verified, and validated for high Reynolds number turbulent flows in a strand- Cartesian solver. Second-order convergence is achieved using the Method of Manufactured Solutions implying correct implementation of the turbulence model. By using the NASA- Langley online resource, specific flow cases are validated with two independent compressible codes: FUN3D and CFL3D. The strand solver is validated with zero-pressure gradient flat plate and bump-in-channel cases, and shows excellent agreement with FUN3D and CFL3D for various aspects of turbulent flow, including: velocity profiles, turbulent viscosity profile, coefficient of surface pressure, and drag. Methods of handling sharp corners with strand grids through combinations of strand vector smoothing, multiple strands emanating from a single surface node, and telescoping Cartesian refinement into corner regions of the near- body grid are investigated for a NACA 0012 case. For standard viscous high-aspect ratio grids, smoothed strands with telescoping Cartesian refinement provide the most accurate results with the least complexity. Mesh discontinuities associated with use of multiple strands at sharp corners produce more error than with smoothed strands. With both strand approaches -- vector smoothing and multiple strands -- targeted Cartesian refinement is critical to capture features near sharp corners where strand grids alone are too coarse to capture. Other results show agreement with FUN3D and CFL3D. By using strand vector smoothing and telescoping Cartesian refinement, a NACA 4412 trailing edge separation case is validated with comparison against CFL3D and FUN3D. Velocity profiles show reasonable agreement with CFL3D; however implementing

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

    NASA Technical Reports Server (NTRS)

    Miller, David P.

    1994-01-01

    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.

  9. 76 FR 46279 - Smart Grid Advisory Committee

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-08-02

    ... National Institute of Standards and Technology Smart Grid Advisory Committee AGENCY: Department of Commerce, National Institute of Standards and Technology ACTION: Notice of open meeting. SUMMARY: The Smart Grid... should be sent to Office of the National Coordinator for Smart Grid Interoperability, National...

  10. Grid Work

    NASA Technical Reports Server (NTRS)

    1998-01-01

    Pointwise Inc.'s, Gridgen Software is a system for the generation of 3D (three dimensional) multiple block, structured grids. Gridgen is a visually-oriented, graphics-based interactive code used to decompose a 3D domain into blocks, distribute grid points on curves, initialize and refine grid points on surfaces and initialize volume grid points. Gridgen is available to U.S. citizens and American-owned companies by license.

  11. Compact-range coordinate system established using a laser tracker.

    SciTech Connect

    Gallegos, Floyd H.; Bryce, Edwin Anthony

    2006-12-01

    Establishing a Cartesian coordinate reference system for an existing Compact Antenna Range using the parabolic reflector is presented. A SMX (Spatial Metrix Corporation) M/N 4000 laser-based coordinate measuring system established absolute coordinates for the facility. Electric field characteristics with positional movement correction are evaluated. Feed Horn relocation for alignment with the reflector axis is also described. Reference points are established for follow-on non-laser alignments utilizing a theodolite.

  12. An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

    NASA Technical Reports Server (NTRS)

    Coirier, William John

    1994-01-01

    A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a

  13. GridPV Toolbox

    SciTech Connect

    Broderick, Robert; Quiroz, Jimmy; Grijalva, Santiago; Reno, Matthew; Coogan, Kyle

    2014-07-15

    Matlab Toolbox for simulating the impact of solar energy on the distribution grid. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving GridPV Toolbox information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feeder on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions.

  14. MAGNETIC GRID

    DOEpatents

    Post, R.F.

    1960-08-01

    An electronic grid is designed employing magnetic forces for controlling the passage of charged particles. The grid is particularly applicable to use in gas-filled tubes such as ignitrons. thyratrons, etc., since the magnetic grid action is impartial to the polarity of the charged particles and, accordingly. the sheath effects encountered with electrostatic grids are not present. The grid comprises a conductor having sections spaced apart and extending in substantially opposite directions in the same plane, the ends of the conductor being adapted for connection to a current source.

  15. An adaptive three-dimensional Cartesian approach for the parallel computation of inviscid flow about static and dynamic configurations

    NASA Astrophysics Data System (ADS)

    Hunt, Jason Daniel

    An adaptive three-dimensional Cartesian approach for the parallel computation of compressible flow about static and dynamic configurations has been developed and validated. This is a further step towards a goal that remains elusive for CFD codes: the ability to model complex dynamic-geometry problems in a quick and automated manner. The underlying flow-solution method solves the three-dimensional Euler equations using a MUSCL-type finite-volume approach to achieve higher-order spatial accuracy. The flow solution, either steady or unsteady, is advanced in time via a two-stage time-stepping scheme. This basic solution method has been incorporated into a parallel block-adaptive Cartesian framework, using a block-octtree data structure to represent varying spatial resolution, and to compute flow solutions in parallel. The ability to represent static geometric configurations has been introduced by cutting a geometric configuration out of a background block-adaptive Cartesian grid, then solving for the flow on the resulting volume grid. This approach has been extended for dynamic geometric configurations: components of a given configuration were permitted to independently move, according to prescribed rigid-body motion. Two flow-solver difficulties arise as a result of introducing static and dynamic configurations: small time steps; and the disappearance/appearance of cell volume during a time integration step. Both of these problems have been remedied through cell merging. The concept of cell merging and its implementation within the parallel block-adaptive method is described. While the parallelization of certain grid-generation and cell-cutting routines resulted from this work, the most significant contribution was developing the novel cell-merging paradigm that was incorporated into the parallel block-adaptive framework. Lastly, example simulations both to validate the developed method and to demonstrate its full capabilities have been carried out. A simple, steady

  16. 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)

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

    2011-06-01

    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.

  17. A HYBRID SOLAR WIND MODEL OF THE CESE+HLL METHOD WITH A YIN-YANG OVERSET GRID AND AN AMR GRID

    SciTech Connect

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

    2011-06-10

    A hybrid three-dimensional (3D) MHD model for solar wind study is proposed in the present paper with combined grid systems and solvers. The computational domain from the Sun to Earth space is decomposed into the near-Sun and off-Sun domains, which are respectively constructed with a Yin-Yang overset grid system and a Cartesian adaptive mesh refinement (AMR) grid system and coupled with a domain connection interface in the overlapping region between the near-Sun and off-Sun domains. The space-time conservation element and solution element method is used in the near-Sun domain, while the Harten-Lax-Leer method is employed in the off-Sun domain. The Yin-Yang overset grid can avoid well-known singularity and polar grid convergence problems and its body-fitting property helps achieve high-quality resolution near the solar surface. The block structured AMR Cartesian grid can automatically capture far-field plasma flow features, such as heliospheric current sheets and shock waves, and at the same time, it can save significant computational resources compared to the uniformly structured Cartesian grid. A numerical study of the solar wind structure for Carrington rotation 2069 shows that the newly developed hybrid MHD solar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by comparisons with multiple solar and interplanetary observations.

  18. High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

    NASA Technical Reports Server (NTRS)

    Pandya, Shishir; Murman, Scott; Aftosmis, Michael

    2003-01-01

    Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.

  19. Moving Geometries and Viscous Flows Using Embedded-boundary Cartesian Grids

    DTIC Science & Technology

    2009-11-30

    from the literature were performed. This is preliminary work in two space dimensions towards our goal of extending Cart3D to be able to simulate three...In the last two years a significant advance is the development of an adjoint module for Cart3D by Aftosmis and Nemec. This is used to automatically...Summary of Research The Cart3D flow solver was extended to include viscous terms in two dimensions. The first step in modifying the steady

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

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    1997-01-01

    This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

  1. Visual analytics for power grid contingency analysis.

    PubMed

    Pak Chung Wong; Zhenyu Huang; Yousu Chen; Mackey, Patrick; Shuangshuang Jin

    2014-01-01

    Contingency analysis employs different measures to model scenarios, analyze them, and then derive the best response to any threats. A proposed visual-analytics pipeline for power grid management can transform approximately 100 million contingency scenarios to a manageable size and form. Grid operators can examine individual scenarios and devise preventive or mitigation strategies in a timely manner. Power grid engineers have applied the pipeline to a Western Electricity Coordinating Council power grid model.

  2. Short characteristics method for two dimensional heterogeneous Cartesian cells

    SciTech Connect

    Masiello, E.; Zmijarevic, I.

    2006-07-01

    The short characteristics method for two-dimensional xy-geometry is extended to heterogeneous Cartesian cells. The new method is intended for realistic neutron transport calculation, as for pressurized water reactor assemblies and bundles, without pin cells homogenization. The pin cell is chosen as the basic element for geometrical mapping. Thus, the heterogeneous cells are modeled by a rectangular element with an arbitrary number of concentric rings. Test problems show that the use of this kind of cells allows a minimal geometrical modeling without a significant lost in precision. (authors)

  3. Claes Hellerström and Cartesian diver microrespirometry

    PubMed Central

    Welsh, Michael

    2016-01-01

    Cartesian diver microrespirometry was introduced by Claes Hellerström at the Department of Histology/Medical Cell Biology at Uppsala University, Sweden, to determine rates of oxygen consumption in islets of Langerhans. The theory behind this method is touched upon and the main findings described. Glucose-stimulated beta cell respiration significantly contributes to increased ATP generation, which is a prerequisite for stimulated insulin secretion and synthesis. This has had major implications for understanding the beta cell stimulus–secretion coupling. PMID:27181825

  4. Scaling laws and accurate small-amplitude stationary solution for the motion of a planar vortex filament in the Cartesian form of the local induction approximation.

    PubMed

    Van Gorder, Robert A

    2013-04-01

    We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.

  5. Beyond grid security

    NASA Astrophysics Data System (ADS)

    Hoeft, B.; Epting, U.; Koenig, T.

    2008-07-01

    While many fields relevant to Grid security are already covered by existing working groups, their remit rarely goes beyond the scope of the Grid infrastructure itself. However, security issues pertaining to the internal set-up of compute centres have at least as much impact on Grid security. Thus, this talk will present briefly the EU ISSeG project (Integrated Site Security for Grids). In contrast to groups such as OSCT (Operational Security Coordination Team) and JSPG (Joint Security Policy Group), the purpose of ISSeG is to provide a holistic approach to security for Grid computer centres, from strategic considerations to an implementation plan and its deployment. The generalised methodology of Integrated Site Security (ISS) is based on the knowledge gained during its implementation at several sites as well as through security audits, and this will be briefly discussed. Several examples of ISS implementation tasks at the Forschungszentrum Karlsruhe will be presented, including segregation of the network for administration and maintenance and the implementation of Application Gateways. Furthermore, the web-based ISSeG training material will be introduced. This aims to offer ISS implementation guidance to other Grid installations in order to help avoid common pitfalls.

  6. Internal coordinate molecular dynamics: a foundation for multiscale dynamics.

    PubMed

    Vaidehi, Nagarajan; Jain, Abhinandan

    2015-01-29

    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.

  7. Internal Coordinate Molecular Dynamics: A Foundation for Multiscale Dynamics

    PubMed Central

    2015-01-01

    Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic, which adversely impacts the complexity and the robustness of the simulations. On the other hand, constraints can be easily placed in BAT coordinates by removing the degrees of freedom that need to be constrained. Thus, the internal coordinate MD (ICMD) offers an attractive alternative to Cartesian coordinate MD for developing multiscale MD method. The torsional MD method is a special adaptation of the ICMD method, where all the bond lengths and bond angles are kept rigid. The advantages of ICMD simulation methods are the longer time step size afforded by freezing high frequency degrees of freedom and performing a conformational search in the more important low frequency torsional degrees of freedom. However, the advancements in the ICMD simulations have been slow and stifled by long-standing mathematical bottlenecks. In this review, we summarize the recent mathematical advancements we have made based on spatial operator algebra, in developing a robust long time scale ICMD simulation toolkit useful for various applications. We also present the applications of ICMD simulations to study conformational changes in proteins and protein structure refinement. We review the advantages of the ICMD simulations over the Cartesian simulations when used with enhanced sampling methods and project the future use of ICMD simulations in protein dynamics. PMID:25517406

  8. Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates

    SciTech Connect

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

    2012-05-01

    Several families of nonlinear accelerator lattices with integrable transverse motion were suggested recently. One of the requirements for the existence of two analytic invariants is a special longitudinal coordinate dependence of fields. This paper presents the particle motion analysis when a problem becomes integrable in the normalized polar coordinates. This case is distinguished from the others: it yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields (since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates). A number of interesting features are revealed: while the frequency of radial oscillations is independent of the amplitude, the spread of angular frequencies in a beam is absolute. A corresponding spread of frequencies of oscillations in the Cartesian coordinates is evaluated via the simulation of transverse Schottky noise.

  9. [Cartesian misunderstanding as a cause of therapeutic failure].

    PubMed

    Isler, H

    1986-01-01

    Headache patients disassociate themselves from their own automatic responses, relying on the traditional separation of body and mind. On the other hand, patients who obtain voluntary control of automatic functions by biofeedback training modify not only vegetative but also voluntary behaviour patterns, losing "neurotic" traits. The basic misconception of the separation of body and mind, Cartesian dualism, is now ingrained in our culture. In the 17th century Descartes asserted that concepts applied to the soul must be entirely different from those used for the body in order to improve comprehension of the immortality of the soul. This dualism also led to "enlightenment" and to many later social and philosophical developments. But his basic neurophysiology was obsolete when he wrote it down. Other models from mainstream natural philosophy were better compatible with observation and experiments. Gassendi assumed a "body soul" consisting of energy as the functional principle of the nervous system, and Willis accommodated a series of anticipations of 19th century discoveries within this model. No comparable progress resulted from Descartes' own medieval model. Cartesian dualism has become untenable in view of recent neuropsychology but it still obstructs our management of functional patients. Instead of reinforcing the delusion of separation of psyche and soma, we ought to encourage patients to understand that their malfunctioning organs are on-line with their emotions, and with their mind.

  10. Coil Compression for Accelerated Imaging with Cartesian Sampling

    PubMed Central

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

    2012-01-01

    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

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

    NASA Technical Reports Server (NTRS)

    Berger, Marsha; Aftosmis, Michael J.

    2011-01-01

    The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

  12. Crystal structures of [Ln(NO3)3(μ2-bpydo)2], where Ln = Ce, Pr or Nd, and bpydo = 4,4′-bi­pyridine N,N′-dioxide: layered coordination networks containing 44 grids

    PubMed Central

    Stromyer, Michael L.; Lilly, Cassandra P.; Dillner, Adam J.; Knaust, Jacqueline M.

    2016-01-01

    Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4′-bi­pyridine N,N′-dioxide (bpydo) are reported, namely poly[[tris­(nitrato-κ2 O,O′)cerium(III)]-bis­(μ2-4,4′-bi­pyridine N,N′-dioxide-κ2 N:N′)], [Ce(NO3)3(C10H8N2O2)2], poly[[tris­(nitrato-κ2 O,O′)praeseodymium(III)]-bis­(μ2-4,4′-bi­pyridine N,N′-dioxide-κ2 N:N′)], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ2 O,O′)neodymium(III)]-bis­(μ2-4,4′-bi­pyridine N,N′-dioxide-κ2 N:N′], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln III cations, forming inter­digitating 44 grid-like layers extending parallel to (-101), where inter­digitation of layers is promoted by C—H⋯O inter­actions between nitrate anions and bpydo ligands. The inter­digitated layers are linked to sets of neighboring layers via further C—H⋯O and π–π inter­actions. PMID:26870578

  13. Crystal structures of [Ln(NO3)3(μ2-bpydo)2], where Ln = Ce, Pr or Nd, and bpydo = 4,4'-bi-pyridine N,N'-dioxide: layered coordination networks containing 4(4) grids.

    PubMed

    Stromyer, Michael L; Lilly, Cassandra P; Dillner, Adam J; Knaust, Jacqueline M

    2016-01-01

    Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4'-bi-pyridine N,N'-dioxide (bpydo) are reported, namely poly[[tris-(nitrato-κ(2) O,O')cerium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Ce(NO3)3(C10H8N2O2)2], poly[[tris-(nitrato-κ(2) O,O')praeseodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ(2) O,O')neodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N'], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln (III) cations, forming inter-digitating 4(4) grid-like layers extending parallel to (-101), where inter-digitation of layers is promoted by C-H⋯O inter-actions between nitrate anions and bpydo ligands. The inter-digitated layers are linked to sets of neighboring layers via further C-H⋯O and π-π inter-actions.

  14. Finite element method formulation in polar coordinates for transient heat conduction problems

    NASA Astrophysics Data System (ADS)

    Duda, Piotr

    2016-04-01

    The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

  15. Noncommuting spherical coordinates

    SciTech Connect

    Bander, Myron

    2004-10-15

    Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a magnetic monopole. Restricting the dynamics to the lowest energy level results in noncommutativity for angular variables and to a definition of a noncommuting spherical product. The values of the commutators of various angular variables are not arbitrary but are restricted by the discrete magnitude of the magnetic monopole charge. An algebra, isomorphic to angular momentum, appears. This algebra is used to define a spherical star product. Solutions are obtained for dynamics in the presence of additional angular dependent potentials.

  16. A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

    SciTech Connect

    Sidler, Rolf; Carcione, José M.; Holliger, Klaus

    2013-02-15

    We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

  17. Features in Continuous Parallel Coordinates.

    PubMed

    Lehmann, Dirk J; Theisel, Holger

    2011-12-01

    Continuous Parallel Coordinates (CPC) are a contemporary visualization technique in order to combine several scalar fields, given over a common domain. They facilitate a continuous view for parallel coordinates by considering a smooth scalar field instead of a finite number of straight lines. We show that there are feature curves in CPC which appear to be the dominant structures of a CPC. We present methods to extract and classify them and demonstrate their usefulness to enhance the visualization of CPCs. In particular, we show that these feature curves are related to discontinuities in Continuous Scatterplots (CSP). We show this by exploiting a curve-curve duality between parallel and Cartesian coordinates, which is a generalization of the well-known point-line duality. Furthermore, we illustrate the theoretical considerations. Concluding, we discuss relations and aspects of the CPC's/CSP's features concerning the data analysis.

  18. Overture: The grid classes

    SciTech Connect

    Brislawn, K.; Brown, D.; Chesshire, G.; Henshaw, W.

    1997-01-01

    Overture is a library containing classes for grids, overlapping grid generation and the discretization and solution of PDEs on overlapping grids. This document describes the Overture grid classes, including classes for single grids and classes for collections of grids.

  19. Some studies on generalized coordinate sets for polyatomic molecules.

    PubMed

    Li, Wenjin; Ma, Ao

    2015-12-14

    Generalized coordinates are widely used in various analyses of the trajectories of polyatomic molecules from molecular dynamics simulations, such as normal mode analysis and force distribution analysis. Here, we presented detailed discussions on the properties of some specific sets of generalized coordinates, which separate translational, rotational, and vibrational motions of a molecule from one another once the trajectories of dynamical systems are known. Efficient methods were suggested for estimating the transformation matrix between generalized and Cartesian coordinates. Some properties of the well-known BAT coordinates (bond length, angle, and torsional coordinates) were discussed as well.

  20. The choice of internal coordinates in complex chemical systems.

    PubMed

    Németh, Károly; Challacombe, Matt; Van Veenendaal, Michel

    2010-07-30

    This article presents several considerations for the appropriate choice of internal coordinates in various complex chemical systems. The appropriate and black box recognition of internal coordinates is of fundamental importance for the extension of internal coordinate algorithms to all fields where previously Cartesian coordinates were the preferred means of geometry manipulations. Such fields range from local and global geometry optimizations to molecular dynamics as applied to a wide variety of chemical systems. We present a robust algorithm that is capable to quickly determine the appropriate choice of internal coordinates in a wide range of atomic arrangements.

  1. Grids = Structure.

    ERIC Educational Resources Information Center

    Barrington, Linda; Carter, Jacky

    2003-01-01

    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)

  2. Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: excited states.

    PubMed

    Issack, Bilkiss B; Roy, Pierre-Nicholas

    2007-01-14

    The authors show that a recently proposed approach [J. Chem. Phys. 123, 084103 (2005)] for the inclusion of geometric constraints in semiclassical initial value representation calculations can be used to obtain excited states of weakly bound complexes. Sample calculations are performed for free and constrained rare gas clusters. The results show that the proposed approach allows the evaluation of excited states with reasonable accuracy when compared to exact basis set calculations.

  3. A Cartesian classical second-quantized many-electron Hamiltonian, for use with the semiclassical initial value representation.

    PubMed

    Li, Bin; Miller, William H

    2012-10-21

    A new classical model for the general second-quantized many-electron Hamiltonian in Cartesian coordinates and momenta is presented; this makes semiclassical (SC) calculations using an initial value representation (IVR) more useful than the classical Hamiltonian in action-angle variables given earlier by Miller and White [J. Chem. Phys. 84, 5059-5066 (1986)]. If only 1-electron terms are included in this Hamiltonian, the classical equations of motion for the Cartesian variables are linear, and the SC-IVR gives exact results for the propagator (and thus for transition probabilities, the energy spectrum, etc.), as confirmed by analytic proof and numerical calculations. Though this new Hamiltonian is not exact when 2-electron interactions are included, we observe good results for the SC-IVR transition probabilities for times that are not too long. Test calculations, for example, show that the SC-IVR is accurate for times long enough to obtain good result for the eigenvalue spectrum (i.e., the energy levels of the electronic system).

  4. General formulation of vibronic spectroscopy in internal coordinates.

    PubMed

    Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo

    2016-02-28

    Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.

  5. General formulation of vibronic spectroscopy in internal coordinates

    NASA Astrophysics Data System (ADS)

    Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo

    2016-02-01

    Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.

  6. Grid technologies empowering drug discovery.

    PubMed

    Chien, Andrew; Foster, Ian; Goddette, Dean

    2002-10-15

    Grid technologies enable flexible coupling and sharing of computers, instruments and storage. Grids can provide technical solutions to the volume of data and computational demands associated with drug discovery by delivering larger computing capability (flexible resource sharing), providing coordinated access to large data resources and enabling novel online exploration (coupling computing, data and instruments online). Here, we illustrate this potential by describing two applications: the use of desktop PC grid technologies for virtual screening, and distributed X-ray structure reconstruction and online visualization.

  7. Practical conversion from torsion space to Cartesian space for in silico protein synthesis.

    PubMed

    Parsons, Jerod; Holmes, J Bradley; Rojas, J Maurice; Tsai, Jerry; Strauss, Charlie E M

    2005-07-30

    Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but computationally consuming task occurs ubiquitously in modeling proteins, DNA, and other polymers as well as in many other fields such as robotics. To find an optimal method, algorithms can be compared by a number of operations, speed, intrinsic numerical stability, and parallelization. We discuss five established methods for growing a protein backbone by serial chain extension from bond angles and bond lengths. We introduce the Natural Extension Reference Frame (NeRF) method developed for Rosetta's chain extension subroutine, as well as an improved implementation. In comparison to traditional two-step rotations, vector algebra, or Quaternion product algorithms, the NeRF algorithm is superior for this application: it requires 47% fewer floating point operations, demonstrates the best intrinsic numerical stability, and offers prospects for parallel processor acceleration. The NeRF formalism factors the mathematical operations of chain extension into two independent terms with orthogonal subsets of the dependent variables; the apparent irreducibility of these factors hint that the minimal operation set may have been identified. Benchmarks are made on Intel Pentium and Motorola PowerPC CPUs.

  8. Radially dependent large-scale dynamos in global cylindrical shear flows and the local cartesian limit

    NASA Astrophysics Data System (ADS)

    Ebrahimi, F.; Blackman, E. G.

    2016-06-01

    For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard `Ω effect' (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations - even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.

  9. The National Grid Project: A system overview

    NASA Technical Reports Server (NTRS)

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

    1995-01-01

    The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.

  10. Grid oscillators

    NASA Technical Reports Server (NTRS)

    Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.

    1988-01-01

    Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.

  11. High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates

    NASA Astrophysics Data System (ADS)

    Mignone, A.

    2014-08-01

    High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.

  12. 77 FR 71169 - Smart Grid Advisory Committee Meeting

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-11-29

    ... recommendations from the Committee's report and to receive presentations on cybersecurity coordination and the... cybersecurity coordination and the NIST Smart Grid Program Plan. The agenda may change to accommodate...

  13. Grid Computing

    NASA Astrophysics Data System (ADS)

    Foster, Ian

    2001-08-01

    The term "Grid Computing" refers to the use, for computational purposes, of emerging distributed Grid infrastructures: that is, network and middleware services designed to provide on-demand and high-performance access to all important computational resources within an organization or community. Grid computing promises to enable both evolutionary and revolutionary changes in the practice of computational science and engineering based on new application modalities such as high-speed distributed analysis of large datasets, collaborative engineering and visualization, desktop access to computation via "science portals," rapid parameter studies and Monte Carlo simulations that use all available resources within an organization, and online analysis of data from scientific instruments. In this article, I examine the status of Grid computing circa 2000, briefly reviewing some relevant history, outlining major current Grid research and development activities, and pointing out likely directions for future work. I also present a number of case studies, selected to illustrate the potential of Grid computing in various areas of science.

  14. Numerical modeling of conjugate heat transfer on complex geometries with diagonal Cartesian method. Part 2: Applications

    SciTech Connect

    Carlson, K.D.; Lin, W.L.; Chen, C.J. |

    1999-05-01

    Part 1 of this study discusses the diagonal Cartesian method for temperature analysis. The application of this method to the analysis of flow and conjugate heat transfer in a compact heat exchanger is given in Part 2. In addition to a regular (i.e., Cartesian-oriented) fin arrangement, two complex fin arrangements are modeled using the diagonal Cartesian method. The pressure drop and heat transfer characteristics of the different configurations are compared. It is found that enhanced heat transfer and reduced pressure drop can be obtained with the modified fin arrangements for this compact heat exchanger.

  15. Grid generation on surfaces in 3 dimensions

    NASA Technical Reports Server (NTRS)

    Eiseman, Peter R.

    1986-01-01

    The development of a surface grid generation algorithm was initiated. The basic adaptive movement technique of mean-value-relaxation was extended from the viewpoint of a single coordinate grid over a surface described by a single scalar function to that of a surface more generally defined by vector functions and covered by a collection of smoothly connected grids. Within the multiconnected assemblage, the application of control was examined in several instances.

  16. Unstructured Grid Generation Techniques and Software

    NASA Technical Reports Server (NTRS)

    Posenau, Mary-Anne K. (Editor)

    1993-01-01

    The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.

  17. Tracking algorithms using log-polar mapped image coordinates

    NASA Technical Reports Server (NTRS)

    Weiman, Carl F. R.; Juday, Richard D.

    1990-01-01

    The use of log-polar image sampling coordinates rather than conventional Cartesian coordinates offers a number of advantages for visual tracking and docking of space vehicles. Pixel count is reduced without decreasing the field of view, with commensurate reduction in peripheral resolution. Smaller memory requirements and reduced processing loads are the benefits in working environments where bulk and energy are at a premium. Rotational and zoom symmetries of log-polar coordinates accommodate range and orientation extremes without computational penalties. Separation of radial and rotational coordinates reduces the complexity of several target centering algorithms, described below.

  18. MESH2D GRID GENERATOR DESIGN AND USE

    SciTech Connect

    Flach, G.; Smith, F.

    2012-01-20

    Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.

  19. Static Aeroelastic Analysis with an Inviscid Cartesian Method

    NASA Technical Reports Server (NTRS)

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

    2014-01-01

    An embedded-boundary Cartesian-mesh flow solver is coupled with a three degree-offreedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves the complete system of aero-structural equations using a modular, loosely-coupled strategy which allows the lower-fidelity structural model to deform the highfidelity CFD model. The approach uses an open-source, 3-D discrete-geometry engine to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. This extended abstract includes a brief description of the architecture, along with some preliminary validation of underlying assumptions and early results on a generic 3D transport model. The final paper will present more concrete cases and validation of the approach. Preliminary results demonstrate convergence of the complete aero-structural system and investigate the accuracy of the approximations used in the formulation of the structural model.

  20. Static Aeroelastic Analysis with an Inviscid Cartesian Method

    NASA Technical Reports Server (NTRS)

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

    2014-01-01

    An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

  1. Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

    This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.

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

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1995-01-01

    A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

  3. Advances in Distance-Based Hole Cuts on Overset Grids

    NASA Technical Reports Server (NTRS)

    Chan, William M.; Pandya, Shishir A.

    2015-01-01

    An automatic and efficient method to determine appropriate hole cuts based on distances to the wall and donor stencil maps for overset grids is presented. A new robust procedure is developed to create a closed surface triangulation representation of each geometric component for accurate determination of the minimum hole. Hole boundaries are then displaced away from the tight grid-spacing regions near solid walls to allow grid overlap to occur away from the walls where cell sizes from neighboring grids are more comparable. The placement of hole boundaries is efficiently determined using a mid-distance rule and Cartesian maps of potential valid donor stencils with minimal user input. Application of this procedure typically results in a spatially-variable offset of the hole boundaries from the minimum hole with only a small number of orphan points remaining. Test cases on complex configurations are presented to demonstrate the new scheme.

  4. An assessment of unstructured grid technology for timely CFD analysis

    NASA Technical Reports Server (NTRS)

    Kinard, Tom A.; Schabowski, Deanne M.

    1995-01-01

    An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.

  5. Resolution enhancement in tilted coordinates

    NASA Astrophysics Data System (ADS)

    Hariri Naghadeh, Diako; Keith Morley, Christopher

    2016-11-01

    Deconvolution is applied to remove source wavelet effects from seismograms. The results are resolution enhancement that enables detection of thin layers. Following enhancement of resolution, low frequency and high angle reflectors, particularly at great depth, appear as low amplitude and semi-invisible reflectors that are difficult to track and pick. A new approach to enhance resolution is introduced that estimates a derivative using continuous wavelet transform in tilted coordinates. The results are compared with sparse spike deconvolution, curvelet deconvolution and inverse quality filtering in wavelet domain. The positive consequence of the new method is to increase sampling of high dip features by changing the coordinate system from Cartesian to tilted. To compare those methods a complex data set was chosen that includes high angle faults and chaotic mass transport complex. Image enhancement using curvelet deconvolution shows a chaotic system as a non-chaotic one. The results show that sparse spike deconvolution and inverse quality filtering in wavelet domain are able to enhance resolution more than curvelet deconvolution especially at great depth but it is impossible to follow steep dip reflectors after resolution enhancement using these methods, especially when their apparent dips are more than 45°. By estimating derivatives in a continuous wavelet transform from tilted data sets similar resolution enhancement as the other deconvolution methods is achieved but additionally steep dipping reflectors are imaged much better than others. Subtracted results of the enhanced resolution data set using new method and the other introduced methods show that steeply dipping reflectors are highlighted as a particular ability of the new method. The results show that high frequency recovery in Cartesian co-ordinate is accompanied by inability to image steeply dipping reflectors especially at great depths. Conversely recovery of high frequency data and imaging of the data

  6. Solving Partial Differential Equations on Overlapping Grids

    SciTech Connect

    Henshaw, W D

    2008-09-22

    We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solution of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.

  7. A mixed volume grid approach for the Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Jorgenson, Philip C. E.

    1996-01-01

    An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.

  8. Multiscale geometric modeling of macromolecules I: Cartesian representation

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  9. Multiscale geometric modeling of macromolecules I: Cartesian representation

    PubMed Central

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

    2013-01-01

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  10. A non-uniform grid for triangular differential quadrature

    NASA Astrophysics Data System (ADS)

    Zhong, HongZhi; Xu, Jia

    2016-12-01

    The triangular differential quadrature method based on a non-uniform grid is proposed in the paper. Explicit expressions of the non-uniform grid point coordinates are given and the weighting coefficients of the triangular differential quadrature method are determined with the aid of area coordinates. Two typical examples are presented to testify the effectiveness of the non-uniform grid. It is shown that rapid convergence is achieved under the non-uniform grid in comparison with those from the uniform grid with the same order of approximation.

  11. Degree of coherence in curvilinear coordinates and its application to scattering.

    PubMed

    Tong, Zhisong

    2012-07-01

    In the traditional treatment of the spectral degree of coherence, the Cartesian coordinate system is deployed to describe the electromagnetic field. In the description of the far field scattered from random media, however, the spherical polar coordinates system is more suitably used due to the field's outgoing spherical form. We hence derive the expression for the spectral degree of coherence in the spherical polar coordinates system. An example of one polychromatic plane wave scattered by a collection of identical particles is given.

  12. TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION

    NASA Technical Reports Server (NTRS)

    Smith, R. E.

    1994-01-01

    TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.

  13. TIGGERC: Turbomachinery interactive grid generator energy distributor and restart code

    NASA Technical Reports Server (NTRS)

    Miller, David P.

    1992-01-01

    A two dimensional multi-block grid generator was developed for a new design and analysis system for studying multi-blade row turbomachinery problems with an axisymmetric viscous/inviscid 'average passage' through flow code. TIGGERC is a mouse driven, fully interactive grid generation program which can be used to modify boundary coordinates and grid packing. TIGGERC generates grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries and the interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC generates a blocked axisymmetric H grid, C grid, I grid, or O grid for studying turbomachinery flow problems. TIGGERC was developed for operation on small high speed graphic workstations.

  14. Analysis of Crustal Magnetisation in Cartesian Vector Harmonics

    NASA Astrophysics Data System (ADS)

    Gubbins, D.; Ivers, D.; Williams, S.

    2015-12-01

    We present a new set of functions, Vector Cartesian Harmonics (VCH), analogous to the Vector Spherical Harmonics that we have applied recently to global models of crustal and lithospheric magnetisation. Like their spherical counterpart, the VCH form a complete, orthogonal set: planar models of magnetisation can be expanded in them. There are 3 distinct types of VCH, one representing that part of the magnetisation which generates the potential magnetic field above the surface, another the potential magnetic field below the surface, and a toroidal function that generates only a non-potential field. One function therefore describes the magnetisation detected by observations of the magnetic anomaly while the other two describe the null space of an inversion of magnetic observations for magnetisation. The formalism is therefore ideal for analysing the results of inversions for magnetic structures in plane layers such as local or regional surveys where Earth's curvature can be ignored. The null space is in general very large, being an arbitrary combination of a doubly-infinite set of vector functions. However, in the absence of remanence and when the inducing field is uniform the null space reduces to only 2 types of structure, uniform susceptibility (Runcorn's Theorem) and a pattern of susceptibility induced by a uniform field, the null space is restricted to uniform magnetisation and 1D patterns of susceptibility aligned with a horizontal inducing field. Both these cases are already well known, but this analysis shows them to be the ONLY members of the null space. We also give results for familiar text-book structures to show the nature of the null space in each case. Curiously, inversion of the magnetic field from a buried dipole returns exactly half the correct magnitude plus a spurious distributed magnetisation. A more complex application is the topographic structure based on the Bishop formation in California (Fairhead and Williams, SEG exp. abstr. 25, 845, 2006

  15. Safe Grid

    NASA Technical Reports Server (NTRS)

    Chow, Edward T.; Stewart, Helen; Korsmeyer, David (Technical Monitor)

    2003-01-01

    The biggest users of GRID technologies came from the science and technology communities. These consist of government, industry and academia (national and international). The NASA GRID is moving into a higher technology readiness level (TRL) today; and as a joint effort among these leaders within government, academia, and industry, the NASA GRID plans to extend availability to enable scientists and engineers across these geographical boundaries collaborate to solve important problems facing the world in the 21 st century. In order to enable NASA programs and missions to use IPG resources for program and mission design, the IPG capabilities needs to be accessible from inside the NASA center networks. However, because different NASA centers maintain different security domains, the GRID penetration across different firewalls is a concern for center security people. This is the reason why some IPG resources are been separated from the NASA center network. Also, because of the center network security and ITAR concerns, the NASA IPG resource owner may not have full control over who can access remotely from outside the NASA center. In order to obtain organizational approval for secured remote access, the IPG infrastructure needs to be adapted to work with the NASA business process. Improvements need to be made before the IPG can be used for NASA program and mission development. The Secured Advanced Federated Environment (SAFE) technology is designed to provide federated security across NASA center and NASA partner's security domains. Instead of one giant center firewall which can be difficult to modify for different GRID applications, the SAFE "micro security domain" provide large number of professionally managed "micro firewalls" that can allow NASA centers to accept remote IPG access without the worry of damaging other center resources. The SAFE policy-driven capability-based federated security mechanism can enable joint organizational and resource owner approved remote

  16. Technology for a NASA Space-Based Science Operations Grid

    NASA Technical Reports Server (NTRS)

    Bradford, Robert N.; Redman, Sandra H.

    2003-01-01

    This viewgraph representation presents an overview of a proposal to develop a space-based operations grid in support of space-based science experiments. The development of such a grid would provide a dynamic, secure and scalable architecture based on standards and next-generation reusable software and would enable greater science collaboration and productivity through the use of shared resources and distributed computing. The authors propose developing this concept for use on payload experiments carried aboard the International Space Station. Topics covered include: grid definitions, portals, grid development and coordination, grid technology and potential uses of such a grid.

  17. Sinusoidal error perturbation reveals multiple coordinate systems for sensorymotor adaptation

    PubMed Central

    Hudson, Todd E.; Landy, Michael S.

    2016-01-01

    A coordinate system is composed of an encoding, defining the dimensions of the space, and an origin. We examine the coordinate encoding used to update motor plans during sensory-motor adaptation to center-out reaches. Adaptation is induced using a novel paradigm in which feedback of reach endpoints is perturbed following a sinewave pattern over trials; the perturbed dimensions of the feedback were the axes of a Cartesian coordinate system in one session and a polar coordinate system in another session. For center-out reaches to randomly chosen target locations, reach errors observed at one target will require different corrections at other targets within Cartesian- and polar-coded systems. The sinewave adaptation technique allowed us to simultaneously adapt both dimensions of each coordinate system (x-y, or reach gain and angle), and identify the contributions of each perturbed dimension by adapting each at a distinct temporal frequency. The efficiency of this technique further allowed us to employ perturbations that were a fraction the size normally used, which avoids confounding automatic adaptive processes with deliberate adjustments made in response to obvious experimental manipulations. Subjects independently corrected errors in each coordinate in both sessions, suggesting that the nervous system encodes both a Cartesian- and polar-coordinate-based internal representation for motor adaptation. The gains and phase lags of the adaptive responses are not readily explained by current theories of sensory-motor adaptation. Motor adaptation is fundamental to the neural control of movement, affording an automatic process to maintain a consistent relationship between motor plans and movement outcomes. That is, adaptation is described as updating an internal mapping between desired motor outcome and motor output (Sanger, 2004; Shadmehr, Smith, & Krakauer, 2010), not a deliberate corrective action. Here, using a method that relies on extremely small perturbations that

  18. Three-dimensional measurements of scalar dispersion in grid turbulence

    NASA Astrophysics Data System (ADS)

    Dimotakis, Paul; Lang, Daniel; Lombeyda, Santiago; Lindheim, Jan

    2006-11-01

    The three-dimensional scalar-dispersion field of a passive Lagrangian-marker contaminant released in grid-generated turbulent flow with an initial Taylor Reynolds number of ˜40, was investigated. The experiments were conducted in the GALCIT Free Surface Water Tunnel using laser-induced fluorescence, a two-dimensional galvanometric optical scanner, and recorded with a fast-framing CCD camera and data acquisition system that sustained 10^8,pix/s, at 12,bits/pix. The resulting data frames were processed to compensate for temporal and spatial skewing, and resampled on a Cartesian grid for subsequent processing. The spatial structure of the scalar field downstream of the grid will be presented and discussed.

  19. Magnetohydrodynamic Modeling of Solar System Processes on Geodesic Grids

    NASA Astrophysics Data System (ADS)

    Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.

    2013-04-01

    This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional "Cartesian" frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

  20. MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

    SciTech Connect

    Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.

    2013-04-01

    This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

  1. Comparison of Cartesian and Non-Cartesian Real-Time MRI Sequences at 1.5T to Assess Velar Motion and Velopharyngeal Closure during Speech

    PubMed Central

    Freitas, Andreia C.; Wylezinska, Marzena; Birch, Malcolm J.; Petersen, Steffen E.; Miquel, Marc E.

    2016-01-01

    Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal

  2. Datums, Ellipsoids, Grids, and Grid Reference Systems

    DTIC Science & Technology

    1992-01-01

    Tunisie Grid, Sud Algerie Grid, Sud Maroc Grid, and Sud Tunisie Grid. 4-1.1.8 The...REFERENCES ON THE SUD ALGERIE AND SUD TUNISIE GRIDS 6-8.5.2 When oil reference boxes cannot be accommodated in the margin, the excess is shown in expanses...GIVING REFERENCES ON THE SUD ALGERIE AND SUD TUNISIE GRIDS 6-21 DMA TM 8358.1 I CHAPTER 7 GRIDS ON MAPS AT 1:250,000 AND 1:500,000 SCALE 7.1 GENERAL.

  3. COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY

    SciTech Connect

    Sebastian Schunert; Yousry Y. Azmy; Damien Fournier

    2011-05-01

    We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.

  4. An improved method for calculating self-motion coordinates for redundant manipulators

    SciTech Connect

    Reister, D.B.

    1997-04-01

    For a redundant manipulator, the objective of redundancy resolution is to follow a specified path in Cartesian space and simultaneously perform another task (for example, maximize an objective function or avoid obstacles) at every point along the path. The conventional methods have several drawbacks: a new function must be defined for each task, the extended Jacobian can be singular, closed cycles in Cartesian space may not yield closed cycles in joint space, and the objective is point-wise redundancy resolution (to determine a single point in joint space for each point in Cartesian space). The author divides the redundancy resolution problem into two parts: (1) calculate self-motion coordinates for all possible positions of a manipulator at each point along a Cartesian path and (2) determination of optimal self-motion coordinates that maximize an objective function along the path. This paper will discuss the first part of the problem. The path-wise approach overcomes all of the drawbacks of conventional redundancy resolution methods: no need to define a new function for each task, extended Jacobian cannot be singular, and closed cycles in extended Cartesian space will yield closed cycles in joint space.

  5. ESMPy and OpenClimateGIS: Python Interfaces for High Performance Grid Remapping and Geospatial Dataset Manipulation

    NASA Astrophysics Data System (ADS)

    O'Kuinghttons, Ryan; Koziol, Benjamin; Oehmke, Robert; DeLuca, Cecelia; Theurich, Gerhard; Li, Peggy; Jacob, Joseph

    2016-04-01

    The Earth System Modeling Framework (ESMF) Python interface (ESMPy) supports analysis and visualization in Earth system modeling codes by providing access to a variety of tools for data manipulation. ESMPy started as a Python interface to the ESMF grid remapping package, which provides mature and robust high-performance and scalable grid remapping between 2D and 3D logically rectangular and unstructured grids and sets of unconnected data. ESMPy now also interfaces with OpenClimateGIS (OCGIS), a package that performs subsetting, reformatting, and computational operations on climate datasets. ESMPy exposes a subset of ESMF grid remapping utilities. This includes bilinear, finite element patch recovery, first-order conservative, and nearest neighbor grid remapping methods. There are also options to ignore unmapped destination points, mask points on source and destination grids, and provide grid structure in the polar regions. Grid remapping on the sphere takes place in 3D Cartesian space, so the pole problem is not an issue as it can be with other grid remapping software. Remapping can be done between any combination of 2D and 3D logically rectangular and unstructured grids with overlapping domains. Grid pairs where one side of the regridding is represented by an appropriate set of unconnected data points, as is commonly found with observational data streams, is also supported. There is a developing interoperability layer between ESMPy and OpenClimateGIS (OCGIS). OCGIS is a pure Python, open source package designed for geospatial manipulation, subsetting, and computation on climate datasets stored in local NetCDF files or accessible remotely via the OPeNDAP protocol. Interfacing with OCGIS has brought GIS-like functionality to ESMPy (i.e. subsetting, coordinate transformations) as well as additional file output formats (i.e. CSV, ESRI Shapefile). ESMPy is distinguished by its strong emphasis on open source, community governance, and distributed development. The user

  6. An accuracy assessment of Cartesian-mesh approaches for the Euler equations

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1995-01-01

    A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

  7. Coordinate transformation by minimizing correlations between parameters

    NASA Technical Reports Server (NTRS)

    Kumar, M.

    1972-01-01

    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.

  8. A high-order adaptive Cartesian cut-cell method for simulation of compressible viscous flow over immersed bodies

    NASA Astrophysics Data System (ADS)

    Muralidharan, Balaji; Menon, Suresh

    2016-09-01

    A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.

  9. Structure sensitive normal coordinate analysis of metal-diethyldithiocarbamate - complexes

    NASA Astrophysics Data System (ADS)

    Mikosch, H.; Bauer, G.; Kellner, R.; Trendafilova, N. S.; St. Nikolov, G.

    1986-03-01

    Symmetry changes in the course of dissolution are assumed to produce frequency shifts in molecular spectra of N, N-Disubstituted Dithiocarbamates. Using (mass-weighted) cartesian coordinates it is possible to calculate eigenvalues both for the site- and the molecular symmetry. Calculated shifts for Cu- and Zn- complexes are of the same order of magnitude as experimental results and calculation of frequencies even for assumed structures is possible.

  10. First experimental comparison between the cartesian and the lissajous trajectory for magnetic particle imaging.

    PubMed

    Werner, Franziska; Gdaniec, Nadine; Knopp, Tobias

    2017-02-20

    Magnetic Particle Imaging (MPI) is a quantitative imaging modality that allows to determine the distribution of superparamagnetic nanoparticles. Sampling is achieved by moving a field-free point (FFP) along a specific trajectory through the volume of interest. The magnetic material that lies along the path or in the close vicinity of the FFP changes its magnetization and induces a voltage in surrounding receive coils. Various trajectories for the FFP are conceivable, but most experimental MPI scanners either use a Cartesian or a Lissajous sampling trajectory. This study for the first time compares both sampling methods experimentally using an MPI scanner that allows to implement both sampling patterns. By default the scanner is capable of scanning 2D and 3D field of views using a Lissajous trajectory. But since it also has a 1D mode, it is possible to perform Cartesian measurements by shifting the 1D scan line in perpendicular direction to the FFP movement using the focus field. These line scans are jointly reconstructed to obtain a 2D image. In a further step, the unidirectional Cartesian trajectory is improved by interchanging the excitation and the focus-field direction leading to a bidirectional Cartesian trajectory. Our findings reveal similar results for the bidirectional Cartesian and the Lissajous trajectory concerning the overall image quality and the sensitivity. In a more detailed view, the bidirectional Cartesian trejectory achieves a slightly higher spatial center resolution, whereas the Lissajous trajectory is more efficient regarding the temporal resolution since less acquisition time is needed to reach an adequate image quality.

  11. Random subspaces for encryption based on a private shared Cartesian frame

    SciTech Connect

    Bartlett, Stephen D.; Hayden, Patrick; Spekkens, Robert W.

    2005-11-15

    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.

  12. A Vertical Grid Module for Baroclinic Models of the Atmosphere

    SciTech Connect

    Drake, John B

    2008-04-01

    The vertical grid of an atmospheric model assigns dynamic and thermo- dynamic variables to grid locations. The vertical coordinate is typically not height but one of a class of meteorological variables that vary with atmo- spheric conditions. The grid system is chosen to further numerical approx- imations of the boundary conditions so that the system is terrain following at the surface. Lagrangian vertical coordinates are useful in reducing the numerical errors from advection processes. That the choices will effect the numercial properties and accuracy is explored in this report. A MATLAB class for Lorentz vertical grids is described and applied to the vertical struc- ture equation and baroclinic atmospheric circulation. A generalized meteo- rolgoical coordinate system is developed which can support σ, isentropic θ vertical coordinate, or Lagrangian vertical coordinates. The vertical atmo- spheric column is a MATLAB class that includes the kinematic and ther- modynamic variables along with methods for computing geopoentials and terms relevant to a 3D baroclinc atmospheric model.

  13. Reversible shuttle action upon dehydration and rehydration processes in cationic coordinatively-bonded (4,4) square-grid nets threaded by supramolecular bonded anions, {[Cu(II)(4,4'-bpy)2(H2O)][Cu(II)(2-pySO3)3](NO3)}·H2O.

    PubMed

    Jiang, Yi-Min; Yin, Zheng; He, Kun-Huan; Zeng, Ming-Hua; Kurmoo, Mohamedally

    2011-03-21

    {[Cu(II)(4,4'-bpy)(2)(H(2)O)][Cu(II)(2-pySO(3))(3)](NO(3))}·H(2)O, obtained serendipitously by the reaction of the constituents in water, consists of parallel coordinatively bonded cationic (4,4) corrugated square-grids polymer of {[Cu(II)(4,4'-bpy)(2)(H(2)O)](2+)}(n) threaded by π-π and H-bonded supramolecular chains of [Cu(II)(2-pySO(3))(3)](-) through the open squares. A single-crystal to single-crystal transformation takes place upon removal of the noncoordinated water by controlled heating. The resulting structure exhibits a rearrangement of the coordination of the copper atoms in the grids, where the Cu-H(2)O bond is elongated from 2.250(3) to 2.628(3) Å while the Cu-NO(3) is shortened from 3.122(3) to 2.796(1) Å. This process is reversible as demonstrated by the single crystal structure after rehydration with corresponding bond distances of 2.224(3) and 3.152(3) Å. Such a cooperative effect may be associated with the Jahn-Teller distortion of the copper(II) ion accompanying the shuttle action of the hydrogen-bonded water and nitrate moiety.

  14. GridMan: A grid manipulation system

    NASA Technical Reports Server (NTRS)

    Eiseman, Peter R.; Wang, Zhu

    1992-01-01

    GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.

  15. caGrid 1.0: An Enterprise Grid Infrastructure for Biomedical Research

    PubMed Central

    Oster, Scott; Langella, Stephen; Hastings, Shannon; Ervin, David; Madduri, Ravi; Phillips, Joshua; Kurc, Tahsin; Siebenlist, Frank; Covitz, Peter; Shanbhag, Krishnakant; Foster, Ian; Saltz, Joel

    2008-01-01

    Objective 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™) 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: https://cabig.nci.nih.gov/workspaces/Architecture/caGrid. Conclusions While caGrid 1.0 is designed to address use cases in cancer research, the requirements associated with discovery, analysis and integration of large scale data, and coordinated studies are common in other biomedical fields. In this respect, caGrid 1.0 is the realization of a framework that can benefit the entire biomedical community. PMID:18096909

  16. Parallel Unsteady Overset Mesh Methodology for Adaptive and Moving Grids with Multiple Solvers

    DTIC Science & Technology

    2010-01-01

    Runge - Kutta time-stepping framework and is capable of up to fifth-order accurate spatial discretizations. Further, the Cartesian grids in the off-body are...no user intervention or explicit hole-map specification is necessary. The capabilities and performance of the package are presented for several test...connectivity approaches have been investigated in the past by various research groups . The prominent among them are PEGASUS5 [5], OVERFLOW-DCF [6, 7], SUGGAR

  17. caGrid 1.0 : an enterprise Grid infrastructure for biomedical research.

    SciTech Connect

    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

    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: Grid>.

  18. A Moving Grid Capability for NPARC

    NASA Technical Reports Server (NTRS)

    Slater, John W.

    1998-01-01

    Version 3.1 of the NPARC computational fluid dynamics flow solver introduces a capability to solve unsteady flow on moving multi-block, structured grids with nominally second-order time accuracy. The grid motion is due to segments of the boundary grid that translate and rotate in a rigid-body manner or deform. The grid is regenerated at each time step to accommodate the boundary grid motion. The flow equations and computational models sense the moving grid through the grid velocities, which are computed from a time-difference of the grids at two consecutive time levels. For three-dimensional flow domains, it is assumed that the grid retains a planar character with respect to one coordinate. The application and accuracy of NPARC v3.1 is demonstrated for flow about a flying wedge, rotating flap, a collapsing bump in a duct, and the upstart / restart flow in a variable-geometry inlet. The results compare well with analytic and experimental results.

  19. Real-time cartesian force feedback control of a teleoperated robot

    NASA Technical Reports Server (NTRS)

    Campbell, Perry

    1989-01-01

    Active cartesian force control of a teleoperated robot is investigated. An economical microcomputer based control method was tested. Limitations are discussed and methods of performance improvement suggested. To demonstrate the performance of this technique, a preliminary test was performed with success. A general purpose bilateral force reflecting hand controller is currently being constructed based on this control method.

  20. [Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].

    PubMed

    Gysel, C

    1979-01-01

    In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.

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

    ERIC Educational Resources Information Center

    Lelwica, Michelle Mary

    2009-01-01

    This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…

  2. A formulation for the boundary-layer equations in general coordinates

    NASA Technical Reports Server (NTRS)

    Steger, Joseph L.; Vandalsem, William R.; Panaras, Argyris G.; Rao, K. V.

    1988-01-01

    This is a working paper in which a formulation is given for solving the boundary-layer equations in general body-fitted curvilinear coordinates while retaining the original Cartesian dependent variables. The solution procedure does not require that any of the coordinates be orthogonal, and much of the software developed for many Navier-Stokes schemes can be readily used. A limited number of calculations has been undertaken to validate the approach.

  3. Smart Grid Risk Management

    NASA Astrophysics Data System (ADS)

    Abad Lopez, Carlos Adrian

    Current electricity infrastructure is being stressed from several directions -- high demand, unreliable supply, extreme weather conditions, accidents, among others. Infrastructure planners have, traditionally, focused on only the cost of the system; today, resilience and sustainability are increasingly becoming more important. In this dissertation, we develop computational tools for efficiently managing electricity resources to help create a more reliable and sustainable electrical grid. The tools we present in this work will help electric utilities coordinate demand to allow the smooth and large scale integration of renewable sources of energy into traditional grids, as well as provide infrastructure planners and operators in developing countries a framework for making informed planning and control decisions in the presence of uncertainty. Demand-side management is considered as the most viable solution for maintaining grid stability as generation from intermittent renewable sources increases. Demand-side management, particularly demand response (DR) programs that attempt to alter the energy consumption of customers either by using price-based incentives or up-front power interruption contracts, is more cost-effective and sustainable in addressing short-term supply-demand imbalances when compared with the alternative that involves increasing fossil fuel-based fast spinning reserves. An essential step in compensating participating customers and benchmarking the effectiveness of DR programs is to be able to independently detect the load reduction from observed meter data. Electric utilities implementing automated DR programs through direct load control switches are also interested in detecting the reduction in demand to efficiently pinpoint non-functioning devices to reduce maintenance costs. We develop sparse optimization methods for detecting a small change in the demand for electricity of a customer in response to a price change or signal from the utility

  4. The all-Cartesian reaction plane Hamiltonian: formulation and application to the H-atom transfer in tropolone.

    PubMed

    Giese, Kai; Kühn, Oliver

    2005-08-01

    In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, that is, the unique plane defined by the two minima and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approximation which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calculations. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramolecular O...H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm(-1) for the normal and deuterated species, respectively. We calculated infrared-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm(-1) upon excitation.

  5. Rototranslational sum rules for electromagnetic hypershielding at the nuclei and related atomic Cartesian derivatives of the optical rotatory power.

    PubMed

    Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo

    2008-06-28

    Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.

  6. Interactive grid generation for turbomachinery flow field simulations

    NASA Technical Reports Server (NTRS)

    Choo, Yung K.; Reno, Charles; Eiseman, Peter R.

    1988-01-01

    The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

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

    USGS Publications Warehouse

    Rutledge, A.T.

    1989-01-01

    A computer program was developed for converting the coordinates of any rectangular grid on a map to coordinates on a grid that is parallel to lines of equal latitude and longitude. Using this program in conjunction with groundwater flow models, the user can extract data and results from models with varying grid orientations and place these data into grid structure that is oriented parallel to lines of equal latitude and longitude. All cells in the rectangular grid must have equal dimensions, and all cells in the latitude-longitude grid measure one minute by one minute. This program is applicable if the map used shows lines of equal latitude as arcs and lines of equal longitude as straight lines and assumes that the Earth 's surface can be approximated as a sphere. The program user enters the row number , column number, and latitude and longitude of the midpoint of the cell for three test cells on the rectangular grid. The latitude and longitude of boundaries of the rectangular grid also are entered. By solving sets of simultaneous linear equations, the program calculates coefficients that are used for making the conversion. As an option in the program, the user may build a groundwater model file based on a grid that is parallel to lines of equal latitude and longitude. The program reads a data file based on the rectangular coordinates and automatically forms the new data file. (USGS)

  8. Algebraic grid generation for wing-fuselage bodies

    NASA Technical Reports Server (NTRS)

    Smith, R. E.; Everton, E. L.; Kudlinski, R. A.

    1984-01-01

    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, and each grid has six 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 using plane-patch intersections, and single-valued functions relating approximate arc lengths along the curves to computational coordinates 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 grids.

  9. Surface grid generation for wing-fuselage bodies

    NASA Technical Reports Server (NTRS)

    Smith, R. E.; Kudlinski, R. A.; Pitts, J. I.

    1984-01-01

    In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.

  10. Easing The Calculation Of Bolt-Circle Coordinates

    NASA Technical Reports Server (NTRS)

    Burley, Richard K.

    1995-01-01

    Bolt Circle Calculation (BOLT-CALC) computer program used to reduce significant time consumed in manually computing trigonometry of rectangular Cartesian coordinates of holes in bolt circle as shown on blueprint or drawing. Eliminates risk of computational errors, particularly in cases involving many holes or in cases in which coordinates expressed to many significant digits. Program assists in many practical situations arising in machine shops. Written in BASIC. Also successfully compiled and implemented by use of Microsoft's QuickBasic v4.0.

  11. Geometry optimization of periodic systems using internal coordinates.

    PubMed

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

    2005-03-22

    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.

  12. Numerical Grid Generation. Proceedings of a Symposium on the Numerical Generation of Curvilinear Coordinate Systems and their Use in the Numerical Solution of Partial Differential Equations, held April 1982, Nashville, Tennessee

    DTIC Science & Technology

    1982-04-01

    to a line on which the coordinate &i is constant. Base vectors, tangents, normals, area, and volume To establish the terminology , consider the...Cauchy-Diemann prohlem is not known it is convenient to r~ner (5) and (7) into more standart form, namely: (8) -f(x’y) H - + =f(X,v)H nx () ffy1 2 av

  13. New approach to gridding using regularization and estimation theory.

    PubMed

    Rosenfeld, Daniel

    2002-07-01

    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

  14. Development of a semi-implicit fluid modeling code using finite-volume method based on Cartesian grids

    NASA Astrophysics Data System (ADS)

    Smith, Matthew R.; Hung, Chieh-Tsan; Lin, Kun-Mo; Wu, Jong-Shinn; Yu, Jen-Perng

    2011-01-01

    Presented is the HLLG (Harten, Lax and van Leer with Gradient inclusion) method for application to the numerical solution of general Partial Differential Equations (PDEs) in conservation form. The HLLG method is based on the traditional HLL method with formal mathematical inclusion of gradients of conserved properties across the control volume employed for flux derivation. The simple extension demonstrates that conventional higher extensions of the HLL method are mathematically inconsistent and produce various numerical instabilities. The HLLG method, with higher order extensions consistent with the flux derivation, is absent of (or less affected by) the said numerical instabilities. The HLLG method is then applied to solutions of the Euler Equations and the simulation of 1D argon RF plasma simulation.

  15. Poisson Coordinates.

    PubMed

    Li, Xian-Ying; Hu, Shi-Min

    2013-02-01

    Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

  16. Plasticity of intermediate mechanics students' coordinate system choice

    NASA Astrophysics Data System (ADS)

    Sayre, Eleanor C.; Wittmann, Michael C.

    2008-12-01

    We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.

  17. Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

    NASA Technical Reports Server (NTRS)

    Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

    1992-01-01

    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.

  18. Evaluating the accuracy of selenodesic reference grids

    NASA Technical Reports Server (NTRS)

    Koptev, A. A.

    1974-01-01

    Estimates were made of the accuracy of reference point grids using the technique of calculating the errors from theoretical analysis. Factors taken into consideration were: telescope accuracy, number of photographs, and libration amplitude. To solve the problem, formulas were used for the relationship between the coordinates of lunar surface points and their images on the photograph.

  19. Two-dimensional rhombohedral grid coordination polymers [M(bbbt)(2)(NCS)(2)](n)(M = Co, Mn, or Cd; bbbt = 1,1'-(1,4-butanediyl) bis-1H-benzotriazole): synthesis, crystal structures, and third-order nonlinear optical properties.

    PubMed

    Hou, Hongwei; Meng, Xiangru; Song, Yinglin; Fan, Yaoting; Zhu, Yu; Lu, Huijie; Du, Chenxia; Shao, Weihua

    2002-07-29

    In this paper, treatment of 1,1'-(1,4-butanediyl) bis-1H-benzotriazole (bbbt) and KSCN with Co(II), Mn(II), or Cd(II) afforded three two-dimensional rhombohedral grid coordination polymers [M(bbbt)(2)(NCS)(2)](n)(M = Co, 1; Mn, 2; Cd, 3). The two-dimensional rhombohedral grids are parallel to the crystallographic ac plane. The rhombohedral grid consists of 44-membered rings of M(4)(bbbt)(4), and gives the dimensions of 12.913 x 10.764 A for polymer 1, 13.106 x 10.797 A for polymer 2, and 13.256 x 10.870 A for polymer 3. The three polymers' third-order nonlinear optical (NLO) properties were determined by Z-scan technique in DMF solution. The results show that all three polymers show very large NLO absorption and strong NLO refraction properties. The third-order NLO absorptive coefficients alpha(2) are 5.4 x 10(-9) m W(-1) for polymer 1, 5.2 x 10(-9) m W(-1) for polymer 2, and 5.0 x 10(-9) m W(-1) for polymer 3. The alpha(2) values are larger than those of all the reported cluster compounds. The NLO refractive index values n(2) of the three polymers are 5.73 x 10(-19), 3.55 x 10(-19), and 3.07 x 10(-19) m(2) W(-1), respectively. Their hyperpolarizability gamma values are calculated to be 2.40 x 10(-30) esu for polymer 1, 1.52 x 10(-30) esu for polymer 2, and 1.50 x 10(-30) esu for polymer 3. The gamma values are comparable to those of clusters and better than those of organometallic compounds, semiconductors, and fullerene.

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

    NASA Astrophysics Data System (ADS)

    Yang, Zhili; Jacob, Mathews

    2014-05-01

    The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when 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.

  1. Aligning Spinoza with Descartes: An informed Cartesian account of the truth bias.

    PubMed

    Street, Chris N H; Kingstone, Alan

    2016-08-11

    There is a bias towards believing information is true rather than false. The Spinozan account claims there is an early, automatic bias towards believing. Only afterwards can people engage in an effortful re-evaluation and disbelieve the information. Supporting this account, there is a greater bias towards believing information is true when under cognitive load. However, developing on the Adaptive Lie Detector (ALIED) theory, the informed Cartesian can equally explain this data. The account claims the bias under load is not evidence of automatic belief; rather, people are undecided, but if forced to guess they can rely on context information to make an informed judgement. The account predicts, and we found, that if people can explicitly indicate their uncertainty, there should be no bias towards believing because they are no longer required to guess. Thus, we conclude that belief formation can be better explained by an informed Cartesian account - an attempt to make an informed judgment under uncertainty.

  2. Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.

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

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

    Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.

  4. A parallel performance study of the Cartesian method for partial differential equations on a sphere

    SciTech Connect

    Drake, J.B.; Coddington, M.P.

    1997-04-01

    A 3-D Cartesian method for integration of partial differential equations on a spherical surface is developed for parallel computation. The target computer architectures are distributed memory, message passing computers such as the Intel Paragon. The parallel algorithms are described along with mesh partitioning strategies. Performance of the algorithms is considered for a standard test case of the shallow water equations on the sphere. The authors find the computation time scale well with increasing numbers of processors.

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

    NASA Technical Reports Server (NTRS)

    Nguyen, Charles C.; Pooran, Farhad J.

    1988-01-01

    The problem of cartesian trajectory control of a closed-kinematic chain mechanism robot manipulator with possible space station applications is considered. The study was performed by both computer simulation and experimentation for tracking of three different paths: a straight line, a sinusoid and a circle. Linearization and pole placement methods are employed to design controller gains. Results show that the controllers are robust and there are good agreements between simulation and experimentation. Excellent tracking quality and small overshoots are also evident.

  6. Parallel Grid Manipulations in Earth Science Calculations

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

    The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a

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

    DOE PAGES

    Michael, J. Robert; Volkov, Anatoliy

    2015-03-01

    The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

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

    SciTech Connect

    Michael, J. Robert; Volkov, Anatoliy

    2015-03-01

    The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7. In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

  9. Extensions of the Zwart-Powell box spline for volumetric data reconstruction on the cartesian lattice.

    PubMed

    Entezari, Alireza; Möller, Torsten

    2006-01-01

    In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline produces a C2 reconstruction that can be considered as a three dimensional extension of the well known Zwart-Powell element in 2D. While its smoothness and approximation power are equivalent to those of the tri-cubic B-spline, we illustrate the superiority of this reconstruction on functions sampled on the Cartesian lattice and contrast it to tensor product B-splines. Our construction is validated through a Fourier domain analysis of the reconstruction behavior of this box spline. Moreover, we present a stable method for evaluation of this box spline by means of a decomposition. Through a convolution, this decomposition reduces the problem to evaluation of a four directional box spline that we previously published in its explicit closed form.

  10. Augmented Lagrangian with variable splitting for faster non-Cartesian L1-SPIRiT MR image reconstruction.

    PubMed

    Weller, Daniel S; Ramani, Sathish; Fessler, Jeffrey A

    2014-02-01

    SPIRiT (iterative self-consistent parallel imaging reconstruction), and its sparsity-regularized variant L1-SPIRiT, are compatible with both Cartesian and non-Cartesian magnetic resonance imaging sampling trajectories. However, the non-Cartesian framework is more expensive computationally, involving a nonuniform Fourier transform with a nontrivial Gram matrix. We propose a novel implementation of the regularized reconstruction problem using variable splitting, alternating minimization of the augmented Lagrangian, and careful preconditioning. Our new method based on the alternating direction method of multipliers converges much faster than existing methods because of the preconditioners' heightened effectiveness. We demonstrate such rapid convergence substantially improves image quality for a fixed computation time. Our framework is a step forward towards rapid non-Cartesian L1-SPIRiT reconstructions.

  11. Parallel grid population

    DOEpatents

    Wald, Ingo; Ize, Santiago

    2015-07-28

    Parallel population of a grid with a plurality of objects using a plurality of processors. One example embodiment is a method for parallel population of a grid with a plurality of objects using a plurality of processors. The method includes a first act of dividing a grid into n distinct grid portions, where n is the number of processors available for populating the grid. The method also includes acts of dividing a plurality of objects into n distinct sets of objects, assigning a distinct set of objects to each processor such that each processor determines by which distinct grid portion(s) each object in its distinct set of objects is at least partially bounded, and assigning a distinct grid portion to each processor such that each processor populates its distinct grid portion with any objects that were previously determined to be at least partially bounded by its distinct grid portion.

  12. Comprehensive Smart Grid Planning in a Regulated Utility Environment

    NASA Astrophysics Data System (ADS)

    Turner, Matthew; Liao, Yuan; Du, Yan

    2015-06-01

    This paper presents the tools and exercises used during the Kentucky Smart Grid Roadmap Initiative in a collaborative electric grid planning process involving state regulators, public utilities, academic institutions, and private interest groups. The mandate of the initiative was to assess the existing condition of smart grid deployments in Kentucky, to enhance understanding of smart grid concepts by stakeholders, and to develop a roadmap for the deployment of smart grid technologies by the jurisdictional utilities of Kentucky. Through involvement of many important stakeholder groups, the resultant Smart Grid Deployment Roadmap proposes an aggressive yet achievable strategy and timetable designed to promote enhanced availability, security, efficiency, reliability, affordability, sustainability and safety of the electricity supply throughout the state while maintaining Kentucky's nationally competitive electricity rates. The models and methods developed for this exercise can be utilized as a systematic process for the planning of coordinated smart grid deployments.

  13. Extension of star coordinates into three dimensions

    NASA Astrophysics Data System (ADS)

    Cooprider, Nathan D.; Burton, Robert P.

    2007-01-01

    Traditional Star Coordinates displays a multi-variate data set by mapping it to two Cartesian dimensions. This technique facilitates cluster discovery and multi-variate analysis, but binding to two dimensions hides features of the data. Three-dimensional Star Coordinates spreads out data elements to reveal features. This allows the user more intuitive freedom to explore and process the data sets. Three-dimensional Star Coordinates is implemented by extending the data structures and transformation facilities of traditional Star Coordinates. We have given high priority to maintaining the simple, traditional interface. We simultaneously extend existing features, such as scaling of axes, and add new features, such as system rotation in three dimensions. These extensions and additions enhance data visualization and cluster discovery. We use three examples to demonstrate the advantage of three-dimensional Star Coordinates over the traditional system. First, in an analysis of customer churn data, system rotation in three dimensions gives the user new insight into the data. Second, in cluster discovery of car data, the additional dimension allows the true shape of the data to be seen more easily. Third, in a multi-variate analysis of cities, the perception of depth increases the degree to which multi-variate analysis can occur.

  14. Scientific Grid computing.

    PubMed

    Coveney, Peter V

    2005-08-15

    We introduce a definition of Grid computing which is adhered to throughout this Theme Issue. We compare the evolution of the World Wide Web with current aspirations for Grid computing and indicate areas that need further research and development before a generally usable Grid infrastructure becomes available. We discuss work that has been done in order to make scientific Grid computing a viable proposition, including the building of Grids, middleware developments, computational steering and visualization. We review science that has been enabled by contemporary computational Grids, and associated progress made through the widening availability of high performance computing.

  15. Dynamic Power Grid Simulation

    SciTech Connect

    Top, Philip; Woodward, Carol; Smith, Steve; Banks, Lawrence; Kelley, Brian

    2015-09-14

    GridDyn is a part of power grid simulation toolkit. The code is designed using modern object oriented C++ methods utilizing C++11 and recent Boost libraries to ensure compatibility with multiple operating systems and environments.

  16. Method of grid generation

    DOEpatents

    Barnette, Daniel W.

    2002-01-01

    The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.

  17. Fast Generation of body conforming grids for 3-D

    NASA Technical Reports Server (NTRS)

    Dulikravich, O.

    1980-01-01

    A fast algorithm was developed for accurately generating boundary conforming, three dimensional, consecutively refined, computational grids applicable to arbitrary axial turbomachinery geometry. The method is based on using a single analytic function to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the hub and the shroud. These grids are of the "O" type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flowfield. Due to the built in additional nonorthogonal coordinate stretching and shearing, the grid lines leaving the trailing of the blade end at downstream infinity, thus simplifying the numerical treatment of the three dimensional trailing vortex sheet.

  18. Advancing Smart Grid Interoperability and Implementing NIST's Interoperability Roadmap

    SciTech Connect

    Basso,T.; DeBlasio, R.

    2010-04-01

    The IEEE American National Standards project P2030TM addressing smart grid interoperability and the IEEE 1547 series of standards addressing distributed resources interconnection with the grid have been identified in priority action plans in the Report to NIST on the Smart Grid Interoperability Standards Roadmap. This paper presents the status of the IEEE P2030 development, the IEEE 1547 series of standards publications and drafts, and provides insight on systems integration and grid infrastructure. The P2030 and 1547 series of standards are sponsored by IEEE Standards Coordinating Committee 21.

  19. Global grid systems for geospatial information: status and thinking

    NASA Astrophysics Data System (ADS)

    Ben, Jin; Tong, Xiaochong; Ji, Song

    2007-06-01

    After brief explanation of the origin of the grid, the author firstly points out the multi-resolution partition of geo-space, which is the basic issue of the specialized spatial information grid, relates to the globe directly as the region of interest expands. And the global grid system is an efficient way to solve problems on spheres. Secondly, the author introduces achievements on geospatial information global grid systems which based on both traditional geographic coordinate system and regular, multi-resolution partitions of polyhedra. At last, this author point out the problems that remains to be studied in this field.

  20. COORDINATED AV.

    ERIC Educational Resources Information Center

    CLEAVES, PAUL C.; AND OTHERS

    THE INSTRUCTIONAL MATERIALS CENTER IS LOCATED IN THE LOCAL HIGH SCHOOL AND SUPPLIES ALL SCHOOLS IN THE AREA. AUDIOVISUAL EQUIPMENT ORDERS, AFTER SELECTIONS ARE MADE BY THE CLASSROOM TEACHER, ARE PROCESSED BY THE CENTER, CONFIRMED AND DELIVERED BY TRUCK THREE TIMES EACH WEEK. EACH SCHOOL HAS A BUILDING COORDINATOR WHO CHECKS THE ORDERS INTO THE…

  1. Parallel unstructured grid generation

    NASA Technical Reports Server (NTRS)

    Loehner, Rainald; Camberos, Jose; Merriam, Marshal

    1991-01-01

    A parallel unstructured grid generation algorithm is presented and implemented on the Hypercube. Different processor hierarchies are discussed, and the appropraite hierarchies for mesh generation and mesh smoothing are selected. A domain-splitting algorithm for unstructured grids which tries to minimize the surface-to-volume ratio of each subdomain is described. This splitting algorithm is employed both for grid generation and grid smoothing. Results obtained on the Hypercube demonstrate the effectiveness of the algorithms developed.

  2. IPG Power Grid Overview

    NASA Technical Reports Server (NTRS)

    Hinke, Thomas

    2003-01-01

    This presentation will describe what is meant by grids and then cover the current state of the IPG. This will include an overview of the middleware that is key to the operation of the grid. The presentation will then describe some of the future directions that are planned for the IPG. Finally the presentation will conclude with a brief overview of the Global Grid Forum, which is a key activity that will contribute to the successful availability of grid components.

  3. Visual SLAM Using Variance Grid Maps

    NASA Technical Reports Server (NTRS)

    Howard, Andrew B.; Marks, Tim K.

    2011-01-01

    An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance

  4. Interactive algebraic grid-generation technique

    NASA Technical Reports Server (NTRS)

    Smith, R. E.; Wiese, M. R.

    1986-01-01

    An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

  5. AstroGrid-PL

    NASA Astrophysics Data System (ADS)

    Stachowski, Greg; Kundera, Tomasz; Ciecielag, Paweł; AstroGridPL Team

    2016-06-01

    We summarise the achievements AstroGrid-PL project, which aims to provide an infrastructure grid computing, distributed storage and Virtual Observatory services to the Polish astronomical community. It was developed from 2011-2015 as a domain grid component within the large PLGrid Plus project for scientific computing in Poland.

  6. GridKit

    SciTech Connect

    Peles, Slaven

    2016-11-06

    GridKit is a software development kit for interfacing power systems and power grid application software with high performance computing (HPC) libraries developed at National Labs and academia. It is also intended as interoperability layer between different numerical libraries. GridKit is not a standalone application, but comes with a suite of test examples illustrating possible usage.

  7. Chimera Grid Tools

    NASA Technical Reports Server (NTRS)

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

    2005-01-01

    Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.

  8. Sampling microcanonical ensembles of trajectories using harmonic approximation in internal coordinates.

    PubMed

    Rybkin, Vladimir V; Ekström, Ulf

    2014-08-14

    In this paper, we modify quasiclassical harmonic sampling of microcanonical ensembles of trajectories by using the curvilinear internal coordinates. The harmonic approximation in the curvilinear normal coordinates provides a more realistic description of the PES than in the conventional rectilinear ones at finite displacements. Therefore, the sampling of vibrations in the internal coordinates significantly improves the quality of the sampling in a block-box fashion, providing more realistic displacements and reducing the errors in the potential energy. In particular, the sampling of large-amplitude torsion vibrations, which is non-realistic in the Cartesian modes, becomes accurate or acceptable in the curvilinear modes.

  9. FermiGrid

    SciTech Connect

    Yocum, D.R.; Berman, E.; Canal, P.; Chadwick, K.; Hesselroth, T.; Garzoglio, G.; Levshina, T.; Sergeev, V.; Sfiligoi, I.; Sharma, N.; Timm, S.; /Fermilab

    2007-05-01

    As one of the founding members of the Open Science Grid Consortium (OSG), Fermilab enables coherent access to its production resources through the Grid infrastructure system called FermiGrid. This system successfully provides for centrally managed grid services, opportunistic resource access, development of OSG Interfaces for Fermilab, and an interface to the Fermilab dCache system. FermiGrid supports virtual organizations (VOs) including high energy physics experiments (USCMS, MINOS, D0, CDF, ILC), astrophysics experiments (SDSS, Auger, DES), biology experiments (GADU, Nanohub) and educational activities.

  10. Grid Architecture 2

    SciTech Connect

    Taft, Jeffrey D.

    2016-01-01

    The report describes work done on Grid Architecture under the auspices of the Department of Electricity Office of Electricity Delivery and Reliability in 2015. As described in the first Grid Architecture report, the primary purpose of this work is to provide stakeholder insight about grid issues so as to enable superior decision making on their part. Doing this requires the creation of various work products, including oft-times complex diagrams, analyses, and explanations. This report provides architectural insights into several important grid topics and also describes work done to advance the science of Grid Architecture as well.

  11. Cartesian contrivances

    NASA Astrophysics Data System (ADS)

    Kemp, Martin

    1998-08-01

    If matter fills the Universe, making everything happen by its interactions, what does it all look like? René Descartes may have been over-mechanistic in his view, but his efforts to visualize the invisible created striking images.

  12. Cartesian visions.

    PubMed

    Fara, Patricia

    2008-12-01

    Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.

  13. Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

    NASA Astrophysics Data System (ADS)

    Hamilton, Nicholas; Cal, Raúl Bayoán

    2015-01-01

    A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean

  14. Which grids are Hamiltonian

    SciTech Connect

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

    1980-01-01

    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)

  15. Free geometric adjustment of the OSU/NGSP global network /solution WN-4/. [coordinates of satellite tracking stations

    NASA Technical Reports Server (NTRS)

    Mueller, I. I.

    1974-01-01

    The paper presents the results of the OSU WN 4 geometric adjustment for the coordinates of 152 satellite tracking stations. The results, when referred to the WN 4 ellipsoid of a = 6,378,127.8 m and 1/f = 298.25 produce geoid undulations consistent with dynamically determined ones. The average standard deviation in a Cartesian coordinate is plus or minus 4.0 m; in height, plus or minus 2.7 m. Comparisons with coordinates obtained from dynamic solutions show significant inconsistencies in the orientation of the coordinate systems.

  16. Understanding The Smart Grid

    SciTech Connect

    2007-11-15

    The report provides an overview of what the Smart Grid is and what is being done to define and implement it. The electric industry is preparing to undergo a transition from a centralized, producer-controlled network to a decentralized, user-interactive one. Not only will the technology involved in the electric grid change, but the entire business model of the industry will change too. A major objective of the report is to identify the changes that the Smart Grid will bring about so that industry participants can be prepared to face them. A concise overview of the development of the Smart Grid is provided. It presents an understanding of what the Smart Grid is, what new business opportunities or risks might come about due to its introduction, and what activities are already taking place regarding defining or implementing the Smart Grid. This report will be of interest to the utility industry, energy service providers, aggregators, and regulators. It will also be of interest to home/building automation vendors, information technology vendors, academics, consultants, and analysts. The scope of the report includes an overview of the Smart Grid which identifies the main components of the Smart Grid, describes its characteristics, and describes how the Smart Grid differs from the current electric grid. The overview also identifies the key concepts involved in the transition to the Smart Grid and explains why a Smart Grid is needed by identifying the deficiencies of the current grid and the need for new investment. The report also looks at the impact of the Smart Grid, identifying other industries which have gone through a similar transition, identifying the overall benefits of the Smart Grid, and discussing the impact of the Smart Grid on industry participants. Furthermore, the report looks at current activities to implement the Smart Grid including utility projects, industry collaborations, and government initiatives. Finally, the report takes a look at key technology

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

    NASA Technical Reports Server (NTRS)

    Aldridge, Hal A.; Juang, Jer-Nan

    1997-01-01

    Joint position sensors are necessary for most robot control systems. A single position sensor failure in a normal robot system can greatly degrade performance. This paper presents a method to obtain position information from Cartesian accelerometers without integration. Depending on the number and location of the accelerometers. the proposed system can tolerate the loss of multiple position sensors. A solution technique suitable for real-time implementation is presented. Simulations were conducted using 5 triaxial accelerometers to recover from the loss of up to 4 joint position sensors on a 7 degree of freedom robot moving in general three dimensional space. The simulations show good estimation performance using non-ideal accelerometer measurements.

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

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

    A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

  19. Efficient and Robust Cartesian Mesh Generation for Building-Cube Method

    NASA Astrophysics Data System (ADS)

    Ishida, Takashi; Takahashi, Shun; Nakahashi, Kazuhiro

    In this study, an efficient and robust Cartesian mesh generation method for Building-Cube Method (BCM) is proposed. It can handle “dirty” geometry data whose surface has cracks, overlaps, and reverse of triangle. BCM mesh generation is implemented by two procedures; cube generation and cell generation in each cube. The cell generation procedure in this study is managed in each cube individually, and parallelized by OpenMP. Efficiency of the parallelized BCM mesh generation is demonstrated for several three-dimensional test cases using a multi-core PC.

  20. Parallel adaptive Cartesian upwind methods for shock-driven multiphysics simulation

    SciTech Connect

    Deiterding, Ralf

    2011-01-01

    The multiphysics fluid-structure interaction simulation of shock-loaded thin-walled structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. By combining a Cartesian embedded boundary approach with dynamic mesh adaptation a generic software framework for such flow solvers has been constructed that allows easy exchange of the specific hydrodynamic finite volume upwind scheme and coupling to various explicit finite element solid dynamics solvers. The paper gives an overview of the computational approach and presents first simulations that couple the software to the general purpose solid dynamics code DYNA3D.

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

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis,Michael J.

    2006-01-01

    Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach

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

    NASA Technical Reports Server (NTRS)

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

    1980-01-01

    Coordination of the limb motion of a vehicle which could perform assembly and maintenance operations on large structures in space is described. Manipulator kinematics and walking robots are described. The basic control scheme of the robot is described. The control of the individual arms are described. Arm velocities are generally described in Cartesian coordinates. Cartesian velocities are converted to joint velocities using the Jacobian matrix. The calculation of a trajectory for an arm given a sequence of points through which it is to pass is described. The free gait algorithm which controls the lifting and placing of legs for the robot is described. The generation of commanded velocities for the robot, and the implementation of those velocities by the algorithm are discussed. Suggestions for further work in the area of robot legged locomotion are presented.

  3. Navigation in Grid Space with the NAS Grid Benchmarks

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    We present a navigational tool for computational grids. The navigational process is based on measuring the grid characteristics with the NAS Grid Benchmarks (NGB) and using the measurements to assign tasks of a grid application to the grid machines. The tool allows the user to explore the grid space and to navigate the execution at a grid application to minimize its turnaround time. We introduce the notion of gridscape as a user view of the grid and show how it can be me assured by NGB, Then we demonstrate how the gridscape can be used with two different schedulers to navigate a grid application through a rudimentary grid.

  4. Spectral Topography Generation for Arbitrary Grids

    NASA Astrophysics Data System (ADS)

    Oh, T. J.

    2015-12-01

    A new topography generation tool utilizing spectral transformation technique for both structured and unstructured grids is presented. For the source global digital elevation data, the NASA Shuttle Radar Topography Mission (SRTM) 15 arc-second dataset (gap-filling by Jonathan de Ferranti) is used and for land/water mask source, the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) 30 arc-second land water mask dataset v5 is used. The original source data is coarsened to a intermediate global 2 minute lat-lon mesh. Then, spectral transformation to the wave space and inverse transformation with wavenumber truncation is performed for isotropic topography smoothness control. Target grid topography mapping is done by bivariate cubic spline interpolation from the truncated 2 minute lat-lon topography. Gibbs phenomenon in the water region can be removed by overwriting ocean masked target coordinate grids with interpolated values from the intermediate 2 minute grid. Finally, a weak smoothing operator is applied on the target grid to minimize the land/water surface height discontinuity that might have been introduced by the Gibbs oscillation removal procedure. Overall, the new topography generation approach provides spectrally-derived, smooth topography with isotropic resolution and minimum damping, enabling realistic topography forcing in the numerical model. Topography is generated for the cubed-sphere grid and tested on the KIAPS Integrated Model (KIM).

  5. Grid enabled Service Support Environment - SSE Grid

    NASA Astrophysics Data System (ADS)

    Goor, Erwin; Paepen, Martine

    2010-05-01

    The SSEGrid project is an ESA/ESRIN project which started in 2009 and is executed by two Belgian companies, Spacebel and VITO, and one Dutch company, Dutch Space. The main project objectives are the introduction of a Grid-based processing on demand infrastructure at the Image Processing Centre for earth observation products at VITO and the inclusion of Grid processing services in the Service Support Environment (SSE) at ESRIN. The Grid-based processing on demand infrastructure is meant to support a Grid processing on demand model for Principal Investigators (PI) and allow the design and execution of multi-sensor applications with geographically spread data while minimising the transfer of huge volumes of data. In the first scenario, 'support a Grid processing on demand model for Principal Investigators', we aim to provide processing power close to the EO-data at the processing and archiving centres. We will allow a PI (non-Grid expert user) to upload his own algorithm, as a process, and his own auxiliary data from the SSE Portal and use them in an earth observation workflow on the SSEGrid Infrastructure. The PI can design and submit workflows using his own processes, processes made available by VITO/ESRIN and possibly processes from other users that are available on the Grid. These activities must be user-friendly and not requiring detailed knowledge about the underlying Grid middleware. In the second scenario we aim to design, implement and demonstrate a methodology to set up an earth observation processing facility, which uses large volumes of data from various geographically spread sensors. The aim is to provide solutions for problems that we face today, like wasting bandwidth by copying large volumes of data to one location. We will avoid this by processing the data where they are. The multi-mission Grid-based processing on demand infrastructure will allow developing and executing complex and massive multi-sensor data (re-)processing applications more

  6. Accurate computation of Zernike moments in polar coordinates.

    PubMed

    Xin, Yongqing; Pawlak, Miroslaw; Liao, Simon

    2007-02-01

    An algorithm for high-precision numerical computation of Zernike moments is presented. The algorithm, based on the introduced polar pixel tiling scheme, does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on Cartesian coordinates. This yields a dramatic improvement of the Zernike moments accuracy in terms of their reconstruction and invariance properties. The introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error. Various comparisons are made between the accuracy of the proposed method and that of commonly used techniques. The results reveal the great advantage of our approach.

  7. DSMC Grid Methodologies for Computing Low-Density, Hypersonic Flows About Reusable Launch Vehicles

    NASA Technical Reports Server (NTRS)

    Wilmoth, Richard G.; LeBeau, Gerald J.; Carlson, Ann B.

    1996-01-01

    Two different grid methodologies are studied for application to DSMC simulations about reusable launch vehicles. One method uses an unstructured, tetrahedral grid while the other uses a structured, variable-resolution Cartesian grid. The relative merits of each method are discussed in terms of accuracy, computational efficiency, and overall ease of use. Both methods are applied to the computation of a low-density, hypersonic flow about a winged single-stage-to-orbit reusable launch vehicle concept at conditions corresponding to an altitude of 120 km. Both methods are shown to give comparable results for both surface and flowfield quantities as well as for the overall aerodynamic behavior. For the conditions simulated, the flowfield about the vehicle is very rarefied but the DSMC simulations show significant departure from free-molecular predictions for the surface friction and heat transfer as well as certain aerodynamic quantities.

  8. Securing smart grid technology

    NASA Astrophysics Data System (ADS)

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

    2013-03-01

    In the developing countries electrical energy is very important for its all-round improvement by saving thousands of dollars and investing them in other sector for development. For Growing needs of power existing hierarchical, centrally controlled grid of the 20th Century is not sufficient. To produce and utilize effective power supply for industries or people we should have Smarter Electrical grids that address the challenges of the existing power grid. The Smart grid can be considered as a modern electric power grid infrastructure for enhanced efficiency and reliability through automated control, high-power converters, modern communications infrastructure along with modern IT services, sensing and metering technologies, and modern energy management techniques based on the optimization of demand, energy and network availability and so on. The main objective of this paper is to provide a contemporary look at the current state of the art in smart grid communications as well as critical issues on smart grid technologies primarily in terms of information and communication technology (ICT) issues like security, efficiency to communications layer field. In this paper we propose new model for security in Smart Grid Technology that contains Security Module(SM) along with DEM which will enhance security in Grid. It is expected that this paper will provide a better understanding of the technologies, potential advantages and research challenges of the smart grid and provoke interest among the research community to further explore this promising research area.

  9. Variable electric fields for high throughput electroporation protocol design in curvilinear coordinates.

    PubMed

    Fernand, Francois; Rubinsky, Liel; Golberg, Alex; Rubinsky, Boris

    2012-08-01

    The mathematical solution to the electric field equation in cylindrical coordinates, has suggested to us a new experimental methodology and device for reducing experimental effort in designing electroporation protocols. Using a new cylindrical electroporation system, we show, with an Escherichia coli cell model, how key electroporation parameters emerge precisely from single experiments rather than through interpolation from numerous experiments in the conventional Cartesian electroporation system.

  10. Satellite Coordination

    NASA Astrophysics Data System (ADS)

    Cohen, R. J.

    2004-06-01

    The Radio Regulations set out complex procedures to ensure that when new systems start to use the frequency bands allocated to them there is minimal disruption to existing systems using the same bands. The process of satellite coordination is described, and the issues for radio astronomy are discussed. In order to be protected by the ITU-R machinery radio telescopes need to be officially registered. The issue of paper satellites highlights the need for early registration to gain priority over incoming systems. Modern developments including the use of complex Monte-Carlo simulations to predict interference levels, and the issue of adjacent band interference, are discussed.

  11. Calculation of rigid-body conformational changes using restraint-driven Cartesian transformations.

    PubMed Central

    Sompornpisut, P; Liu, Y S; Perozo, E

    2001-01-01

    We present an approach for calculating conformational changes in membrane proteins using limited distance information. The method, named restraint-driven Cartesian transformations, involves 1) the use of relative distance changes; 2) the systematic sampling of rigid body movements in Cartesian space; 3) a penalty evaluation; and 4) model refinement using energy minimization. As a test case, we have analyzed the structural basis of activation gating in the Streptomyces lividans potassium channel (KcsA). A total of 10 pairs of distance restraints derived from site-directed spin labeling and electron paramagnetic resonance (SDSL-EPR) spectra were used to calculate the open conformation of the second transmembrane domains of KcsA (TM2). The SDSL-EPR based structure reveals a gating mechanism consistent with a scissoring-type motion of the TM2 segments that includes a pivot point near middle of the helix. The present approach considerably reduces the amount of time and effort required to establish the overall nature of conformational changes in membrane proteins. It is expected that this approach can be implemented into restrained molecular dynamics protocol to calculate the structure and conformational changes in a variety of membrane protein systems. PMID:11606268

  12. Darwin's evolution theory, brain oscillations, and complex brain function in a new "Cartesian view".

    PubMed

    Başar, Erol; Güntekin, Bahar

    2009-01-01

    Comparatively analyses of electrophysiological correlates across species during evolution, alpha activity during brain maturation, and alpha activity in complex cognitive processes are presented to illustrate a new multidimensional "Cartesian System" brain function. The main features are: (1) The growth of the alpha activity during evolution, increase of alpha during cognitive processes, and decrease of the alpha entropy during evolution provide an indicator for evolution of brain cognitive performance. (2) Human children younger than 3 years are unable to produce higher cognitive processes and do not show alpha activity till the age of 3 years. The mature brain can perform higher cognitive processes and demonstrates regular alpha activity. (3) Alpha activity also is significantly associated with highly complex cognitive processes, such as the recognition of facial expressions. The neural activity reflected by these brain oscillations can be considered as constituent "building blocks" for a great number of functions. An overarching statement on the alpha function is presented by extended analyzes with multiple dimensions that constitute a "Cartesian Hyperspace" as the basis for oscillatory function. Theoretical implications are considered.

  13. Documentation of program AFTBDY to generate coordinate system for 3D after body using body fitted curvilinear coordinates, part 1

    NASA Technical Reports Server (NTRS)

    Kumar, D.

    1980-01-01

    The computer program AFTBDY generates a body fitted curvilinear coordinate system for a wedge curved after body. This wedge curved after body is being used in an experimental program. The coordinate system generated by AFTBDY is used to solve 3D compressible N.S. equations. The coordinate system in the physical plane is a cartesian x,y,z system, whereas, in the transformed plane a rectangular xi, eta, zeta system is used. The coordinate system generated is such that in the transformed plane coordinate spacing in the xi, eta, zeta direction is constant and equal to unity. The physical plane coordinate lines in the different regions are clustered heavily or sparsely depending on the regions where physical quantities to be solved for by the N.S. equations have high or low gradients. The coordinate distribution in the physical plane is such that x stays constant in eta and zeta direction, whereas, z stays constant in xi and eta direction. The desired distribution in x and z is input to the program. Consequently, only the y-coordinate is solved for by the program AFTBDY.

  14. Time-Accurate Computation of Viscous Flow Around Deforming Bodies Using Overset Grids

    SciTech Connect

    Fast, P; Henshaw, W D

    2001-04-02

    Dynamically evolving boundaries and deforming bodies interacting with a flow are commonly encountered in fluid dynamics. However, the numerical simulation of flows with dynamic boundaries is difficult with current methods. We propose a new method for studying such problems. The key idea is to use the overset grid method with a thin, body-fitted grid near the deforming boundary, while using fixed Cartesian grids to cover most of the computational domain. Our approach combines the strengths of earlier moving overset grid methods for rigid body motion, and unstructured grid methods for Aow-structure interactions. Large scale deformation of the flow boundaries can be handled without a global regridding, and in a computationally efficient way. In terms of computational cost, even a full overset grid regridding is significantly cheaper than a full regridding of an unstructured grid for the same domain, especially in three dimensions. Numerical studies are used to verify accuracy and convergence of our flow solver. As a computational example, we consider two-dimensional incompressible flow past a flexible filament with prescribed dynamics.

  15. Numerical grid generation in 3D Euler-flow simulation

    NASA Astrophysics Data System (ADS)

    Boerstoel, J. W.

    1988-04-01

    The technical problems with grid generation are analyzed and an overview of proposed solutions is given. The usefulness of grid-generation techniques, for the numerical simulation of Euler (and Navier-Stokes) flows around complex three-dimensional aerodynamic configurations, is illustrated. It is shown that the core of the grid-generation problem is a topology problem. The following remarks are sketched: grid generation is a subtask in a numerical simulation of a flow in industrial and research environments; the design requirements of a grid generation concern the geometrical imput, the desired grid as output, the technical means to control grid resolution and quality and turnaround time performance; the construction of a blocked grid can be subdivided in a block-decomposition task and a grid-point distribution task. A technique for using connectivity relations to define conventions about local coordinate systems in edges, faces and blocks is presented. Experiences are reported and an example concerning a 96-blocked grid around a complex aerodynamic configuration is given. Concepts for improvements in the presented technique are discussed.

  16. Grid generation using differential systems techniques

    NASA Technical Reports Server (NTRS)

    Thompson, J. F.; Mastin, C. W.

    1980-01-01

    The errors in approximating the derivatives of a function by traditional central differences at grid points of a curvilinear coordinate system were examined. The implications concerning the accuracy of the numerical solution of a partial differential equation are explained by considering several numerical examples. Although this study only considers the two dimensional case, the techniques and implications are equally valid for three dimensional grids. An interesting feature of the error analysis is its simplicity. Most of the results follow by merely working with the truncation terms of some power series expansion. These series expansions also give rise to higher order difference approximations which can significantly reduce error when the grid spacing changes rapidly, as might be the case in problems with shock waves or thin boundary layers.

  17. Understanding the Grid

    SciTech Connect

    2016-01-14

    The electric power grid has been rightly celebrated as the single most important engineering feat of the 20th century. The grid powers our homes, offices, hospitals, and schools; and, increasingly, it powers our favorite devices from smartphones to HDTVs. With those and other modern innovations and challenges, our grid will need to evolve. Grid modernization efforts will help the grid make full use of today’s advanced technologies and serve our needs in the 21st century. While the vast majority of upgrades are implemented by private sector energy companies that own and operate the grid, DOE has been investing in technologies that are revolutionizing the way we generate, store and transmit power.

  18. Challenges facing production grids

    SciTech Connect

    Pordes, Ruth; /Fermilab

    2007-06-01

    Today's global communities of users expect quality of service from distributed Grid systems equivalent to that their local data centers. This must be coupled to ubiquitous access to the ensemble of processing and storage resources across multiple Grid infrastructures. We are still facing significant challenges in meeting these expectations, especially in the underlying security, a sustainable and successful economic model, and smoothing the boundaries between administrative and technical domains. Using the Open Science Grid as an example, I examine the status and challenges of Grids operating in production today.

  19. A grid amplifier

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

    A 50-MESFET grid amplifier is reported that has a gain of 11 dB at 3.3 GHz. The grid isolates the input from the output by using vertical polarization for the input beam and horizontal polarization for the transmitted output beam. The grid unit cell is a two-MESFET differential amplifier. A simple calibration procedure allows the gain to be calculated from a relative power measurement. This grid is a hybrid circuit, but the structure is suitable for fabrication as a monolithic wafer-scale integrated circuit, particularly at millimeter wavelengths.

  20. Unstructured surface grid generation

    NASA Technical Reports Server (NTRS)

    Samareh-Abolhassani, Jamshid

    1993-01-01

    Viewgraphs on unstructured surface grid generation are presented. Topics covered include: requirements for curves, surfaces, solids, and text; surface approximation; triangulation; advancing; projection; mapping; and parametric curves.

  1. Numerical generation of two-dimensional grids by the use of Poisson equations with grid control at boundaries

    NASA Technical Reports Server (NTRS)

    Sorenson, R. L.; Steger, J. L.

    1980-01-01

    A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).

  2. Collaboration in a Wireless Grid Innovation Testbed by Virtual Consortium

    NASA Astrophysics Data System (ADS)

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

    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.

  3. A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

    NASA Technical Reports Server (NTRS)

    Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

    1991-01-01

    The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

  4. SAGE - MULTIDIMENSIONAL SELF-ADAPTIVE GRID CODE

    NASA Technical Reports Server (NTRS)

    Davies, C. B.

    1994-01-01

    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

  5. Enabling Radiative Transfer on AMR grids in CRASH

    NASA Astrophysics Data System (ADS)

    Hariharan, N.; Graziani, L.; Ciardi, B.; Miniati, F.; Bungartz, H.-J.

    2017-01-01

    We introduce CRASH-AMR, a new version of the cosmological Radiative Transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately ionisation and temperature patterns in high density regions. We have tested CRASH-AMR by simulating the evolution of an ionised region produced by a single source embedded in gas at constant density, as well as by a more realistic configuration of multiple sources in an inhomogeneous density field. While we find an excellent agreement with the previous version of CRASH when the AMR feature is disabled, showing that no numerical artifact has been introduced in CRASH-AMR, when additional refinement levels are used the code can simulate more accurately the physics of ionised gas in high density regions. This result has been attained at no computational loss, as RT simulations on AMR grids with maximum resolution equivalent to that of a uniform cartesian grid can be run with a gain of up to 60% in computational time.

  6. Security for grids

    SciTech Connect

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

    2005-08-14

    Securing a Grid environment presents a distinctive set of challenges. This paper groups the activities that need to be secured into four categories: naming and authentication; secure communication; trust, policy, and authorization; and enforcement of access control. It examines the current state of the art in securing these processes and introduces new technologies that promise to meet the security requirements of Grids more completely.

  7. Internet 2 Access Grid.

    ERIC Educational Resources Information Center

    Simco, Greg

    2002-01-01

    Discussion of the Internet 2 Initiative, which is based on collaboration among universities, businesses, and government, focuses on the Access Grid, a Computational Grid that includes interactive multimedia within high-speed networks to provide resources to enable remote collaboration among the research community. (Author/LRW)

  8. Geometric grid generation

    NASA Technical Reports Server (NTRS)

    Ives, David

    1995-01-01

    This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.

  9. Anharmonic state counts and partition functions for molecules via classical phase space integrals in curvilinear coordinates.

    PubMed

    Kamarchik, Eugene; Jasper, Ahren W

    2013-05-21

    An algorithm is presented for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules using Monte Carlo integration of classical phase space. The algorithm includes numerical evaluations of the elements of the Jacobian and is general enough to allow for sampling in arbitrary curvilinear or rectilinear coordinate systems. Invariance to the choice of coordinate system is demonstrated for vibrational state densities of methane, where we find comparable sampling efficiency when using curvilinear z-matrix and rectilinear Cartesian normal mode coordinates. In agreement with past work, we find that anharmonicity increases the vibrational state density of methane by a factor of ∼2 at its dissociation threshold. For the vinyl radical, we find a significant (∼10×) improvement in sampling efficiency when using curvilinear z-matrix coordinates relative to Cartesian normal mode coordinates. We attribute this improved efficiency, in part, to a more natural curvilinear coordinate description of the double well associated with the H2C-C-H wagging motion. The anharmonicity correction for the vinyl radical state density is ∼1.4 at its dissociation threshold. Finally, we demonstrate that with trivial parallelizations of the Monte Carlo step, tractable calculations can be made for the vinyl radical using direct ab initio potential energy surface evaluations and a composite QCISD(T)/MP2 method.

  10. Numerical relativity in spherical polar coordinates: Evolution calculations with the BSSN formulation

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

    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.

  11. Research on the comparison of extension mechanism of cellular automaton based on hexagon grid and rectangular grid

    NASA Astrophysics Data System (ADS)

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

    2009-10-01

    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

  12. Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

    DOE PAGES

    Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam

    2012-07-03

    We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within themore » context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.« less

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    A supersonic rolling missile with two synchronous canard control surfaces is analyzed using an automated, inviscid, Cartesian method. Sequential-static and time-dependent dynamic simulations of the complete motion are computed for canard dither schedules for level flight, pitch, and yaw maneuver. The dynamic simulations are compared directly against both high-resolution viscous simulations and relevant experimental data, and are also utilized to compute dynamic stability derivatives. The results show that both the body roll rate and canard dither motion influence the roll-averaged forces and moments on the body. At the relatively, low roll rates analyzed in the current work these dynamic effects are modest, however the dynamic computations are effective in predicting the dynamic stability derivatives which can be significant for highly-maneuverable missiles.

  14. Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

    SciTech Connect

    Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam

    2012-03-22

    Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

  15. Investigation of Radar Propagation in Buildings: A 10 Billion Element Cartesian-Mesh FETD Simulation

    SciTech Connect

    Stowell, M L; Fasenfest, B J; White, D A

    2008-01-14

    In this paper large scale full-wave simulations are performed to investigate radar wave propagation inside buildings. In principle, a radar system combined with sophisticated numerical methods for inverse problems can be used to determine the internal structure of a building. The composition of the walls (cinder block, re-bar) may effect the propagation of the radar waves in a complicated manner. In order to provide a benchmark solution of radar propagation in buildings, including the effects of typical cinder block and re-bar, we performed large scale full wave simulations using a Finite Element Time Domain (FETD) method. This particular FETD implementation is tuned for the special case of an orthogonal Cartesian mesh and hence resembles FDTD in accuracy and efficiency. The method was implemented on a general-purpose massively parallel computer. In this paper we briefly describe the radar propagation problem, the FETD implementation, and we present results of simulations that used over 10 billion elements.

  16. Construction of freeforms in illumination systems via generalized Cartesian oval representation

    NASA Astrophysics Data System (ADS)

    Michaelis, D.; Schreiber, P.; Li, Chen; Bräuer, A.

    2011-10-01

    Freeforms in illumination systems are directly constructed by adapting some ideas of Oliker and co-workers [1]. The freeform is created by a set of primitive surface elements which are generalized Cartesian ovals including the optical response of the residual system. Hamiltonian theory of ray optics can be used to determine the family of primitives which is in particular a simple task if the freeform is the exit surface of the illumination system. For simple optical systems an analytical description of the primitives is possible. Contrarily, for more complex optics a conventional raytracer is additionally utilized to determine the required system's information, like the optical path lengths or mixed characteristics. To this end a discrete set of rays is traced through the residual systems and the required relations are interpolated to obtain a quasi-analytic representation of the primitives. The potential of this approach is demonstrated by some examples, e.g. freeform optics including collimating or deflection elements.

  17. Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

    SciTech Connect

    Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam

    2012-07-03

    We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.

  18. Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method

    NASA Technical Reports Server (NTRS)

    Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.

    2004-01-01

    Inlets and exhaust nozzles are often omitted in aerodynamic simulations of aircraft due to the complexities involved in the modeling of engine details and flow physics. However, the omission is often improper since inlet or plume flows may have a substantial effect on vehicle aerodynamics. A method for modeling the effect of inlets and exhaust plumes using boundary conditions within an inviscid Cartesian flow solver is presented. This approach couples with both CAD systems and legacy geometry to provide an automated tool suitable for parameter studies. The method is validated using two and three-dimensional test problems which are compared with both theoretical and experimental results. The numerical results demonstrate excellent agreement with theory and available data, even for extremely strong jets and very sensitive inlets.

  19. Why physical medicine, physical disability and physical rehabilitation? We should abandon Cartesian dualism.

    PubMed

    Wade, Derick

    2006-03-01

    Adjectives are supposed to describe the associated noun more fully or definitively, and the adjective physical is sometimes added to words such as medicine, rehabilitation and disability. What increase in description does its use allow? The adjective was probably added when rehabilitation started to develop for several reasons: it contrasted the mode of treatment with pharmacology and surgery; it contrasted the nature of the supposed aetiology with emotionally generated disorders, especially shell-shock; and it justified the presence of rehabilitation within the profession of medicine. Its continued use, however, perpetuates a Cartesian, dualist philosophy. This editorial uses the World Health Organization International Classification of Functioning (WHO ICF) model of illness to analyse its continued use, and concludes that its continued use may disadvantage both patients and the practice of rehabilitation.

  20. Algebraic grid generation about wing-fuselage bodies

    NASA Technical Reports Server (NTRS)

    Smith, R. E.

    1986-01-01

    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.

  1. Optimization Of A Computational Grid

    NASA Technical Reports Server (NTRS)

    Pearce, Daniel G.

    1993-01-01

    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.

  2. A conservative approach for flow field calculations on multiple grids

    NASA Technical Reports Server (NTRS)

    Kathong, Monchai; Tiwari, Surendra N.

    1988-01-01

    In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

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

    NASA Technical Reports Server (NTRS)

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

    2001-01-01

    This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

  4. Accelerating functional MRI using fixed‐rank approximations and radial‐cartesian sampling

    PubMed Central

    Graedel, Nadine N.; McNab, Jennifer A.; Smith, Stephen M.; Miller, Karla L.

    2016-01-01

    Purpose Recently, k‐t FASTER (fMRI Accelerated in Space‐time by means of Truncation of Effective Rank) was introduced for rank‐constrained acceleration of fMRI data acquisition. Here we demonstrate improvements achieved through a hybrid three‐dimensional radial‐Cartesian sampling approach that allows posthoc selection of acceleration factors, as well as incorporation of coil sensitivity encoding in the reconstruction. Methods The multicoil rank‐constrained reconstruction used hard thresholding and shrinkage on matrix singular values of the space‐time data matrix, using sensitivity encoding and the nonuniform Fast Fourier Transform to enforce data consistency in the multicoil non‐Cartesian k‐t domain. Variable acceleration factors were made possible using a radial increment based on the golden ratio. Both retrospective and prospectively under‐sampled data were used to assess the fidelity of the enhancements to the k‐t FASTER technique in resting and task‐fMRI data. Results The improved k‐t FASTER is capable of tailoring acceleration factors for recovery of different signal components, achieving up to R = 12.5 acceleration in visual‐motor task data. The enhancements reduce data matrix reconstruction errors even at much higher acceleration factors when compared directly with the original k‐t FASTER approach. Conclusion We have shown that k‐t FASTER can be used to significantly accelerate fMRI data acquisition with little penalty to data quality. Magn Reson Med 76:1825–1836, 2016. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26777798

  5. Design of a Vector-Vorticity Dynamical Core on a Hexagonal Grid (Hex-VVDC)

    NASA Astrophysics Data System (ADS)

    Konor, C. S.; Heikes, R. P.; Jung, J.; Randall, D.; Arakawa, A.

    2009-05-01

    We are developing a Global Cloud-Resolving Model (GCRM) based on the vector-vorticity dynamical core (VVDC) that predicts three-dimensional vorticity. The VVDC in an anelastic framework has been originally designed by Jung and Arakawa and used in a Cartesian grid. As the first step in developing the GCRM, we have constructed an intermediate model with the VVDC using a hexagonal grid on a planar quasi-rectangular horizontal domain, which we call the hexagonal VVDC (Hex-VVDC). The purpose of developing the Hex-VVDC is to test and verify the discretization of equations of the VVDC on a hexagonal grid before applying them to the geodesic hexagon/pentagon grid that will be used for the GCRM. It is found that having twice as many as cell walls and three times as many as cell corners than the cell centers in a hexagonal grid produces a computational mode in horizontal and vertical components of vorticity and horizontal velocity fields, which the dynamics cannot control. We have designed a special scheme to treat this computational mode. With this treatment, the Hex-VVDC seems to work well. Currently, we are performing further tests with the Hex-VVDC and also continuing the application of the dynamical core to the geodesic hexagon/pentagon grid. In this presentation, we will discuss the computational design of the Hex-VVDC and show simulated results primarily focusing on vertical transports of vorticity and momentum by convection.

  6. Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates.

    PubMed

    Baddour, Natalie

    2010-10-01

    For functions that are best described with spherical coordinates, the three-dimensional Fourier transform can be written in spherical coordinates as a combination of spherical Hankel transforms and spherical harmonic series. However, to be as useful as its Cartesian counterpart, a spherical version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the spherical version of the standard Fourier operation toolset. In particular, convolution in various forms is discussed in detail as this has important consequences for filtering. It is shown that standard multiplication and convolution rules do apply as long as the correct definition of convolution is applied.

  7. Flexible Residential Smart Grid Simulation Framework

    NASA Astrophysics Data System (ADS)

    Xiang, Wang

    Different scheduling and coordination algorithms controlling household appliances' operations can potentially lead to energy consumption reduction and/or load balancing in conjunction with different electricity pricing methods used in smart grid programs. In order to easily implement different algorithms and evaluate their efficiency against other ideas, a flexible simulation framework is desirable in both research and business fields. However, such a platform is currently lacking or underdeveloped. In this thesis, we provide a simulation framework to focus on demand side residential energy consumption coordination in response to different pricing methods. This simulation framework, equipped with an appliance consumption library using realistic values, aims to closely represent the average usage of different types of appliances. The simulation results of traditional usage yield close matching values compared to surveyed real life consumption records. Several sample coordination algorithms, pricing schemes, and communication scenarios are also implemented to illustrate the use of the simulation framework.

  8. Decentral Smart Grid Control

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

    Stable operation of complex flow and transportation networks requires balanced supply and demand. For the operation of electric power grids—due to their increasing fraction of renewable energy sources—a pressing challenge is to fit the fluctuations in decentralized supply to the distributed and temporally varying demands. To achieve this goal, common smart grid concepts suggest to collect consumer demand data, centrally evaluate them given current supply and send price information back to customers for them to decide about usage. Besides restrictions regarding cyber security, privacy protection and large required investments, it remains unclear how such central smart grid options guarantee overall stability. Here we propose a Decentral Smart Grid Control, where the price is directly linked to the local grid frequency at each customer. The grid frequency provides all necessary information about the current power balance such that it is sufficient to match supply and demand without the need for a centralized IT infrastructure. We analyze the performance and the dynamical stability of the power grid with such a control system. Our results suggest that the proposed Decentral Smart Grid Control is feasible independent of effective measurement delays, if frequencies are averaged over sufficiently large time intervals.

  9. The open science grid

    SciTech Connect

    Pordes, R.; /Fermilab

    2004-12-01

    The U.S. LHC Tier-1 and Tier-2 laboratories and universities are developing production Grids to support LHC applications running across a worldwide Grid computing system. Together with partners in computer science, physics grid projects and active experiments, we will build a common national production grid infrastructure which is open in its architecture, implementation and use. The Open Science Grid (OSG) model builds upon the successful approach of last year's joint Grid2003 project. The Grid3 shared infrastructure has for over eight months provided significant computational resources and throughput to a range of applications, including ATLAS and CMS data challenges, SDSS, LIGO, and biology analyses, and computer science demonstrators and experiments. To move towards LHC-scale data management, access and analysis capabilities, we must increase the scale, services, and sustainability of the current infrastructure by an order of magnitude or more. Thus, we must achieve a significant upgrade in its functionalities and technologies. The initial OSG partners will build upon a fully usable, sustainable and robust grid. Initial partners include the US LHC collaborations, DOE & NSF Laboratories and Universities & Trillium Grid projects. The approach is to federate with other application communities in the U.S. to build a shared infrastructure open to other sciences and capable of being modified and improved to respond to needs of other applications, including CDF, D0, BaBar, and RHIC experiments. We describe the application-driven, engineered services of the OSG, short term plans and status, and the roadmap for a consortium, its partnerships and national focus.

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

    PubMed Central

    Konagaya, Akihiko

    2006-01-01

    Background Grid computing has great potential to become a standard cyberinfrastructure for life sciences which often require high-performance computing and large data handling which exceeds the computing capacity of a single institution. Results This survey reviews the latest grid technologies from the viewpoints of computing grid, data grid and knowledge grid. Computing grid technologies have been matured enough to solve high-throughput real-world life scientific problems. Data grid technologies are strong candidates for realizing "resourceome" for bioinformatics. Knowledge grids should be designed not only from sharing explicit knowledge on computers but also from community formulation for sharing tacit knowledge among a community. Conclusion Extending the concept of grid from computing grid to knowledge grid, it is possible to make use of a grid as not only sharable computing resources, but also as time and place in which people work together, create knowledge, and share knowledge and experiences in a community. PMID:17254294

  11. A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

    NASA Technical Reports Server (NTRS)

    Constantinescu, G.S.; Lele, S. K.

    2000-01-01

    using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

  12. Assembly of a photoreactive coordination polymer containing rectangular grids.

    PubMed

    Michaelides, Adonis; Skoulika, Stavroula; Siskos, Michael G

    2004-11-07

    We describe the synthesis, crystal structure and solid state reactivity of cadmium fumarate dihydrate, which is made up of planar H-bonded metal-organic layers and undergoes, upon irradiation, a topochemical [2 + 2] cycloaddition reaction.

  13. Coordinate systems integration for development of malaysian craniofacial database.

    PubMed

    Rajion, Zainul; Suwardhi, Deni; Setan, Halim; Chong, Albert; Majid, Zulkepli; Ahmad, Anuar; Rani Samsudin, Ab; Aziz, Izhar; Wan Harun, W A R

    2005-01-01

    This study presents a data registration method for craniofacial spatial data of different modalities. The data consists of three dimensional (3D) vector and raster data models. The data is stored in object relational database. The data capture devices are Laser scanner, CT (Computed Tomography) scan and CR (Close Range) Photogrammetry. The objective of the registration is to transform the data from various coordinate systems into a single 3-D Cartesian coordinate system. The standard error of the registration obtained from multimodal imaging devices using 3D affine transformation is in the ranged of 1-2 mm. This study is a step forward for storing the spatial craniofacial data in one reference system in database.

  14. CaGrid Workflow Toolkit: A taverna based workflow tool for cancer grid

    PubMed Central

    2010-01-01

    Background In biological and medical domain, the use of web services made the data and computation functionality accessible in a unified manner, which helped automate the data pipeline that was previously performed manually. Workflow technology is widely used in the orchestration of multiple services to facilitate in-silico research. Cancer Biomedical Informatics Grid (caBIG) is an information network enabling the sharing of cancer research related resources and caGrid is its underlying service-based computation infrastructure. CaBIG requires that services are composed and orchestrated in a given sequence to realize data pipelines, which are often called scientific workflows. Results CaGrid selected Taverna as its workflow execution system of choice due to its integration with web service technology and support for a wide range of web services, plug-in architecture to cater for easy integration of third party extensions, etc. The caGrid Workflow Toolkit (or the toolkit for short), an extension to the Taverna workflow system, is designed and implemented to ease building and running caGrid workflows. It provides users with support for various phases in using workflows: service discovery, composition and orchestration, data access, and secure service invocation, which have been identified by the caGrid community as challenging in a multi-institutional and cross-discipline domain. Conclusions By extending the Taverna Workbench, caGrid Workflow Toolkit provided a comprehensive solution to compose and coordinate services in caGrid, which would otherwise remain isolated and disconnected from each other. Using it users can access more than 140 services and are offered with a rich set of features including discovery of data and analytical services, query and transfer of data, security protections for service invocations, state management in service interactions, and sharing of workflows, experiences and best practices. The proposed solution is general enough to be

  15. Research on Grid Size Suitability of Gridded Population Distribution in Urban Area: A Case Study in Urban Area of Xuanzhou District, China

    PubMed Central

    Dong, Nan; Yang, Xiaohuan; Cai, Hongyan; Xu, Fengjiao

    2017-01-01

    The research on the grid size suitability is important to provide improvement in accuracies of gridded population distribution. It contributes to reveal the actual spatial distribution of population. However, currently little research has been done in this area. Many well-modeled gridded population dataset are basically built at a single grid scale. If the grid cell size is not appropriate, it will result in spatial information loss or data redundancy. Therefore, in order to capture the desired spatial variation of population within the area of interest, it is necessary to conduct research on grid size suitability. This study summarized three expressed levels to analyze grid size suitability, which include location expressed level, numeric information expressed level, and spatial relationship expressed level. This study elaborated the reasons for choosing the five indexes to explore expression suitability. These five indexes are consistency measure, shape index rate, standard deviation of population density, patches diversity index, and the average local variance. The suitable grid size was determined by constructing grid size-indicator value curves and suitable grid size scheme. Results revealed that the three expressed levels on 10m grid scale are satisfying. And the population distribution raster data with 10m grid size provide excellent accuracy without loss. The 10m grid size is recommended as the appropriate scale for generating a high-quality gridded population distribution in our study area. Based on this preliminary study, it indicates the five indexes are coordinated with each other and reasonable and effective to assess grid size suitability. We also suggest choosing these five indexes in three perspectives of expressed level to carry out the research on grid size suitability of gridded population distribution. PMID:28122050

  16. Surface grid generation for multi-block structured grids

    NASA Astrophysics Data System (ADS)

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

    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.

  17. Grid Computing Education Support

    SciTech Connect

    Steven Crumb

    2008-01-15

    The GGF Student Scholar program enabled GGF the opportunity to bring over sixty qualified graduate and under-graduate students with interests in grid technologies to its three annual events over the three-year program.

  18. Space Development Grid Portal

    NASA Technical Reports Server (NTRS)

    Vaziri, Arsi

    2004-01-01

    This viewgraph presentation provides information on the development of a portal to provide secure and distributed grid computing for Payload Operations Integrated Center and Mission Control Center ground services.

  19. Efficient Procedure for the Numerical Calculation of Harmonic Vibrational Frequencies Based on Internal Coordinates

    SciTech Connect

    Miliordos, Evangelos; Xantheas, Sotiris S.

    2013-08-15

    We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson’s GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N – 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. Finally, in all cases the frequencies based on internal coordinates differ on average by <1 cm–1 from those obtained from Cartesian coordinates.

  20. Growing string method with interpolation and optimization in internal coordinates: method and examples.

    PubMed

    Zimmerman, Paul M

    2013-05-14

    The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.