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Coordinates and the Cartesian Plane
NSDL National Science Digital Library
The lesson begins with a short refresher lecture on how points are written in (x,y) format and orientation with the Cartesian plane axes. The lecture also covers which directions are positive and which are negative on an x-y plane. Students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points. Prerequisite knowledge: Familiarity with the coordinate plane, coordinates, and equations are helpful, but not required.
VU Bioengineering RET Program, School of Engineering,; Mckelvey, Aubrey
Explicitly computing geodetic coordinates from Cartesian coordinates
NASA Astrophysics Data System (ADS)
This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.
Zeng, H.
Coordinates and the Cartesian Plane
NSDL National Science Digital Library
A brief refresher on the Cartesian plane includes how points are written in (x,y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.
VU Bioengineering RET Program, School of Engineering,
Transonic airfoil analysis and design using Cartesian coordinates
NASA Technical Reports Server (NTRS)
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.
Carlson, L. A.
On the Remapping of Radar Estimates onto Cartesian Coordinates
NASA Astrophysics Data System (ADS)
A precise method for remapping of radar estimates onto Cartesian grids of different sizes was introduced. The method is straightforward and the algorithm developed for this study can be used to perform averaging over grids of any size or shape. Comparison of rainfall estimates using this method and estimates computed using a simple averaging method typically used by hydrologists reveals that there can be significant differences. Differences are expected to be much larger if precise remapping is compared to simpler methods such as the nearest neighbor. The method is particularly useful if products from more that one radar are to be merged. Using this method it is not necessary to interpolate estimates from two radars over Cartesian grid before merging is performed. In addition, gauge-radar comparisons and bias computation can be more consistent when precise remapping is used. Another advantage of precise remapping is that it will be very easy to account for the variability of the power within the radar bin using this scheme because the contribution from each radar bin is defined geometrically in a precise way. Grids constructed this way are the closest representation of radar observation of the atmosphere in Cartesian coordinates. The same approach was used to remap rainfall estimates from one radar onto the bin of another radar of lower resolution. Precise remapping was used in comparing estimates of the higher-resolution NCAR's S-band radar (S-Pol) and a WSR-88D radar. Detailed comparison of fields of instantaneous rain rate reveals that the correlation between the estimates of the two systems varies spatially. The correlation is highest at the mid-point between the two radars and decreases with distance from this point.
Sharif, H.; Ogden, F.
On the Remapping of Radar Estimates onto Cartesian Coordinates
A precise method for remapping of radar estimates onto Cartesian grids of different sizes was introduced. The method is straightforward and the algorithm developed for this study can be used to perform averaging over grids of any size or shape. Comparison of rainfall estimates using this method and estimates computed using a simple averaging method typically used by hydrologists reveals
H. Sharif; F. Ogden
Efficient Fluid Dynamic Design Optimization Using Cartesian Grids.
National Technical Information Service (NTIS)
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 ...
A. Dadone B. Grossman B. Sellers
Solution of the Euler equations on Cartesian grids
A method is presented for the solution of the two-dimensional Euler equations on Cartesian grids. The method utilizes a conservative cell vertex Euler solver with Lax�Wendroff time-stepping. Results are presented for transonic flow for Ni's 2D channel flow problem and also for transonic flow about a circular cylinder.
Ainslie D. French
Cartesian Grid Methods for Fluid Flow in Complex Geometries
\\u000a Biological fluid dynamics typically involves geometrically complicated structures which are often deforming in time. We give\\u000a a brief overview of some approaches based on using fixed Cartesian grids instead of attempting to use a grid which conforms\\u000a to the boundary. Both finite-difference and finite-volume methods are discussed, as well as a combined approach which has\\u000a recently been used for computing
Randall J. Leveque; Donna Calhoun
Hamiltonian formalism for semiflexible molecules in Cartesian coordinates
NASA Astrophysics Data System (ADS)
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.
Kneller, G. R.
Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm
NASA Astrophysics Data System (ADS)
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 (?) 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.
Civicioglu, Pinar
Triangle geometry processing for surface modeling and cartesian grid generation
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Aftosmis, Michael J. (San Mateo, CA) [San Mateo, CA; Melton, John E. (Hollister, CA) [Hollister, CA; Berger, Marsha J. (New York, NY) [New York, NY
Describing three-dimensional structures with spherical and Cartesian coordinates
NSDL National Science Digital Library
Analyzing three-dimensional orientation data using a stereonet is an important component of any structural geology course, ideally helping students to visualize structural geometry and serving as a springboard for more advanced topics such as fault and fold kinematics. Rather than teaching my students about stereonets using tracing paper and pushpins, I use the newest version of Rick Allmendinger and N�stor Cardozo's OSXStereonet program, which includes elegant, interactive three-dimensional view options. Simultaneously, I teach students transformation of orientation data between spherical coordinates and Cartesian coordinates, using MATLAB functions to carry out the conversions. We simultaneously solve problems involving orientation data using OSXStereonet and MATLAB, allowing students to gain an understanding of the mathematics that OSXStereonet carries out behind the scenes while using the visualization capabilities of OSXStereonet to reinforce the three-dimensional concepts. Keywords: Stereonet, OSXStereonet, Matlab, spherical, Cartesian, visualization
Loveless, Jack
Cartesian based grid generation/adaptive mesh refinement
NASA Technical Reports Server (NTRS)
Grid adaptation has recently received attention in the computational fluid dynamics (CFD) community as a means to capture the salient features of a flowfield by either moving grid points of a structured or by adding cells in an unstructured manner. An approach based on a background cartesian mesh is investigated from which the geometry is 'cut' out of the mesh. Once the mesh is obtained, a solution on this coarse grid is found, that indicates which cells need to be refined. This process of refining/solving continues until the flow is grid refined in terms of a user specified global parameter (such as drag coefficient etc.). The advantages of this approach are twofold: the generation of the base grid is independent of the topology of the bodies or surfaces around/through which the flow is to be computed, and the resulting grid (in uncut regions) is highly isotropic, so that the truncation error is low. The flow solver (which, along with the grid generation is still under development) uses a completely unstructured data base, and is a finite volume, upwinding scheme. Current and future work will address generating Navier-Stokes suitable grids by using locally aligned and normal face/cell refining. The attached plot shows a simple grid about two turbine blades.
Coirier, William J.
A cartesian grid embedded boundary method for hyperbolic conservation laws
We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J.; Modiano, David
Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley's Method
NASA Astrophysics Data System (ADS)
By using Halley�s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the �latitude equation�, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley�s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, -10 km ? h ? 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring�s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.
Fukushima, Toshio
GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows
NASA Technical Reports Server (NTRS)
With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.
Simulation of complex biological flows and flow control problems on Cartesian grids
A recently developed Cartesian grid based immersed boundary method is used to simulate a variety of biological flows as well as flows associated with active flow control. The key feature of the method is that it allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. In this paper we present a brief outline of the method
R. Mittal; F. M. Najjar; R. Byrganhalli; V. Seshadri; H. Singh
Adaptive Cartesian coordinate control of space based robot manipulators
NASA Technical Reports Server (NTRS)
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.
Walker, Michael W.; Wee, Liang-Boon
The Best Approximation to the Lunar Ephemeris: Comparison Between Cartesian and Spherical Coordinates
NASA Astrophysics Data System (ADS)
A comparison between Cartesian and spherical coordinates is made for the uniform approximation to the lunar ephemeris. Best results apply for Cartesian coordinates where polynomials of degree 29 are valid for 31 days at the precision of The Astronomical Almanac ``Daily Polynomials''.
Lara, M.; Lopez Moratalla, T.
A Cartesian coordinate algorithm for power system state estimation
This paper presents a new steady-state estimator based on the Cartesian coordinate formulation of nodal and line flow equations and minimization of weighted least squares (WLS) of the residuals. The fact that the rectangular coordinate version of network performance equations is completely expressible in a Taylor series and contains terms up to the second order derivatives only, results in a fast exact second order state (FESOS) estimator. In this estimator, the Jacobian and information matrices are constant, and hence need to be computed once only. The size of the mathematical model for the new estimator is the same as that of the widely used fast decoupled state (FDS) estimator, and hence characterized by comparable computational requirements (storage and time per iteration). Digital simulation results are presented on several sample power systems (well-conditioned/ill-conditioned) under normal as well as unusual operating modes to illustrate the range of application of the method vis-a-vis the FDS estimator. It is found that the exactness of the FESOS algorithm provides an accurate solution during all modes of system operation, and assures convergence to the right solution in spite of network ill-conditioning.
Rao, N.D.; Roy, L.
Various parameterizations of "latitude" equation - Cartesian to geodetic coordinates transformation
NASA Astrophysics Data System (ADS)
The paper presents a solution to one of the basic problems of computational geodesy - conversion between Cartesian and geodetic coordinates on a biaxial ellipsoid. The solution is based on what is known in the literature as "latitude equation". The equation is presented in three different parameterizations commonly used in geodesy - geodetic, parametric (reduced) and geocentric latitudes. Although the resulting equations may be derived in many ways, here, we present a very elegant one based on vectors orthogonality. As the "original latitude equations" are trigonometric ones, their representation has been changed into an irrational form after Fukushima (1999, 2006). Furthermore, in order to avoid division operations we have followed Fukushima's strategy again and rewritten the equations in a fractional form (a pair of iterative formulas). The resulting formulas involving parametric latitude are essentially the same as those introduced by Fukushima (2006) (considered the most efficient today). All the resulting variants are solved with Newton's second-order and Halley's third-order formulas. It turns out that all parameterizations of the "latitude equation" show a comparable level of performance.
Ligas, M.
An Investigation of Two-Dimensional CAD Generated Models with Body Decoupled Cartesian Grids for DSMC
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.
About invariance of the potential function in Cartesian coordinates according to the isotope substitution
NASA Astrophysics Data System (ADS)
On the basis of the analysis of influence of isotope substitution on system of the electronic and nuclear equations for any molecular system conditions of invariance are formulated relatively to the isotope substitution surfaces of the potential energy expressed in the Cartesian coordinates. Except for that it is shown, that this property of potential function is the consequence of the appropriate property of this function expressed in curvilinear internal coordinates, that, in its turn, allows at theoretical research of vibration - rotation spectra of isotope substituted molecules, and also at the solution of a direct and the inverse anharmonic problems to avoid the use of curvilinear internal coordinates, having replaced them by Cartesian.
Makhniov, Anatoli S.
Flutter prediction by an Euler method on non-moving Cartesian grids with gridless boundary conditions
A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is implemented for the treatment of surface boundary conditions. For steady flows, the gridless method applies surface boundary conditions using a weighted average of the flow
D. J. Kirshman; F. Liu
A sharp interface nite volume method for elliptic equations on Cartesian grids
We present a second order sharp interface nite volume method for the solution of the three-dimensional elliptic equation r ~x ru ~x f ~x with variable coe- cients on Cartesian grids. In particular, we focus on interface problems with discon- tinuities in the coecient, the source term, the solution, and the uxes across the interface. The method uses standard piecewiese
M. Oevermann; C. Scharfenberg; R. Klein
A Cartesian Grid Finite-Volume Method for the Advection-Diffusion Equation in Irregular Geometries
We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a �capacity function� to model the fact that some cells are only partially available to the fluid. The advection portion then uses
Donna Calhoun; Randall J. LeVeque
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
Buning, Pieter G.; Pulliam, Thomas H.
Large-Eddy Simulation of Ship Flows with Wall-Layer Models on Cartesian Grids
The recent development of CFDShip-Iowa Version 6, a high-performance, high-fidelity Cartesian grid solver for computational ship hydrodynamics, is presented. First, a wall function approach has been introduced for wall-layer modeling based on the immersed boundary method and the one-equation Spalart-Allmaras turbulence model. Second, in order to develop more advanced wall-layer modeling schemes, an orthogonal curvilinear grid solver based on the
Jianming Yang; Shanti Bhushan; Jung Soo Suh; Zhaoyuan Wang; Bonguk Koo; Nobuaki Sakamoto; Tao Xing; Frederick Stern
Computing reaching dynamics in motor cortex with Cartesian spatial coordinates
How neurons in the primary motor cortex control arm movements is not yet understood. Here we show that the equations of motion governing reaching simplify when expressed in spatial coordinates. In this fixed reference frame, joint torques are the sums of vector cross products between the spatial positions of limb segments and their spatial accelerations and velocities. The consequences that follow from this model explain many properties of neurons in the motor cortex, including directional broad, cosinelike tuning, nonuniformly distributed preferred directions dependent on the workspace, and the rotation of the population vector during arm movements. Remarkably, the torques can be directly computed as a linearly weighted sum of responses from cortical motoneurons, and the muscle tensions can be obtained as rectified linear sums of the joint torques. This allows the required muscle tensions to be computed rapidly from a trajectory in space with a feedforward network model.
Sejnowski, Terrence J.
A cartesian grid embedded boundary method for the heat equationand poisson's equation in three dimensions
We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60-85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60-85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.
Schwartz, Peter; Barad, Michael; Colella, Phillip; Ligocki, Terry
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
We 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. We 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
Hans Johansen; Phillip Colella
Fluid-Structure Interaction on Cartesian Grids: Flow Simulation and Coupling Environment
Despite their frequently supposed problems concerning the approximation of complicated and changing geometries, hierarchical\\u000a Cartesian grids such as those defined by spacetrees have proven to be advantageous in many simulation scenarios. Probably\\u000a their most important advantage is the simple, efficient, and flexible interface they offer and which allows for an elegant\\u000a embedding of numerical simulations in some broader context, as
Markus Brenk; Hans-Joachim Bungartz; Miriam Mehl; Tobias Neckel
LES of Flow around a Circular Cylinder at a Subcritical Reynolds Number with Cartesian Grids
NASA Astrophysics Data System (ADS)
Large eddy simulations (LES) of turbulent flow around a circular cylinder are performed with a novel technique using Cartesian grids. Several test cases investigate the influence of the subgrid-scale model (Smagorinsky vs. dynamic Germano) and the grid resolution. The results show overall fair agreement between LES and a recently performed DNS. An important issue turns out to be the proper prediction of the mean recirculation length. Results are also compared with experimental data for the near and far wake regions. The shape of the mean streamwise velocity profile inside the recirculation bubble remains an open question.
Tremblay, F.; Manhart, M.; Friedrich, R.
X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates
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
Guohua Cao; Theron J. Hamilton; Christoph Rose-Petruck; Gerald J. Diebold
Cartesian grid simulations of gas-solids flow systems with complex geometry
Complex geometries encountered in many applications of gas�solids flow need special treatment in most legacy multiphase flow solvers with Cartesian numerical grid. This paper briefly outlines the implementation of a cut cell technique in the open-source multiphase flow solver�MFIX for accurate representation of complex geometries. Specifically, applications of the Cartesian cut cell method to different gas�solids fluidization systems including a small scale bubbling fluidized bed with submerged tube bundle and a complete pilot-scale circulating fluidized bed will be presented. In addition to qualitative predictions on the general flow behaviors inside each system, quantitative comparison with the available experimental data will be presented. Furthermore, some results on extending the current cut-cell technique to Lagrangian�Eulerian simulations will be presented.
Dietiker, Jean-Francois; Li, Tingwen; Garg, Rahul; Mehrdad Shahnam
Numerical method for calculation of the incompressible flow in general curvilinear co-ordinates with double staggered grid
A solution methodology has been developed for incompressible flow in general curvilinear co-ordinates. Two staggered grids are used to discretize the physical domain. The first grid is a MAC quadrilateral mesh with pressure arranged at the centre and the Cartesian velocity components located at the middle of the sides of the mesh. The second grid is so displaced that its
A. Shklyar; A. Arbel
A sharp interface finite volume method for elliptic equations on Cartesian grids
NASA Astrophysics Data System (ADS)
We present a second order sharp interface finite volume method for the solution of the three-dimensional elliptic equation ?�(?(x?)?u(x?))=f(x?) with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewise trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M. Oevermann, R. Klein, A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, Journal of Computational Physics 219 (2006) 749-769] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases - including large ?-ratios and non-smooth interfaces - the method achieves second order of accuracy in the L? and L2 norm.
Oevermann, M.; Scharfenberg, C.; Klein, R.
Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates.
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. PMID:25005281
Sittel, Florian; Jain, Abhinav; Stock, Gerhard
Development of a Cartesian-grid finite-volume characteristic flux model for marine applications
NASA Astrophysics Data System (ADS)
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.
Leroy, C.; Le Touz�, D.; Alessandrini, B.
A Cartesian-grid integrated-RBF method for viscoelastic flows
NASA Astrophysics Data System (ADS)
This paper is concerned with the use of integrated radial-basis-function networks (IRBFNs), Cartesian-grids and point collocation for numerically solving 2D flows of viscoelastic fluids. In the proposed method, RBFNs, which are constructed through integration, are employed to approximate the field variables including stresses, and the governing equations are discretised by means of point collocation. Advantages gained from the integration process over differentiated RBFNs process are (i) better accuracy (ii) more straightforward implementation of boundary conditions and (iii) more stable solutions. The method is verified through several test problems, e.g. planar Poiseuille flow and fully-developed flow in a square duct, with different types of viscoelastic fluids, namely Oldroyd-B and CEF. The obtained results show that (i) The proposed method is easy to implement; (ii) Its pre-processing is simple and (iii) Accurate results are obtained using relatively-coarse grids.
Ho-Minh, D.; Mai-Duy, N.; Tran-Cong, T.
A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains
The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.
Johansen, H. [Univ. of California, Berkeley, CA (United States). Dept. of Mechanical Engineering; Colella, P. [Lawrence Berkeley National Lab., CA (United States). Center for Computational Sciences and Engineering
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. PMID:18059966
Bandres, Miguel A; Guti�rrez-Vega, Julio C
Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates
NASA Technical Reports Server (NTRS)
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.
Myhill, Elizabeth A.; Boss, Alan P.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h{sup 3}) convergence in the grid-size h=O(n{sup -1}). Moreover, this requires O(3rn+r{sup 3}) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH{sub 4} molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10{sup -6} hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
Khoromskij, B.N. [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig (Germany)], E-mail: email@example.com; Khoromskaia, V.; Chinnamsetty, S.R. [Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig (Germany); Flad, H.-J. [TU Berlin, Sekretariat MA 3-3, Strasse des 17, Juni 136, D-10623 Berlin (Germany)
A Cartesian grid embedded boundary method for the heat equation on irregular domains
We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60--85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank--Nicolson time discretization is unstable, requiring us to use the L{sub 0}-stable implicit Runge--Kutta method of Twizell, Gumel, and Arigu.
McCorquodale, Peter; Colella, Phillip; Johansen, Hans
Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations
In the present study a methodology to perform large-eddy simulations around complex boundaries on fixed Cartesian grids is presented. A novel interpolation scheme which is applicable to boundaries of arbitrary shape, does not involve special treatments, and allows the accurate imposition of the desired boundary conditions is introduced. A method to overcome the problems associated with the computation of the
Elias Balaras
A Computer Program To Increase Comprehension of the Cartesian Rectangular Coordinate System in High School Pre-Algebra Students.
ERIC Educational Resources Information Center
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�
Exley, I. Sheck
A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries
NASA Technical Reports Server (NTRS)
Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids
NASA Astrophysics Data System (ADS)
In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell's equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee's scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.
Chung, Eric T.; Ciarlet, Patrick; Yu, Tang Fei
An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates
A newly developed hybrid-coordinate ocean circulation model is documented and tested. Coordinate surfaces in this model adhere to isopycnals wherever this does not violate minimum layer thickness requirements; elsewhere, coordinate surfaces are geometrically constrained. The intent of this approach, some of whose features are reminiscent of the Arbitrary Lagrangian�Eulerian (ALE) technique, is to combine the best features of isopycnic-coordinate and
Rainer Bleck
Optimized three-dimensional FDTD discretizations of Maxwell�s equations on Cartesian grids
NASA Astrophysics Data System (ADS)
In this paper, novel finite-difference time-domain (FDTD) schemes are introduced for the numerical solution of Maxwell's equations on dual staggered Cartesian three-dimensional lattices. The proposed techniques are designed to accomplish optimized performance according to certain features and requirements dictated by the investigated problems, thus making efficient use of the available computational resources. Starting from only few initial assumptions, a construction process based on the minimization of specific error formulae is developed, which is later exploited to derive the final form of the finite-difference operators. Previously, an elaborate analysis of the proposed indicators is provided, targeting at global error control over all propagation angles. Our methodology guarantees upgraded flexibility, as accuracy can be maximized within either narrow or wider frequency bands, without practically inducing significant computational overhead. Attractive qualities such as high convergence rates are now the natural consequence of the effective design process, rather than the minimization of the truncation errors of the difference expressions. In fact, the proposed FDTD approaches verify the possibility to attain improved levels of accuracy, without resorting to the traditional - Taylor based - forms of the individual operators. A theoretical analysis of the inherent dispersion artifacts reveals the full potential of the new algorithms, while numerical tests and comparisons unveil their unquestionable merits in practical applications.
Zygiridis, Theodoros T.; Tsiboukis, Theodoros D.
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
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�
Gawryszewski, Luiz G.; Carreiro, Luiz Renato R.; Magalhaes, Fabio V.
A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse
NASA Astrophysics Data System (ADS)
An Eulerian, sharp interface, Cartesian grid method is developed for the numerical simulation of the response of materials to impact, shocks and detonations. The mass, momentum, and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain. These equations are cast in Eulerian conservation law form. The Mie-Gr�neisen equation of state is used to obtain pressure and the material is modeled as a Johnson-Cook solid. The ENO scheme is employed to capture shocks in combination with a hybrid particle level set technique to evolve sharp immersed boundaries. The numerical technique is able to handle collisions between multiple materials and can accurately compute the dynamics of the immersed boundaries. Results of calculations for axisymmetric Taylor bar impact and penetration of a Tungsten rod into steel plate show good agreement with moving finite element solutions and experimental results. Qualitative agreement with theory is shown for the void collapse phenomenon in an impacted material containing a spherical void.
Tran, L. B.; Udaykumar, H. S.
Generalized Coordinates for Cellular Automata Grids
After some cellular automata basics here is stated an approach of universal data organization for different automata grids.\\u000a It allows to identify any cell with only one non-negative integer index even for multidimensional grids
Lev Naumov; Saint-Peterburg State
Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes
In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD
Yang Hao; Chris J. Railton
NSDL National Science Digital Library
This introduction to the labeling of points on a plane by their Cartesian coordinates can optionally be extended to coordinates in 3-dimensional space, to plane polar coordinates and to 3-dimensional polar coordinates. Students should learn to use Cartesian coordinates (x,y) for defining the position of a point in two dimensions and to use Cartesian coordinates (x,y,z) in 3-dimensional space and learn to appreciate the two ways of defining the z axis. Students should also become familiar with some of the tools and terms used by surveyors such as theodolite, azimuth, elevation, and zenith. Optional items for students familiar with trigonometry and with the theorem of Pythagoras are polar coordinates (r,f ) on the plane, Converting (r,f) to (x,y) and vice versa, at least for r, and Spherical polar coordinates (r,q, f) in 3-dimensional space.
Stern, David
Base sequence criteria and Cartesian coordinates for stable B/Z and B/Z/B junctions in relaxed DNA.
It seems increasingly evident that if the Z form of DNA exists in the genome it must exist as short sections of alternating pyrimidine-purine sequences in the midst of very long sections of B-form DNA. We have determined the minimum length of a string of alternating CG base pairs that can go into the Z form in the middle of a long B form. Self-complimentary oligomers of the form T(M)(CG)(N)A(M) were synthesized. The conformation of the resulting duplex was determined in 6M aqueous NaCl solution by Raman scattering. We have found that 12 alternating CG base pairs is the minimum length required to form a stable Z form of DNA inside of a long B form section. Only the 4 center CG base pairs go into the Z form. These 4 CG base pairs in the Z form are flanked on each side by 4 CG base pairs in a non-Z (probably B) form as well as the ..TT.. ..AA.. sequences in the B form. We propose a model of the B/Z junction in which the double helix flips directly from the B form to the Z form so that there are no base pairs in the junction. In this model the B form is nucleated in the AT base pairs on each end and is propagated into the CG base pairs in the center. This model is supported by isotopic H/D exchange experiments that shows that the H/D exchange of the non-Z form CG base pairs is highly retarded and indicates that they remain in the B form. A Thermodynamic analysis of the concentration dependence of the melting point of the duplexes in both low and high salt, supports our model and rules out the possibility of hairpin formation. The enthalpy for the formation of a B/Z junction is determined to be about +16 kcal/junction. A comparison of these results with recent results on B/Z junctions in super-coiled DNA is given. Molecular modeling calculations permit us to obtain values for the coordinates and torsional angles of the oligomers showing both B/Z and B/Z/B junctions. The Cartesian coordinates for these oligomers as well as stereo figures of these models in color are available from the authors. PMID:1637507
Dai, Z; Dauchez, M; Thomas, G; Peticolas, W L
A new computational method for computing flow over complex aerodynamic configurations and its application to rotor/body computation using Cartesian grids
NASA Astrophysics Data System (ADS)
A new numerical method for efficiently computing vortex-dominated flows over complex aerodynamic configurations is developed. This method uses only a fixed, uniform Cartesian grid, no body conforming grid is required. The complex geometry surface is described by a smooth scalar function "F", which is defined at each grid node. By using Vorticity Confinement, this method effectively confines the vorticity to a narrow region even on coarse computational grids and for low order discretization schemes. The flow both inside and outside the configuration is considered, although in aerodynamic applications, the internal flow is fictitious. The no-slip boundary condition is imposed on solid body surfaces by eliminating the flow inside the configuration. Unlike other general Cartesian methods, no specific logic is needed to determine the body surface in the present method. Also, the vorticity can be shed from smooth surface as well as surfaces with sharp corners. Vorticity Confinement involves adding a simple term to the Navier-Stokes fluid dynamic equations. When discretized and solved, these modified equations admit convecting, concentrated vortices which maintain a fixed size and do not spread, even if there is numerical diffusion. Numerical results are presented for flows around simple and complex configurations which were investigated with the present method. As an application of this method, preliminary numerical flow solutions of a combined helicopter blade and real helicopter body are presented.
Wenren, Yonghu
Computing UV/vis spectra from the adiabatic and vertical Franck-Condon schemes with the use of Cartesian and internal coordinates
NASA Astrophysics Data System (ADS)
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.
G�tze, Jan P.; Karasulu, Bora; Thiel, Walter
NSDL National Science Digital Library
In this quick activity (page 1 of the PDF), learners will build a simple Cartesian Diver in an empty 2-liter bottle. Use this activity to demonstrate the principle of buoyancy, similar to the bladder system many fish rely on to move up and down in their watery environment. Relates to the linked video, DragonflyTV GPS: California Fish.
Twin Cities Public Television, Inc.
Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates
NASA Technical Reports Server (NTRS)
Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.
Deane, Anil E.
NSDL National Science Digital Library
This activity has students create a Cartesian diver, which will act in some ways like a submarine. Students will adjust the amount of air and water in an inverted test tube (the "diver") so that it at first barely floats in a water-filled bottle. Then, they will squeeze the closed bottle to create higher water pressure, causing the diver to sink. Releasing the bottle allows the diver to float again. Written instructions, a list of materials, and illustrations are included.
Three-dimensional anisotropic seismic wave modelling in spherical coordinates by a collocated-grid finite-difference method
NASA Astrophysics Data System (ADS)
To simulate seismic wave propagation in the spherical Earth, the Earth's curvature has to be taken into account. This can be done by solving the seismic wave equation in spherical coordinates by numerical methods. In this paper, we use an optimized, collocated-grid finite-difference scheme to solve the anisotropic velocity-stress equation in spherical coordinates. To increase the efficiency of the finite-difference algorithm, we use a non-uniform grid to discretize the computational domain. The grid varies continuously with smaller spacing in low velocity layers and thin layer regions and with larger spacing otherwise. We use stress-image setting to implement the free surface boundary condition on the stress components. To implement the free surface boundary condition on the velocity components, we use a compact scheme near the surface. If strong velocity gradient exists near the surface, a lower-order scheme is used to calculate velocity difference to stabilize the calculation. The computational domain is surrounded by complex-frequency shifted perfectly matched layers implemented through auxiliary differential equations (ADE CFS-PML) in a local Cartesian coordinate. We compare the simulation results with the results from the normal mode method in the isotropic and anisotropic models and verify the accuracy of the finite-difference method.
Zhang, Wei; Shen, Yang; Zhao, Li
Parallelization of TWOPORFLOW, a Cartesian Grid based Two-phase Porous Media Code for Transient Thermo-hydraulic Simulations
NASA Astrophysics Data System (ADS)
TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.
Trost, Nico; Jim�nez, Javier; Imke, Uwe; Sanchez, Victor
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.
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. PMID:17279495
Lee, Sang-Ho; Palmo, Kim; Krimm, Samuel
G-GPE Squares on a coordinate grid
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In the picture below a square is outlined whose vertices lie on the coordinate grid points: The area of this particular square is 16 square units. For ...
A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid
NASA Astrophysics Data System (ADS)
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A �buffer zone� methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.
Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.
Recognizing Patterns In Log-Polar Coordinates
NASA Technical Reports Server (NTRS)
Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.
Weiman, Carl F. R.
Electronic Absolute Cartesian Autocollimator
NASA Technical Reports Server (NTRS)
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 mirror is slightly tilted. Hence, one can determine the amount and direction of tilt from the coordinates of the target image on the viewing plane.
Leviton, Douglas B.
Agent Concept for Intelligent Distributed Coordination in the Electric Power Grid
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.
Agent Concept for Intelligent Distributed Coordination in the Electric Power Grid
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.
Coordinated reactive power control of DFIG rotor and grid sides converters
Doubly fed induction generators used in grid interfaced wind energy systems are increasingly being called upon to address voltage regulation and provide adequate reactive power support. This paper presents a new coordinated control strategy using both the grid and rotor side converters for voltage regulation and reactive power support considering operational limits and network side voltage fluctuations. The central idea
Rasool Aghatehrani; Lingling Fan; Rajesh Kavasseri
Discretization formulas for unstructured grids
NASA Technical Reports Server (NTRS)
The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.
Baumeister, Kenneth J.
Numerical Recirculating Flow Calculation Using a Body-Fitted Coordinate System
A finite-difference algorithm for recirculating flow problem! in a body-fitted coordinate system is presented. A fully staggered grid system is adopted for the velocity components and the scalar variables. The strong conservation law form of the governing equations is written in the general curvilinear coordinates. The SIMPLE calculation procedure originally developed in Cartesian coordinates is extended to the present curvilinear
W. Shyy; S. S. Tong; S. M. Correa
Moving grids for magnetic reconnection via Newton-Krylov methods
NASA Astrophysics Data System (ADS)
This paper presents a set of computationally efficient, adaptive grids for magnetic reconnection phenomenon where the current density can develop large gradients in the reconnection region. Four-field extended MagnetoHydroDynamics (MHD) equations with hyperviscosity terms are transformed so that the curvilinear coordinates replace the Cartesian coordinates as the independent variables, and moving grids' velocities are also considered in this transformed system as a part of interpolating the physical solutions from the old grid to the new grid as time advances. The curvilinear coordinates derived from the current density through the Monge-Kantorovich (MK) optimization approach help to reduce the resolution requirements during the computation.
Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E.
Using Coordination to Parallelize Sparse-Grid Methods for 3-D CFD Problems
The good parallel computing properties of sparse-grid solution techniques are investigated.For this, an existing sequential CFD code for a standard 3D problem from computationalaerodynamics is restructured into a parallel application. The restructuring is organized accordingto a master\\/slave protocol. The coordinator modules developed thereby are implementedin the coordination language MANIFOLD and are generally applicable. Performanceresults are given for both the sequential
Kees Everaars; Barry Koren
Coordinated control of grid-connected three-level NPC converter under distorted grid voltage
This paper presents complete control algorithm for grid-connected Pulse Width Modulated (PWM) AC\\/DC converter intended for industrial drives and renewable energy applications. The objective of control is to limit current harmonics distortion and provide ride through capability during voltage dips. Following improvements to Voltage Oriented Control are presented: synchronization loop with positive sequence extraction, resonant current controllers for higher harmonics
Krzysztof Rafal; Malgorzata Bobrowska-Rafal; Szymon Piasecki; Marek Jasinski
Coordinated Control of DFIG's Rotor and Grid Side Converters During Network Unbalance
This paper proposes a coordinated control of the rotor side converters (RSCs) and grid side converters (GSCs) of doubly-fed induction generator (DFIG) based wind generation systems under unbalanced voltage conditions. System behaviors and operations of the RSC and GSC under unbalanced voltage are illustrated. To provide enhanced operation, the RSC is controlled to eliminate the torque oscillations at double supply
Lie Xu
Functions of a local controller to coordinate distributed resources in a smart grid
This paper describes requirements for an intelligent local controller for smart grids. The controller manages the operation of a portion of the power system to achieve customer-configured preferences for reliability and power quality through the combined use of local generation and storage sources, responsive load, power conditioning, and standby electric service from the supply system. The controller coordinates the set
Angela Chuang; Mark McGranaghan
Agent Concept for Intelligent Distributed Coordination in the Electric Power Grid.
National Technical Information Service (NTIS)
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 Area...
D. C. Smathers S. Y. Goldsmith
Is there continuity between categorical and coordinate spatial relations coding? Evidence from a grid/no-grid working memory paradigm.
We ask the question whether the coding of categorical versus coordinate spatial relations depends on different neural networks showing hemispheric specialization or whether there is continuity between these two coding types. The 'continuous spatial coding' hypothesis would mean that the two coding types rely essentially on the same neural network consisting of more general-purpose processes, such as visuo-spatial attention, but with a different weighting of these general processes depending on exact task requirements. With event-related fMRI, we have studied right-handed male subjects performing a grid/no-grid visuo-spatial working memory task inducing categorical and coordinate spatial relations coding. Our data support the 'continuous spatial coding' hypothesis, indicating that, while based on the same fronto-parieto-occipital neural network than categorical spatial relations coding, the coding of coordinate spatial relations relies more heavily on attentional and executive processes, which could induce hemispheric differences similar to those described in the literature. The results also show that visuo-spatial working memory consists of a short-term posterior store with a capacity of up to three elements in the parietal and extrastriate cortices. This store depends on the presence of a visible space categorization and thus can be used for the coding of categorical spatial relations. When no visible space categorization is given or when more than three elements have to be coded, additional attentional and executive processes are recruited, mainly located in the dorso-lateral prefrontal cortex. PMID:18037455
Martin, Romain; Houssemand, Claude; Schiltz, Christine; Burnod, Yves; Alexandre, Fr�d�ric
Variable Correlation of Grid Coordinates to Core Location in Template Prostate Biopsy
Purpose Transperineal template prostate biopsy has been proposed to facilitate systematic biopsy in patients undergoing repeat biopsy who are at high risk for cancer. Advocates tout the reliability of the grid to define biopsy location compared to hand-held transrectal ultrasound guided biopsy. However, accuracy of the biopsy needle depends on bevel position, tissue deformity, and technique. Due to this potential for error, we sought to determine whether the use of transperineal template biopsy would assure reproducibly accurate needle placement. Materials and Methods A standard 0.5 cm brachytherapy grid was utilized for transperineal biopsy. A single grid hole was used to obtain biopsies. The bevel of the needle was rotated to a different position with each biopsy, and the angle of the needle was varied to test the ability of the grid to �map� the prostate. Results We observed wide variation of needle location through a single brachytherapy grid hole. We are able to show that at 5 cm depth, an area of 2.47 mm2 is possible to biopsy and at a depth of 25 cm; approximately 7.56 mm2 is possible to biopsy. This gives a precision of biopsy of at the most shallow depth 22% and at the deepest 7%. Conclusion There is potential for technical and equipment associated error with transperineal template guided prostate biopsy. The grid alone can account for substantial sources of error, so technique remains critical if the grid coordinates are to be used to predict presence or extent of cancer.
Brede, Christopher M.; Douville, Nicholas J.; Jones, Stephen
More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs.
Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code. PMID:23682203
Gai, Jiading; Obeid, Nady; Holtrop, Joseph L; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P; Hwu, Wen-Mei W; Liang, Zhi-Pei; Sutton, Bradley P
More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs
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.
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.
A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh
NASA Astrophysics Data System (ADS)
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable nonaxisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios and on quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows such as accretion disks and mass-transferring binary systems.
Byerly, Zachary D.; Adelstein-Lelbach, Bryce; Tohline, Joel E.; Marcello, Dominic C.
Recognizing Cartesian graph bundles
Graph bundles generalize the notion of covering graphs and graph products. In this paper we extend some of the methods for recognizing Cartesian product graphs to graph bundles. Two main notions are used. The first one is the well-known equivalence relation ?? defined on the edge-set of a graph. The second one is the concept of k-convex subgraphs. A subgraph
Wilfried Imrich; Tomaz Pisanski; Janez Zerovnik
A virtual power plant (VPP) is the concept of pooling distributed electricity gener- ating (DEG) units. In addition to the grid-connection, they are attached to a tele- communication network. The following paper presents a method that works without extra communication channels. The grid itself and the observation of the product flow parameters are used by DEG units to coordinate their
Gunnar Kaestle
NSDL National Science Digital Library
Investigate the first quadrant of the Cartesian coordinate system through identifying the coordinates of randomly generated points, or requesting that a particular point be plotted. Simple Coordinates Game is one of the Interactivate assessment explorers.
Development and Applications of 3D Cartesian CFD Technology
NASA Technical Reports Server (NTRS)
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.
Melton, John E.; Berger, Marsha J.; VanDalsem, William (Technical Monitor)
A fast dynamic grid adaption scheme for meteorological flows
The continuous dynamic grid adaption (CDGA) technique is applied to a compressible, three-dimensional model of a rising thermal. The computational cost, per grid point per time step, of using CDGA instead of a fixed, uniform Cartesian grid is about 53% of the total cost of the model with CDGA. The use of general curvilinear coordinates contributes 11.7% to this total, calculating and moving the grid 6.1%, and continually updating the transformation relations 20.7%. Costs due to calculations that involve the gridpoint velocities (as well as some substantial unexplained costs) contribute the remaining 14.5%. A simple way to limit the cost of calculating the grid is presented. The grid is adapted by solving an elliptic equation for gridpoint coordinates on a coarse grid and then interpolating the full finite-difference grid. In this application, the additional costs per grid point of CDGA are shown to be easily offset by the savings resulting from the reduction in the required number of grid points. In simulation of the thermal costs are reduced by a factor of 3, as compared with those of a companion model with a fixed, uniform Cartesian grid. 8 refs., 8 figs.
Fiedler, B.H.; Trapp, R.J. (Univ. of Oklahoma, Norman, OK (United States))
A nested grid, nonhydrostatic, elastic model using a terrain-following coordinate transformation - The radiative-nesting boundary conditions
NASA Technical Reports Server (NTRS)
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.
Chen, Chaing
Software for Automated Generation of Cartesian Meshes
NASA Technical Reports Server (NTRS)
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.
Aftosmis, Michael J.; Melton, John E.; Berger, Marshal J.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme.
National Technical Information Service (NTIS)
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 subdivis...
W. J. Coirier K. G. Powell
Flexible Two-Dimensional Square-Grid Coordination Polymers: Structures and Functions
Coordination polymers (CPs) or metal-organic frameworks (MOFs) have attracted considerable attention because of the tunable diversity of structures and functions. A 4,4?-bipyridine molecule, which is a simple, linear, exobidentate, and rigid ligand molecule, can construct two-dimensional (2D) square grid type CPs. Only the 2D-CPs with appropriate metal cations and counter anions exhibit flexibility and adsorb gas with a gate mechanism and these 2D-CPs are called elastic layer-structured metal-organic frameworks (ELMs). Such a unique property can make it possible to overcome the dilemma of strong adsorption and easy desorption, which is one of the ideal properties for practical adsorbents.
Kajiro, Hiroshi; Kondo, Atsushi; Kaneko, Katsumi; Kanoh, Hirofumi
Finite difference calculations of electro-magnetic fields in arbitrary curvilinear coordinates for coaxial microwave plasma sources
We present a finite difference frequency domain (FDFD) algorithm for the vector wave equation. Employing covariant formulations, arbitrary curvilinear, non-orthogonal computational grids are mapped onto equidistant Cartesian coordinates. This provides an intrinsic method for a local increase of computational accuracy and application of standard finite difference expressions. As an example this technique is applied to the microwave plasma torch (MPT).
A. M. Bilgic; K. Garloff; E. Voges
Cartesian stiffness control of the JPL\\/Stanford\\/Salisbury hand
To be useful as a dexterous end effector in assembly operations, a multifingered hand must be position-controlled to allow preshaping, and force-controlled to apply and regulate grasp forces. The author describes an implementation of stiffness control on the Salisbury hand, from tendon tension control to coordinated Cartesian object stiffness control. Substantial joint friction effects were observed which were predicted well
G. P. Starr
Determining the role of geospatial technologies for stigmergic coordination in situation management: Implications of the wireless grid
Abs tract�Geospatial technologies in conjunction with wireless grids will offer a context for locating and coordinating team activities in such a way that the nature of each team member's effort may be known and understood by other members. This constructed group knowledge enables teams to respond to unforeseen and emergent contingencies and act in concert through the active interpretation of
Janet Marsden
Interconversion between Truncated Cartesian and Polar Expansions of Images
In this paper we propose an algorithm for lossless conversion of data between Cartesian and polar coordinates, when the data is sampled from a two dimensional real-valued function (a mapping : ?2 ? ?) 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.
Park, Wooram; Chirikjian, Gregory S.
A Cartesian embedded boundary method for hyperbolic conservation laws
The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Sjogreen, B; Petersson, N A
NPSS on NASA's Information Power Grid: Using CORBA and Globus to Coordinate Multidisciplinary Aeroscience Applications.
National Technical Information Service (NTIS)
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...
B. Ginsburg D. Woodford G. J. Follen I. Foster I. Lopez O. Larsson R. Gutierrez S. Martin S. Tuecke
Numerical grid generation; Proceedings of the Symposium on Numerical Generation of Curvilinear Coordinate Systems and Their Use in the Numerical Solution of Partial Differential Equations, Nashville, TN, April 13-16, 1982
NASA Technical Reports Server (NTRS)
General curvilinear coordinate systems are considered along with the error induced by coordinate systems, basic differential models for coordinate generation, elliptic grid generation, conformal grid generation, algebraic grid generation, orthogonal grid generation, patched coordinate systems, and solid mechanics applications of boundary fitted coordinate systems. Attention is given to coordinate system control and adaptive meshes, the application of body conforming curvilinear grids for finite difference solution of external flow, the use of solution adaptive grids in solving partial differential equations, adaptive gridding for finite difference solutions to heat and mass transfer problems, and the application of curvilinear coordinate generation techniques to the computation of internal flows. Other topics explored are related to the solution of nonlinear water wave problems using boundary-fitted coordinate systems, the numerical modeling of estuarine hydrodynamics on a boundary-fitted coordinate system, and conformal grid generation for multielement airfoils.
Thompson, J. F. (editor)
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for 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.
Alter, Stephen J.
NSDL National Science Digital Library
The Ejs Free Fall Cartesian model displays the dynamics of a ball dropped near the surface of Earth onto a platform. The initial conditions for the ball are an initial positive velocity in the x direction and zero initial velocity in the y direction. The coefficient of restitution for the ball�s collision with the platform is less than one. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting �Open Ejs Model� from the pop-up menu item. Ejs Free Fall Cartesian model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_newton_FreeFallCartesian.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for Newtonian mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.
Christian, Wolfgang
Coordinating plug-in electric vehicle charging with electric grid: Valley filling and target load following
NASA Astrophysics Data System (ADS)
Plug-in electric vehicles (PEVs) shift energy consumption from petroleum to electricity for the personal transportation sector. This work proposes a decentralized charging protocol for PEVs with grid operators updating the cost signal. Each PEV calculates its own optimal charging profile only once based on the cost signal, after it is plugged in, and sends the result back to the grid operators. Grid operators only need to aggregate charging profiles and update the load and cost. The existing PEV characteristics, national household travel survey (NHTS), California Independent System Operator (CAISO) demand, and estimates for future renewable generation in California are used to simulate PEV operation, PEV charging profiles, grid demand, and grid net load (demand minus renewable). Results show the proposed protocol has good performance for overnight net load valley filling if the costs to be minimized are proportional to the net load. Annual results are shown in terms of overnight load variation and comparisons are made with grid level valley filling results. Further, a target load can be approached in the same manner by using the gap between current load and the target load as the cost. The communication effort involved is quite modest.
Zhang, Li; Jabbari, Faryar; Brown, Tim; Samuelsen, Scott
76 FR 72203 - Voltage Coordination on High Voltage Grids; Notice of Reliability Workshop Agenda
Federal Register 2010, 2011, 2012, 2013
...power resources in the distribution system or loads and coordinate with higher voltage systems. Panelists: Kedall Demaree, Alstom Rod Sulte, GE Soorya Kuloor, Gridiant Marija Ilic, New Electricity Transmission Software Solutions (NETSS)...
Coordinating regulation and demand response in electric power grids using multirate model predictive control
We propose a framework for reducing demand- supply imbalances in the grid, by jointly controlling both the supply-side electric power regulation together with the demand- side energy consumption by residential and commercial con- sumers demand response. We focus on performance improve- ments that arise from the complementary dynamics: regulation allows for frequent control updates but suffers from slower dynamics; demand
Haitham Hindi; Daniel Greene; Caitlin Laventall
Using the pseudospectral method on curved grids for 2D elastic forward modeling
When applying the conventional Fourier pseudospectral method (FSM) on a Cartesian grid that has a sufficient size to propagate a pulse, spurious diffractions from the staircase representation of the curved interfaces appear in the wavefield. It is demonstrated that these non-physical diffractions can be eliminated by using curved grids that conform to all the interfaces of the subsurface. Methods for solving the 2D acoustic wave equation using such curved grids have been published previously by the authors. Here the extensions to the full 2D elastic wave equations are presented. The curved grids are generated by using the so-called multiblock strategy which is a well-known concept in computational fluid dynamics. In principle the subsurface is divided into a number of contiguous subdomains. A separate grid is generated for each subdomain patching the grid lines across domain boundaries to obtain a globally continuous grid. Using this approach, even configurations with pinch outs can be handled. The curved grid is taken to constitute a generalized curvilinear coordinate system. Thus, the elastic equations have to be written in a curvilinear frame before applying the numerical scheme. The method implies that twice the number of spatial derivatives have to be evaluated compared to the conventional FSM on a Cartesian grid. However, it is demonstrated that the extra terms are more than compensated for by the fewer grid points needed in the curved approach.
Nielsen, P. [Haldor Topsoe A/S, Lyngby (Denmark); If, F. [COWIconsult, Lyngby (Denmark); Berg, P. [Danish Hydraulic Inst., Horsholm (Denmark); Skovgaard, O. [Technical Univ. of Denmark, Lyngby (Denmark). Mathematical Inst.
Cartesian feedback for RF power amplifier linearization
We discuss two control problems that arise in connection with Cartesian feedback radio-frequency power amplifiers. New solutions to both problems are described, and the results of a working prototype are presented. The prototype, a integrated circuit (IC) fabricated in National Semiconductor's 0.25 \\/spl mu\\/m CMOS process, represents the first known fully integrated implementation of the Cartesian feedback concept.
Joel L. Dawson; Thomas H. Lee
ElectricICT: Low voltage loads and generators coordination towards the SmartGrid paradigm
ElectricICT is a multi-disciplinary project aimed at developing a Energy Management System (EMS) which schedules and manages home loads and dispersed generators (DG). The final goal is to improve the overall SmartGrid approach performance. ElectricICT involves scientific and technical aspects in three research area: energy, telecommunication and operations research. The project is based on a model representations of each appliance,
A. Capone; G. Carello; M. Merlo
Coordination of active and reactive distributed resources in a smart grid
The authors present a methodology for assessing centralized control of active and reactive distributed resources in a smart distribution grid. The methodology is based on three- phase optimal power flow and is able to deal properly with unbalanced conditions and both single-phase and three-phase control resources. Single-phase resources that can be exploited by means of this approach are domestic loads,
Marco Bronzini; Sergio Bruno; Massimo La Scala; Roberto Sbrizzai
Complex frequency-shifted multi-axial perfectly matched layer for elastic wave modelling on curvilinear grids
NASA Astrophysics Data System (ADS)
Perfectly matched layer (PML) is an efficient absorbing technique for numerical wave simulations. Since it appeared, various improvements have been made. The complex frequency-shifted PML (CFS-PML) improves the absorbing performance for near-grazing incident waves and evanescent waves. The auxiliary differential equation (ADE) formulation of the PML provides a convenient unsplit-field PML implementation that can be directly used with high order time marching schemes. The multi-axial PML (MPML) stabilizes the PML on anisotropic media. However, these improvements were generally developed for Cartesian grids. In this paper, we extend the ADE CFS-PML to general curvilinear (non-orthogonal) grids for elastic wave modelling. Unlike the common implementations to absorb the waves in the computational space, we apply the damping along the perpendicular direction of the PML layer in the local Cartesian coordinates. Further, we relate the perpendicular and parallel components of the gradient operator in the local Cartesian coordinates to the derivatives in the curvilinear coordinates, to avoid mapping the wavefield to the local Cartesian coordinates. It is thus easy to be incorporated with numerical schemes on curvilinear grids. We derive the PML equations for the interior region and for the free surface separately because the free surface boundary condition modifies the elastic wave equations. We show that the elastic wave modelling on curvilinear grids exhibits anisotropic effects in the computational space, which may lead to unstable simulations. To stabilize the simulation, we adapt the MPML strategy to also absorb the wavefield along the two parallel directions of the PML. We illustrate the stability of this ADE CFS-MPML for finite-difference elastic wave simulations on curvilinear grids by two numerical experiments.
Zhang, Zhenguo; Zhang, Wei; Chen, Xiaofei
Complex frequency-shifted multi-axial perfectly matched layer for elastic wave modelling on curvilinear grids
NASA Astrophysics Data System (ADS)
Perfectly matched layer (PML) is an efficient absorbing technique for numerical wave simulations. Since it appeared, various improvements have been made. The complex frequency-shifted PML (CFS-PML) improves the absorbing performance for near-grazing incident waves and evanescent waves. The auxiliary differential equation (ADE) formulation of the PML provides a convenient unsplit-field PML implementation that can be directly used with high order time marching schemes. The multi-axial PML (MPML) stabilizes the PML on anisotropic media. However, these improvements were generally developed for Cartesian grids. In this paper, we extend the ADE CFS-PML to general curvilinear (non-orthogonal) grids for elastic wave modelling. Unlike the common implementations to absorb the waves in the computational space, we apply the damping along the perpendicular direction of the PML layer in the local Cartesian coordinates. Further, we relate the perpendicular and parallel components of the gradient operator in the local Cartesian coordinates to the derivatives in the curvilinear coordinates, to avoid mapping the wavefield to the local Cartesian coordinates. It is thus easy to be incorporated with numerical schemes on curvilinear grids. We derive the PML equations for the interior region and for the free surface separately because the free surface boundary condition modifies the elastic wave equations. We show that the elastic wave modelling on curvilinear grids exhibits anisotropic effects in the computational space, which may lead to unstable simulations. To stabilize the simulation, we adapt the MPML strategy to also absorb the wavefield along the two parallel directions of the PML. We illustrate the stability of this ADE CFS-MPML for finite-difference elastic wave simulations on curvilinear grids by two numerical experiments.
Zhang, Zhenguo; Zhang, Wei; Chen, Xiaofei
Adjoint Formulation for an Embedded-Boundary Cartesian Method
NASA Technical Reports Server (NTRS)
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
Shape Coding Using Polar Coordinates and the Discrete Cosine Transform
This paper discusses a new technique for shape coding for mobile video communication using polar coordinates and the DCT. First the Cartesian x and y shape coordinate functions are transformed to the domain of polar coordinates yielding an r and a ? function. Then these functions are transformed using a DCT. Using Cartesian coordinates means describing the shape in terms
Frank H. P. Spaan; Reginald L. Lagendijk; Jan Biemond
Development of accurate standardized algorithms for conversion between SRP grid coordinates and latitude/longitude
The Savannah Rive Plant (SRP) is a nuclear production facility operated by E.I. du Pont de Nemours and Co. for the United States Department of Energy. SRP is located along the Savannah River in South Carolina. Construction of SRP began in the early 1950's. At the time the plant was built, a local coordinate system was developed to assist in defining the locations of plant facilities. Over the years, large quantities of data have been developed using SRP Coordinates.'' These data include: building locations, plant boundaries, environmental sampling locations, waste disposal area locations, and a wide range of other geographical information. Currently, staff persons at SRP are organizing these data into automated information systems to allow more rapid, more robust and higher quality interpretation, interchange and presentation of spatial data. A key element in this process is the ability to incorporate outside data bases into the systems, as well as to share SRP data with interested organizations outside as SRP. Most geographical information outside of SRP is organized using latitude and longitude. Thus, straightforward, accurate and consistent algorithms to convert SRP Coordinates to/from latitude and longitude are needed. Appropriate algorithms are presented in this document.
Looney, B.B.; Marsh, J.T. Jr.; Hayes, D.W.
Development of accurate standardized algorithms for conversion between SRP grid coordinates and latitude/longitude
The Savannah Rive Plant (SRP) is a nuclear production facility operated by E.I. du Pont de Nemours and Co. for the United States Department of Energy. SRP is located along the Savannah River in South Carolina. Construction of SRP began in the early 1950`s. At the time the plant was built, a local coordinate system was developed to assist in defining the locations of plant facilities. Over the years, large quantities of data have been developed using ``SRP Coordinates.`` These data include: building locations, plant boundaries, environmental sampling locations, waste disposal area locations, and a wide range of other geographical information. Currently, staff persons at SRP are organizing these data into automated information systems to allow more rapid, more robust and higher quality interpretation, interchange and presentation of spatial data. A key element in this process is the ability to incorporate outside data bases into the systems, as well as to share SRP data with interested organizations outside as SRP. Most geographical information outside of SRP is organized using latitude and longitude. Thus, straightforward, accurate and consistent algorithms to convert SRP Coordinates to/from latitude and longitude are needed. Appropriate algorithms are presented in this document.
Looney, B.B.; Marsh, J.T. Jr.; Hayes, D.W.
Index integral representations for connection between cartesian, cylindrical, and spheroidal systems
In this paper, we present two new index integral representations for connection between cartesian, cylindrical, and spheroidal coordinate systems in terms of Bessel, MacDonald, and conical functions. Our result is mainly motivated by solution of the boundary value problems in domains composed of both cartesian and hyperboloidal boundaries, and the need for new integral representations that facilitate the transformation between these coordinates. As a by-product, the special cases of our results will produce new proofs to known index integrals and provide some new integral identities.
Passian, Ali [ORNL; Koucheckian, Sherwin [University of South Florida, Tampa; Yakubovich, Semyon [University of Porto, Portugal
Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.
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.
Rabow, A. A.; Scheraga, H. A.
Parameter Studies, time-dependent simulations and design with automated Cartesian methods
NASA Technical Reports Server (NTRS)
Over the past decade, NASA has made a substantial investment in developing adaptive Cartesian grid methods for aerodynamic simulation. Cartesian-based methods played a key role in both the Space Shuttle Accident Investigation and in NASA's return to flight activities. The talk will provide an overview of recent technological developments focusing on the generation of large-scale aerodynamic databases, automated CAD-based design, and time-dependent simulations with of bodies in relative motion. Automation, scalability and robustness underly all of these applications and research in each of these topics will be presented.
Aftosmis, Michael
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)
A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.
Smith, R. E.
The Cartesian method for solving partial differential equations in spherical geometry
Cartesian coordinates are used to solve the nonlinear shallow-water equations on the sphere. The two-dimensional equations, in spherical coordinates, are first embedded in a three-dimensional system in a manner that preserves solutions of the two-dimensional system. That is, solutions of the three-dimensional system, with appropriate initial conditions, also solve the two-dimensional system on the surface of the sphere. The higher
Paul N. Swarztrauber; David L. Williamson; John B. Drake
Maintain rigid structures in Verlet based cartesian molecular dynamics simulations.
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. PMID:23039588
Tao, Peng; Wu, Xiongwu; Brooks, Bernard R
Maintain rigid structures in Verlet based Cartesian molecular dynamics simulations
NASA Astrophysics Data System (ADS)
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.
Tao, Peng; Wu, Xiongwu; Brooks, Bernard R.
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)
Diverse (4,4) grid layers are exemplified in five two-dimensional coordination polymers with dual �2-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.
Liu, Guang-Zhen; Li, Xiao-Dong; Xin, Ling-Yun; Li, Xiao-Ling; Wang, Li-Ya
Calculation of fluid flows with staggered and nonstaggered curvilinear nonorthogonal grids. I - The theory. II - A comparison
NASA Astrophysics Data System (ADS)
Tensor calculus is presently employed to furnish both necessary coordinate and velocity transformations in the present use of two different finite-volume methods for discretization of conservation equations in 3D curvilinear nonorthogonal coordinates. While one method is based on the nonstaggered grid arrangement and employs Cartesian velocity components as dependent variables in the momentum equations, the other combines a staggered grid arrangement with physical covariant velocity projections in a locally fixed coordinate system. In the second part of this work, a comparative evaluation of the two methods indicates that while results of comparable accuracy are achieved after a similar number of iterations, the staggered method may be recommended for curvilinear nonorthogonal coordinate problems due to its reduced memory and computational requirements.
Melaaen, M. C.
Graphing and the Coordinate Plane
NSDL National Science Digital Library
This lesson is designed to introduce students to graphing coordinates and lines in the Cartesian coordinate plane. This lesson provides links to discussions and activities related to graphing as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.
Adaptation of a matrix parameterization of the middle atmospheric radiative cooling for an arbitrary vertical coordinate grid
NASA Astrophysics Data System (ADS)
Matrices corresponding to a revised vertical grid are shown to be derived from the original grid by integrating the radiative cooling rate over model layers. The method is applied to temperature profiles that represent average or extreme atmospheric conditions and a range of vertical resolutions. The example makes use of the 15-micron CO2 band parameterization proposed by Akmaev and Shved (1982) for the LTE region of the middle atmosphere. Cooling rate errors provided by the present method are not more than 0.11 K/day for a vertical grid spacing of less than 5 km. The matrix transformation method is shown to be valuable for adapting effective matrix parameterizations of middle atmosphere cooling to atmospheric models with arbitrary vertical resolutions.
Akmaev, R. A.; Fomichev, V. I.
A Community Benchmark for 2D Cartesian Compressible Convection
NASA Astrophysics Data System (ADS)
The results from five Cartesian, compressible mantle convection codes are reported for constant viscosity and temperature-dependent viscosity calculations in a unit aspect ratio domain from Rayleigh numbers 104 to 106 and dissipation numbers from 0 to 2.0 are compared. Four codes are finite element codes and one is a finite volume code. The finite element codes include both Uzawa and direct solution techniques and use either a penalty or integrated method (Taylor Hood elements). All five codes agree to better than 2% when comparing surface heat flux and rms velocity for constant viscosity, steady, Bousinessq convecion (Blankenbach, 1989 1a, 1b, 1c) with approximately 60 by 60 grid points (elements). All five codes agree to better than 2% when comparing surface heat flux and rms velocity for constant viscosity, steady, extended Bousinessq and Truncated Anelastic liquid convecion with approximately 60 by 60 grid points up to Rayleigh numbers of 2 times 105. Some codes settle on one-cell solutions while other codes settle on two-cell solutions, and this has a significant effect on the global flow diagnostics. We do not yet know if the one-cell versus two-cell solutions result from differences in grids, initial conditions or reflects differences in the time-evolution algorithm. For temperature-dependent problems, the difference between one-cell solutions and two-cell solutions is more pronounced. As has been previously noted, the balance between work and viscous dissipation is better when the pressure effect of density is included in the buoyancy (Anelastic Liquid versus Truncated Anelastic Liquid) although the effect on the surface heat flow and rms-velocity is less than 1-2%.
King, S. D.; Lee, C.; Leng, W.; Zhong, S.; van Keken, P.; Tan, E.; Gurnis, M.; Tosi, N.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Method and system for generating an elliptic grid in generalized coordinates in two or three dimensions, where one or more decay parameters near a boundary segment of a grid are determined as part of the grid solution, rather than being prescribed initially by a user. The decay parameters may vary with one or more generalized coordinates and determine the rate(s) at which separation distances between adjacent grid lines change as one moves toward or away from a grid boundary segment.
Kaul, Upender K. (Editor)
A Cartesian Adaptive Level Set Method for Two-Phase Flows
NASA Technical Reports Server (NTRS)
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Ham, F.; Young, Y.-N.
How do spatial learning and memory occur in the brain? Coordinated learning of entorhinal grid cells and hippocampal place cells.
Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and exhibit remarkable regular hexagonal spatial firing patterns. They also exhibit a gradient of spatial scales along the dorsoventral axis of the MEC, with neighboring cells at a given dorsoventral location having different spatial phases. A neural model shows how a hierarchy of self-organizing maps, each obeying the same laws, responds to realistic rat trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with unimodal firing fields that fit neurophysiological data about their development in juvenile rats. The hippocampal place fields represent much larger spaces than the grid cells to support navigational behaviors. Both the entorhinal and hippocampal self-organizing maps amplify and learn to categorize the most energetic and frequent co-occurrences of their inputs. Top-down attentional mechanisms from hippocampus to MEC help to dynamically stabilize these spatial memories in both the model and neurophysiological data. Spatial learning through MEC to hippocampus occurs in parallel with temporal learning through lateral entorhinal cortex to hippocampus. These homologous spatial and temporal representations illustrate a kind of "neural relativity" that may provide a substrate for episodic learning and memory. PMID:22288394
Pilly, Praveen K; Grossberg, Stephen
How Do Spatial Learning and Memory Occur in the Brain? Coordinated Learning of Entorhinal Grid Cells and Hippocampal Place Cells
Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and
Praveen K. Pilly; Stephen Grossberg
How Do Spatial Learning and Memory Occur in the Brain? Coordinated Learning of Entorhinal Grid Cells and Hippocampal Place Cells
Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and
Praveen K. Pilly; Stephen Grossberg
A Cartesian method for fitting the bathymetry and tracking the dynamic position of the shoreline in a three-dimensional, hydrodynamic model
This paper presents a Cartesian method for the simultaneous fitting of the bathymetry and shorelines in a three-dimensional, hydrodynamic model for free-surface flows. The model, named LESS3D (Lake & Estuarine Simulation System in Three Dimensions), solves flux-based finite difference equations in the Cartesian-coordinate system (x,y,z). It uses a bilinear bottom to fit the bottom topography and keeps track the dynamic
Xinjian Chen
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
NASA Technical Reports Server (NTRS)
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.
NASA Technical Reports Server (NTRS)
A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.
Rumsey, Christopher Lockwood
Self-assembly of three new coordination complexes: Formation of 2-D square grid, 1-D chain and tape structures
NASA Astrophysics Data System (ADS)
Three distinct coordination complexes, viz., [Co(imi) 2(tmb) 2] ( 1) [where imi = imidazole], {[Ni(tmb) 2(H 2O) 3]�2H 2O} n ( 2) and [Cu 2(?-tmb) 4(CH 3OH) 2] ( 3), have been synthesized hydrothermally by the reactions of metal acetates, 2,4,6-trimethylbenzoic acid (Htmb) and with or without appropriate amine. The Ni analogue of 1 and the Co analogue of 2 have also been synthesized. X-ray single-crystal diffraction suggests that complex 1 represents discrete mononuclear species and complex 2 represents a 1D chain coordination polymer in which the Ni(II) ions are connected by the bridging water molecules. Complex 3 represents a neutral dinuclear complex. In 1, the central metal ions are associated by the carboxylate moiety and imidazole ligands, whereas the central metal atom is coordinated to the carboxylate moiety and the respective solvent molecules in 2 and 3. In 3, the four 2,4,6-trimethylbenzoate moieties act as a bridge connecting two copper (II) ions and the O atoms of methanol coordinate in an anti arrangement to form a square pyramidal geometry, with the methanol molecule at the apical position. In all the three structures the central metal atom sits on a crystallographic inversion centre. In all the cases, the coordination entities are further organized via hydrogen bonding interactions to generate multifarious supramolecular networks. Complexes 1, 2 and 3 have also been characterized by spectroscopic (UV/Vis and IR) and thermal analysis (TGA). In addition, the complexes were found to exhibit antimicrobial activity.The magnetic susceptibility measurements, measured from 8 to 300 K, revealed antiferromagnetic interactions between the Co(II) ions in compound 1 and the Ni(II) ions in 1a, respectively.
Indrani, Murugan; Ramasubramanian, Ramasamy; Fronczek, Frank R.; Vasanthacharya, N. Y.; Kumaresan, Sudalaiandi
A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction
NASA Technical Reports Server (NTRS)
This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.
Hood, Caroline; Frendi, Abdelkader
Kohut and Contextualism: Toward a Post-Cartesian Psychoanalytic Theory
This article portrays Heinz Kohut as a pivotal transitional figure in the development of a post-Cartesian, fully contextual psychoanalytic psychology. Despite his contextualization of narcissism and movement toward phenomenology and perspectivalism, remnants of Cartesian, isolated-mind thinking persisted in his metapsychology of the self and in his view of analytic empathy.
Robert D. Stolorow; George E. Atwood; Donna M. Orange
Graphing Equations on the Cartesian Plane: Slope
NSDL National Science Digital Library
The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slope occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y- axes on the plane in both the positive and negative directions.
VU Bioengineering RET Program, School of Engineering,; Mckelvey, Aubrey
Grid-based methods for diatomic quantum scattering problems III: Double photoionization of molecular hydrogen in prolate spheroidal coordinates
Our previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H$_2$ with fixed-nuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.
Tao, Liang; McCurdy, Bill; Rescigno, Tom
Structured background grids for generation of unstructured grids by advancing front method
NASA Technical Reports Server (NTRS)
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.
Pirzadeh, Shahyar
NASA Technical Reports Server (NTRS)
The "Grid" is an emerging infrastructure for coordinating access across autonomous organizations to distributed, heterogeneous computation and data resources. Data grids are being built around the world as the next generation data handling systems for sharing, publishing, and preserving data residing on storage systems located in multiple administrative domains. A data grid provides logical namespaces for users, digital entities and storage resources to create persistent identifiers for controlling access, enabling discovery, and managing wide area latencies. This paper introduces data grids and describes data grid use cases. The relevance of data grids to digital libraries and persistent archives is demonstrated, and research issues in data grids and grid dataflow management systems are discussed.
Moore, Reagan W.; Jagatheesan, Arun; Rajasekar, Arcot; Wan, Michael; Schroeder, Wayne
On automating domain connectivity for overset grids
NASA Technical Reports Server (NTRS)
An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.
Chiu, Ing-Tsau; Meakin, Robert L.
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
Coirier, William J.; Powell, Kenneth G.
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.
Coirier, William J.; Powell, Kenneth G.
Coherence Pathways with Cartesian Product Operators. The C3PO Method
NASA Astrophysics Data System (ADS)
The product-operator formalism using the Cartesian operator basis was modified, and the notation of Ix(?) = Ixcos ? + Iysin ? and Iy(?) = Iycos ? - Ixsin ? simplified the product-operator description of uncoupled or weakly coupled spins in multipulse sequences with arbitrary pulse phases and chemical-shift precessions. The compact Cartesian coordinate product- operator (C3PO) formalism is more compact than any other proposed basis set, easily provides complete coherence-pathway information, and provides better visualization than the original Cartesian basis set. Formulas for evolution under radiofrequency pulses, chemical-shift precession with spin-spin coupling, and multiple-quantum coherences are provided for weakly coupled IS and I 3S spin systems ( I = S = {1}/{2}) and for a strongly coupled IS (AB) spin system. Formulas are also provided for a spin coupled to an S = 1 spin. The C3PO formalism is compared with the spherical basis set, and examples are provided for STEAM-localized spectroscopy, COSY, and a strongly coupled AB spin system.
Kingsley, P. B.
Adaptation of a k-epsilon Model to a C artesian Grid Based Methodology
Despite the high cost of memory and CPU time required to resolve the boundary layer, a viscous unstructured grid solver has many advantages over a structured grid solver such as the convenience in automated grid generation and vortex capturing by solution adaption. In present study, an unstructured Cartesian grid solver is developed on the basis of the existing viscous solver,
Stephen M. Ruffin; Jae-Doo Lee
Parallel implementation of the Dirac equation in three Cartesian dimensions.
National Technical Information Service (NTIS)
We describe the numerical methods used to solve the time-dependent Dirac equation on a three-dimensional Cartesian lattice. Efficient algorithms are required for computationally intensive studies of vacuum-pair production in relativistic heavy-ion collisi...
J. C. Wells M. R. Strayer V. E. Oberacker A. S. Umar
Evaluation of gridded scanning ARM cloud radar reflectivity observations and vertical doppler velocity retrievals
NASA Astrophysics Data System (ADS)
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.
Lamer, K.; Tatarevic, A.; Jo, I.; Kollias, P.
Evaluation of gridded Scanning ARM Cloud Radar reflectivity observations and vertical Doppler velocity retrievals
NASA Astrophysics Data System (ADS)
The Scanning ARM Cloud Radars (SACR's) 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 common scan strategy is to repetitively slice the atmosphere from horizon to horizon as clouds advect over the radar (Cross-Wind Range Height Indicator - CWRHI). Here, the processing and gridding of the SACR CW-RHI scans are presented. First, the SACR sample observations from the ARM Oklahoma (SGP) and Cape-Cod (PVC) sites are post-processed (detection mask, velocity de-aliasing and gaseous attenuation correction). The resulting radial Doppler moment fields are then mapped to Cartesian coordinates with time as one of the dimension. The Cartesian-gridded Doppler velocity fields are next 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 clouds dynamical representations up to 25-30� off zenith. The proposed gridded products are expected to advance our understanding of 3-D cloud morphology, dynamics, anisotropy and lead to more realistic 3-D radiative transfer calculations.
Lamer, K.; Tatarevic, A.; Jo, I.; Kollias, P.
NSDL National Science Digital Library
In this lesson, students will use their knowledge of coordinates and coordinate pairs in a real life situation as they become archaeologists excavating a dig site. They will measure their site, label the grids with correct coordinates and use coordinate pairs to record the location of the artifacts they discover.
Driggers, Diane
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
NASA Technical Reports Server (NTRS)
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.
Nemec, Marian; Aftosmis, Michael J.
NASA Technical Reports Server (NTRS)
Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.
Swinbank, Richard; Purser, James
FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates
NASA Technical Reports Server (NTRS)
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Kaul, Upender K.
Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz
NASA Astrophysics Data System (ADS)
Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of r-refinement adaptive grids obtained from solving a single Monge-Amp�re (MA) equation addresses the high-resolution requirements near the x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated.
Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E.
Biangular Coordinates Redux: Discovering a New Kind of Geometry
ERIC Educational Resources Information Center
Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the�
Winkel, Brian; Naylor, Michael
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers
A modified Cartesian feedback method called �frequency-offset Cartesian feedback� and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems. In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200�1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90� phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback. In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems.
Zanchi, Marta G.; Pauly, John M.; Scott, Greig C.
Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations
NASA Astrophysics Data System (ADS)
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 C0, C1 or C2 levels. The C0 and C1 reconstructions fit the equation of state and enthalpy relations separately, while the C2 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 C1 method requiring slightly less storage than those for the C0 and C2 reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C1 and C2 methods are approximately a factor of two slower than the C0 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 levels.
Xia, Guoping; Li, Ding; Merkle, Charles L.
Cartesian base predictive control of robotic manipulators
A multi-input multi-output (MIMO) controlled auto regressive integrated moving average (CARIMA) model which has the input vector consisting of the joint torques and the output vector consisting of the velocities of the gripper expressed in the world coordinate system, is proposed for the motion of the end-effector of a robotic manipulator system. Since the manipulator is a time-varying system, because
C. Ozsoy; R. Kazan
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.
Aftosmis, M. J.; Murman, S. M.; Berger, M. J.
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.
Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.
On Multigrid for Overlapping Grids
The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other important features include optimizations for Cartesian component grids, the use of over-relaxed Red-Black smoothers and the generation of coarse grid operators through Galerkin averaging. Numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for both Dirichlet and Neumann/mixed boundary conditions. A comparison to Krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory.
Henshaw, W
String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of ?-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.
Branduardi, Davide; Faraldo-Gomez, Jose D.
Application of high resolution NVD and TVD differencing schemes to the discrete ordinates method using unstructured grids
NASA Astrophysics Data System (ADS)
High order resolution schemes based on the NVD and TVD boundedness criteria are applied to radiative transfer problems using the DOM in two-dimensional unstructured triangular grids. The implementation of these schemes in unstructured grids requires approximations, and two implementations reported in the literature are compared with a new one. Three different methods have been used to calculate the gradient of the radiation intensity at the center of the control volumes. The various schemes are applied to several test problems, the results are compared with those obtained using the step scheme, the mean flux interpolation scheme and another high order scheme based on a truncated Taylor series expansion, and the most accurate implementations are identified. It is concluded that although the high order schemes perform much better than the others, they are not as accurate as in Cartesian coordinates, and their order of convergence is lower than in that case.
Coelho, Pedro J.
On the use of a high order overlapping grid method for coupling in CFD\\/CAA
This paper presents a theoretical analysis and two applications of a high-order overlapping grid method for coupling Cartesian and curvilinear grids, developed in order to simulate aerodynamic noise. First, the overlapping grid method based on Lagrange interpolating polynomials is described and a theoretical analysis of the interpolation operator is then carried out. It shows that the interpolation generates spurious modes
G. Desquesnes; M. Terracol; E. Manoha; P. Sagaut
76 FR 46279 - Smart Grid Advisory Committee
Federal Register 2010, 2011, 2012, 2013
...Institute of Standards and Technology Smart Grid Advisory Committee AGENCY: Department...SUMMARY: The Smart Grid Advisory Committee (SGAC or Committee...Office of the National Coordinator for Smart Grid Interoperability, National...
A CUDA-based reverse gridding algorithm for MR reconstruction.
MR raw data collected using non-Cartesian method can be transformed on Cartesian grids by traditional gridding algorithm (GA) and reconstructed by Fourier transform. However, its runtime complexity is O(K�N(2)), where resolution of raw data is N�N and size of convolution window (CW) is K. And it involves a large number of matrix calculation including modulus, addition, multiplication and convolution. Therefore, a Compute Unified Device Architecture (CUDA)-based algorithm is proposed to improve the reconstruction efficiency of PROPELLER (a globally recognized non-Cartesian sampling method). Experiment shows a write-write conflict among multiple CUDA threads. This induces an inconsistent result when synchronously convoluting multiple k-space data onto the same grid. To overcome this problem, a reverse gridding algorithm (RGA) was developed. Different from the method of generating a grid window for each trajectory as in traditional GA, RGA calculates a trajectory window for each grid. This is what "reverse" means. For each k-space point in the CW, contribution is cumulated to this grid. Although this algorithm can be easily extended to reconstruct other non-Cartesian sampled raw data, we only implement it based on PROPELLER. Experiment illustrates that this CUDA-based RGA has successfully solved the write-write conflict and its reconstruction speed is 7.5 times higher than that of traditional GA. PMID:22898698
Yang, Jingzhu; Feng, Chaolu; Zhao, Dazhe
OVERGRID: A Unified Overset Grid Generation Graphical Interface
NASA Technical Reports Server (NTRS)
This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.
Chan, William M.; Akien, Edwin W. (Technical Monitor)
The Cartesian Diver as an Aid for Teaching Respiratory Physiology
ERIC Educational Resources Information Center
The mechanism by which air enters the mammalian lung is difficult for many students of physiology. In particular, some students have trouble seeing how pressure can be transmitted through a fluid such as the intrapleural fluid and how the magnitude of that pressure can change. A Cartesian diver, an old-time child's toy, may be used as a visual aid�
Fitch, Greg K.
Representation and the Intrapsychic: Cartesian Barriers to Empathic Contact
This paper argues for a radical relational perspective that explicitly challenges the notion of the intrapsychic and the related Cartesian assumptions of representationalism. Conceptual tools derived from the school of embodied cognition provide an alternative theoretical language that depicts a new understanding of experience as an emergent and distributed phenomenon of a dialogic communicative system. Clinical vignettes illustrate how this
Maxwell S. Sucharov
A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G H. We prove that the metric dimension of G G
The Structure of Integral Dimensions: Contrasting Topological and Cartesian Representations
ERIC Educational Resources Information Center
Diverse evidence shows that perceptually integral dimensions, such as those composing color, are represented holistically. However, the nature of these holistic representations is poorly understood. Extant theories, such as those founded on multidimensional scaling or general recognition theory, model integral stimulus spaces using a Cartesian�
Jones, Matt; Goldstone, Robert L.
Boolean and Cartesian Abstraction for Model Checking C Programs
The problem of model checking a specification in form of a C program with recursive procedures and many thousands of lines of code has not been addressed before. In this paper, we show how we attack this problem using an abstraction that is formalized with the Cartesian abstraction. It is implemented through a source-to-source transformation into a `Boolean\\
Thomas Ball; Andreas Podelski; Sriram K. Rajamani
An Adaptively Refined Cartesian Mesh Solver for the Euler Equations
A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann
Darren Dezeeuw; Kenneth G. Powell
A Lot of Good Physics in the Cartesian Diver
ERIC Educational Resources Information Center
The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When�
De Luca, Roberto; Ganci, Salvatore
A finite-volume method with hexahedral multiblock grids for modeling flow in porous media
This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and\\/or unstruc- tured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids.
S. H. Lee; P. Jenny; H. A. Tchelepi
A Hybrid Cartesian\\/Immersed-Boundary Finite-Element Method for Simulating Heat and Flow Patterns in a Two-Roll Mill
This article describes numerical investigations of the flow and heat patterns in a two-roll mill using the immersed-boundary finite-element method over a fixed Cartesian grid. The second-order projection method is used to advance the solution in time, and a structured linear-triangle element is employed for the spatial discretization. An easily implemented interpolation scheme is adopted to allow accurate imposition of
D. L. Young; C. L. Chiu; C. M. Fan
Equipartition Principle for Internal Coordinate Molecular Dynamics
The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has �kT of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordinates and includes cross-terms. Due to this coupled structure, no such equipartition principle holds for ICMD models. In this paper we introduce non-canonical modal coordinates to recover some of the structural simplicity of Cartesian models and develop a new equipartition principle for ICMD models. We derive low-order recursive computational algorithms for transforming between the modal and physical coordinates. The equipartition principle in modal coordinates provides a rigorous method for initializing velocities in ICMD simulations thus replacing the ad hoc methods used until now. It also sets the basis for calculating conformational entropy using internal coordinates.
Jain, Abhinandan; Park, In-Hee; Vaidehi, Nagarajan
Kalman Filter Techniques for Accelerated Cartesian Dynamic Cardiac Imaging
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 SNR. 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.
Feng, Xue; Salerno, Michael; Kramer, Christopher M.; Meyer, Craig H.
Frequency-offset Cartesian feedback for MRI power amplifier linearization.
High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency (RF) field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and dc offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called "frequency-offset Cartesian feedback" (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than dc, so that quadrature ghosts and dc errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system. PMID:20959264
Zanchi, Marta G; Stang, Pascal; Kerr, Adam; Pauly, John M; Scott, Greig C
On the Cartesian definition of orientational order parameters
NASA Astrophysics Data System (ADS)
Orientational order parameters can be effectively and economically defined using spherical tensors. However, their definition in terms of Cartesian tensors can sometimes provide a clearer physical intuition. We show that it is possible to build a fully Cartesian theory of the orientational order parameters which is consistent with the traditional spherical tensor approach. The key idea is to build a generalised multi-pole expansion of the orientational probability distribution function in terms of outer products of rotation matrices. Furthermore, we show that the Saupe ordering super-matrix, as found, for example, in the text by de Gennes and Prost [The Physics of Liquid Crystals, 2nd ed. (Oxford University Press, Oxford, UK, 1995)] and which is used to define the Cartesian second-rank orientational order parameters, is not consistent with its spherical tensor counterpart. We then propose a symmetric version of the Saupe super-matrix which is fully consistent with the spherical tensor definition. The proposed definition is important for a correct description of liquid crystal materials composed of low symmetry molecules.
Turzi, Stefano S.
Sensor Grid: Integration of Wireless Sensor Networks and the Grid
Wireless sensor networks have emerged as an exciting technology for a wide range of important applications that acquire and process information from the physical world. Grid computing has evolved as a standards-based approach for coordinated resource sharing. Sensor grids combine these two promising technologies by extending the grid computing paradigm to the sharing of sensor resources in wireless sensor networks.
Hock Beng Lim; Yong Meng Teo; Protik Mukherjee; Weng Fai Wong; Simon See
Black-hole excision with multiple grid patches
NASA Astrophysics Data System (ADS)
When using black-hole excision to numerically evolve a black-hole spacetime with no continuous symmetries, most 3 + 1 finite differencing codes use a Cartesian grid. It is difficult to do excision on such a grid because the natural r = constant excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth 'LEGO1 sphere' which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme which uses multiple {r � (angular coordinates)} grid patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth r = constant 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries (I use a ghost-zone scheme), the number and shape of the patches (I use a 6-patch 'inflated-cube' scheme), the details of how the ghost zones are 'synchronized' by interpolation from neighbouring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN \\tilde{\\Gamma}^i (I use a scheme which requires ghost zones which are twice as wide for the BSSN conformal factor phgr as for \\tilde{\\Gamma}^i and the other BSSN field variables). I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using fourth-order finite differencing in space and time. Using Kerr initial data with J/m2 = 0.6, I present evolutions to t gap 1500m. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme.
Thornburg, Jonathan
Anisotropic wave propagation through finite-difference grids
An algorithm is presented to solve the elastic-wave equation by replacing the partial differentials with finite differences. It enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models. The space derivatives are calculated using discrete convolution sums, while the time derivatives are replaced by a truncated Taylor expansion. A centered finite difference scheme in cartesian coordinates is used for the space derivatives leading to staggered grids. The use of finite difference approximations to the partial derivatives results in a frequency-dependent error in the group and phase velocities of waves. For anisotropic media, the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the Hook sum. This interpolation induces an additional error in the wave properties. The overall error depends on the precision of the derivative and interpolation operators, the anisotropic symmetry system, its orientation and the degree of anisotropy. The dispersion relation for the homogeneous case was derived for the proposed scheme. Since the authors use a general description of convolution sums to describe the finite difference operators, the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model. In particular, phase and group velocities of the three wave types can be determined in any direction. They demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed.
Igel, H.; Mora, P.; Riollet, B. [Institut de Physique du Globe, Paris (France). Dept. de Sismologie] [Institut de Physique du Globe, Paris (France). Dept. de Sismologie
Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in
William D. Henshaw; Donald W. Schwendeman
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in
W D Henshaw; D W Schwendeman
A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems
NASA Technical Reports Server (NTRS)
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.
Levy, R.; Mcdonald, H.; Briley, W. R.; Kreskovsky, J. P.
Parallel implementation of the Dirac equation in three Cartesian dimensions
We describe the numerical methods used to solve the time-dependent Dirac equation on a three-dimensional Cartesian lattice. Efficient algorithms are required for computationally intensive studies of vacuum-pair production in relativistic heavy-ion collisions. Discretization is achieved through the lattice-collocation method. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube, making full use of parallelism. We discuss our solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers.
Wells, J.C.; Strayer, M.R. [Oak Ridge National Lab., TN (United States); Oberacker, V.E.; Umar, A.S. [Oak Ridge National Lab., TN (United States)]|[Vanderbilt Univ., Nashville, TN (United States). Dept. of Physics and Astronomy
The Cartesian diver, surface tension and the Cheerios effect
NASA Astrophysics Data System (ADS)
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 reduced, the diver is attracted to the side of the vessel. This phenomenon is known as the �Cheerios effect�. Creation of both the repulsive and the attractive phases of the Cheerios effect is feasible by changing the external pressure of the vessel.
Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai
A Fast Sinc Function Gridding Algorithm for Fourier Inversion in Computer Tomography
The Fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the Cartesian grid required for fast numerical Fourier inversion. Although the Fourier inversion method is recognized as being computationally faster than the back-projection method for parallel ray projection data, the
J. D. O'Sullivan
Compact-range coordinate system established using a laser tracker.
Establishing a Cartesian coordinate reference system for an existing Compact Antenna Range using the parabolic reflector is presented. A SMX (Spatial Metrix Corporation) M/N 4000 laser-based coordinate measuring system established absolute coordinates for the facility. Electric field characteristics with positional movement correction are evaluated. Feed Horn relocation for alignment with the reflector axis is also described. Reference points are established for follow-on non-laser alignments utilizing a theodolite.
Gallegos, Floyd H.; Bryce, Edwin Anthony
Simulation of wave-structure interaction by hybrid Cartesian/immersed boundary and arbitrary Lagrangian-Eulerian finite-element method
NASA Astrophysics Data System (ADS)
This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.
Wu, C. S.; Young, D. L.; Chiu, C. L.
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.
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 Schr�dinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely. PMID:23679541
Van Gorder, Robert A
Minerva: Cylindrical coordinate extension for Athena
NASA Astrophysics Data System (ADS)
Minerva is a cylindrical coordinate extension of the Athena astrophysical MHD code of Stone, Gardiner, Teuben, and Hawley. The extension follows the approach of Athena's original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport (CT), a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully.
Skinner, M. Aaron; Ostriker, Eve C.
A robust unstructured grid discretization for 3-dimensional hydrostatic flows in spherical geometry: A new numerical structure for ocean general circulation modeling
Current models of the general circulation of the global oceans employ a spatial discretization of the relevant hydrodynamic fields on Cartesian rectilinear grids. For many applications, significant benefit would be expected to accrue from the versatility offered by unstructured grids. However, until very recently, available numerical methods for performing integrations on unstructured grids could not conserve discrete dynamical invariants, a
G. R. Stuhne; W. R. Peltier
An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.
NASA Technical Reports Server (NTRS)
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.
Coirier, William John
Differentiating Plasmodium falciparum alleles by transforming Cartesian X,Y data to polar coordinates
BACKGROUND: Diagnosis of infectious diseases now benefits from advancing technology to perform multiplex analysis of a growing number of variables. These advances enable simultaneous surveillance of markers characterizing species and strain complexity, mutations associated with drug susceptibility, and antigen-based polymorphisms in relation to evaluation of vaccine effectiveness. We have recently developed assays detecting single nucleotide polymorphisms (SNPs) in the P.
Jeana T DaRe; Drew P Kouri; Peter A Zimmerman; Peter J Thomas
77 FR 71169 - Smart Grid Advisory Committee Meeting
Federal Register 2010, 2011, 2012, 2013
...Institute of Standards and Technology Smart Grid Advisory Committee Meeting AGENCY...SUMMARY: The Smart Grid Advisory Committee (SGAC or Committee...cybersecurity coordination and the NIST Smart Grid Program Plan. The agenda may...
Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow
NASA Technical Reports Server (NTRS)
The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data
Berger, Marsha; Aftosmis, Michael J.
Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle
In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.
Li, Tingwen; Dietiker, Jean-Francois; Zhang, Yongmin; Shahnam, Mehrdad
Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle
In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.
Li, Tingwen; Dietiker, Jean-Francois; Zhang, Yongmin; Shahnam, Mehrdad
Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle
In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and
Tingwen Li; Jean-Fran�ois Dietiker; Yongmin Zhang; Mehrdad Shahnam
Features in Continuous Parallel Coordinates.
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. PMID:22034308
Lehmann, Dirk J; Theisel, Holger
A kinetic scheme for gas dynamics on arbitrary grids
NASA Astrophysics Data System (ADS)
Cartesian meshes for domains with complicated boundaries give rise to cut cells with arbitrarily small volumes. Explicit integration schemes over such meshes have a time step restriction proportional to the smallest cell volume. This thesis gives an extension of the kinetic scheme for gas dynamics by Perthame [SIAM J. Num. Anal., 27:1305--1421] on arbitrary Cartesian meshes. The formulation allows a time step based only on the underlying regular cell size, and retains L1 -stability, positivity and second order convergence. Numerical convergence studies on irregular grids in one and two space dimensions are presented.
Keen, Benjamin James
Cartesian Impedance Control Techniques for Torque Controlled LightWeight Robots
The paper compares various approaches to imple- menting a compliant Cartesian behavior for robotic manipulators: impedance, admittance and stifiness control. A new controller structure is proposed, which consists of an impedance controller enhanced by lo- cal stifiness control. This structure consistently takes into account the two time scale property of the joint and Cartesian control loops. The DLR light-weight robot,
Alin Albu-sch�ffer; Gerd Hirzinger
Calculation of Rigid-Body Conformational Changes Using Restraint-Driven Cartesian Transformations
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
Pornthep Sompornpisut; Yi-Shiuan Liu; Eduardo Perozo
Open-Loop Digital Predistortion Using Cartesian Feedback for Adaptive RF Power Amplifier Linearization
We present a new adaptive power amplifier (PA) linearization technique. We leverage analog Cartesian feedback (CFB) to train a Cartesian look-up table, reducing DSP and power amplifier modeling requirements to a minimum and eliminating model convergence as a design issue. Because the CFB system does not continuously operate, we overcome the bandwidth limitation traditionally associated with this technique. In addition,
SungWon Chung; Jack W. Holloway; Joel L. Dawson
Direct adaptive control of manipulators in Cartesian space
NASA Technical Reports Server (NTRS)
A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.
Seraji, H.
Multi-fault Tolerance for Cartesian Data Distributions
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale sys- tems. Algorithm-based fault tolerance (ABFT) is a promising approach that involves modications to the algorithm to recover from faults with lower over- heads than replicated storage and a signicant reduction in lost work compared to checkpoint-restart techniques. Fault-tolerant linear algebra (FTLA) algo- rithms employ additional processors that store parities along the dimensions of a matrix to tolerate multiple, simultaneous faults. Existing approaches as- sume regular data distributions (blocked or block-cyclic) with the failures of each data block being independent. To match the characteristics of failures on parallel computers, we extend these approaches to mapping parity blocks in several important ways. First, we handle parity computation for generalized Cartesian data distributions with each processor holding arbitrary subsets of blocks in a Cartesian-distributed array. Second, techniques to handle corre- lated failures, i.e., multiple processors that can be expected to fail together, are presented. Third, we handle the colocation of parity blocks with the data blocks and do not require them to be on additional processors. Several al- ternative approaches, based on graph matching, are presented that attempt to balance the memory overhead on processors while guaranteeing the same fault tolerance properties as existing approaches that assume independent fail- ures on regular blocked data distributions. The evaluation of these algorithms demonstrates that the additional desirable properties are provided by the pro- posed approach with minimal overhead.
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
A comparison of coordinate systems for use in determining a radiotherapy delineation margin for whole breast
NASA Astrophysics Data System (ADS)
Cartesian co-ordinates, traditionally used for radiotherapy margins, calculated at 6 points, may not adequately represent changes in inter-observer contour variation as necessary to define a delineation margin. As a first step, this study compared the standard deviation (SD) in contour delineation using Polar and Cartesian co-ordinates for whole breast. Whole breast Clinical Target Volumes (CTV) were delineated by eight observers for 9 patients. The SD of contour position was determined for Polar co-ordinates at 1� increments for 5 slices and averaged across all patients. The mean centre of mass (COM) was used as the origin for the right breast, for the left the COM was shifted 1cm superiorly to avoid clipping. The SD was determined for Cartesian co-ordinates for medial-lateral and anterior-posterior positions. At slice Z=0cm considering Polar co-ordinates, the SD peaked medially reaching 3.55cm at 15� for the right breast, and 1.44cm at 171� for the left. The SD of the remaining slices maintained a similar distribution, with variation in the peak occurring within 10� of the Z=0cm positions. By comparison, for Cartesian co-ordinates at slice Z=0cm, the largest SD in the medial-lateral and anterior-posterior directions was 0.54/0.57cm and 1.03/0.67cm respectively for right/left breasts. The SD for inter-observer variation for whole breast varies with anatomical position. The maximum SD determined with Polar co-ordinates was greater than with Cartesian coordinates. A delineation margin may thus need to vary with angle over the entire structure and Cartesian co-ordinates may not be the best approach for margin determination for whole breast.
Pogson, E. M.; Bell, L.; Batumalai, V.; Koh, E. S.; Delaney, G.; Metcalfe, P.; Holloway, L.
Grid Computing and Applications
'Grid' computing has emerged as an important new field, distinguished from conventional distributed computing by its focus on large-scale resource sharing, innovative applications, and, in some cases, high-performance orientation. In this talk, Dr. Foster defines this new field. First, he reviews the 'Grid problem,' which he defines as flexible, secure, coordinated resource sharing among dynamic collections of individuals, institutions, and resources - what he refers to as virtual organizations. In such settings, we encounter unique authentication, resource access, resource discovery, and other challenges. It is this class of problem that is addressed by Grid technologies. He presents an extensible and open Grid architecture, in which protocols, services, application programming interfaces, and software development kits are categorized according to their roles in enabling resource sharing. He also reviews major Grid projects worldwide and describes how they are contributing to the realization of this architecture.
Accurate Computation of Zernike Moments in Polar Coordinates
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
Yongqing Xin; Miroslaw Pawlak; Simon X. Liao
Orbital Stability for Rotating Planar Vortex Filaments in the Cartesian and Arclength Forms of the Local Induction Approximation
NASA Astrophysics Data System (ADS)
The local induction approximation (LIA) is commonly used to study the motion of a vortex filament in a fluid. The fully nonlinear form of the LIA is equivalent to a type of derivative nonlinear Schr�dinger (NLS) equation, and stationary solutions of this equation correspond to rotating planar vortex filaments. Such solutions were first discussed in the plane by Hasimoto [J. Phys. Soc. Jpn. 31 (1971) 293], and have been described both in Cartesian three-space and in the arclength formulation in subsequent works. Despite their interest, fully analytical stability results have been elusive. In the present paper, we present elegant and simple proofs of the orbital stability for the stationary solutions to the derivative nonlinear Schr�dinger equations governing the self-induced motion of a vortex filament under the LIA, in both the extrinsic (Cartesian) and intrinsic (arclength) coordinate representations. Such results constitute an exact criterion for the orbital stability of rotating planar vortex filament solutions for the vortex filament problem under the LIA.
Van Gorder, Robert A.
A Cartesian classical second-quantized many-electron Hamiltonian, for use with the semiclassical initial value representation
NASA Astrophysics Data System (ADS)
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).
Li, Bin; Miller, William H.
Verification and validation of the Spalart-Allmaras turbulence model for strand grids
NASA Astrophysics Data System (ADS)
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 preconditioning to the solver in the future may increase the accuracy of the solution.
Tong, Oisin
Validation of a new grid-based Boltzmann equation solver for dose calculation in radiotherapy with photon beams
A new grid-based Boltzmann equation solver, Acuros�, was developed specifically for performing accurate and rapid radiotherapy dose calculations. In this study we benchmarked its performance against Monte Carlo for 6 and 18 MV photon beams in heterogeneous media. Acuros solves the coupled Boltzmann transport equations for neutral and charged particles on a locally adaptive Cartesian grid. The Acuros solver is
Oleg N. Vassiliev; Todd A. Wareing; John McGhee; Gregory Failla; Mohammad R. Salehpour; Firas Mourtada
The Overgrid Interface for Computational Simulations on Overset Grids
NASA Technical Reports Server (NTRS)
Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.
Chan, William M.; Kwak, Dochan (Technical Monitor)
Iterative reconstruction method for three-dimensional non-cartesian parallel MRI
NASA Astrophysics Data System (ADS)
Parallel magnetic resonance imaging (MRI) with non-Cartesian sampling pattern is a promising technique that increases the scan speed using multiple receiver coils with reduced samples. However, reconstruction is challenging due to the increased complexity. Three reconstruction methods were evaluated: gridding, blocked uniform resampling (BURS) and non-uniform FFT (NUFFT). Computer simulations of parallel reconstruction were performed. Root mean square error (RMSE) of the reconstructed images to the simulated phantom were used as image quality criterion. Gridding method showed best RMSE performance. Two type of a priori constraints to reduce noise and artifacts were evaluated: edge preserving penalty, which suppresses noise and aliasing artifact in image while preventing over-smoothness, and object support penalty, which reduces background noise amplification. A trust region based step-ratio method that iteratively calculates the penalty coefficient was proposed for the penalty functions. Two methods to alleviate computation burden were evaluated: smaller over sampling ratio, and interpolation coefficient matrix compression. The performance were individually tested using computer simulations. Edge preserving penalty and object support penalty were shown to have consistent improvement on RMSE. The performance of calculated penalty coefficients on the two penalties were close to the best RMSE. Oversampling ratio as low as 1.125 was shown to have impact of less than one percent on RMSE for the radial sampling pattern reconstruction. The value reduced the three dimensional data requirement to less than 1/5 of what the conventional 2x grid needed. Interpolation matrix compression with compression ratio up to 50 percent showed small impact on RMSE. The proposed method was validated on 25MR data set from a GEMR scanner. Six image quality metrics were used to evaluate the performance. RMSE, normalized mutual information (NMI) and joint entropy (JE) relative to a reference image from a separate body coil scan were used to verify the fidelity of reconstruction to the reference. Region of interest (ROI) signal to noise ratio (SNR), two-data SNR and background noise were used to validate the quality of the reconstruction. The proposed method showed higher ROI SNR, two-data SNR, and lower background noise over conventional method with comparable RMSE, NMI and JE to the reference image at reduced computer resource requirement.
Jiang, Xuguang
Accessibility Analysis for Planning of Dimensional Inspection with Coordinate Measuring Machines
Abstract Quality and process control activities in a mechanical product's life cycle require that components be measured, or dimensionally inspected. Computer-controlled dimensional inspection is typically performed with Coordinate Measuring Machines (CMMs), which are very precise Carte-sian robots that use touch probes to measure the coordinates of points on a workpiece's surfaces. Automatic planning and programming of inspection tasks with a
S. n. Spitz; A. j. Spyridi; A. g. Requicha
Accessibility analysis for planning of dimensional inspection with coordinate measuring machines
Computer-controlled dimensional inspection is typically performed with coordinate measuring machines (CMMs), which are very precise Cartesian robots that use touch probes to measure the coordinates of points on a workpiece's surfaces. Automatic planning and programming of inspection tasks with a CMM involve spatial reasoning, to determine how to orient the part on the CMM, which probes to use, how to
Steven N. Spitz; Antonia J. Spyridi; Aristides A. G. Requicha
A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition
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.
Sidler, Rolf, E-mail: firstname.lastname@example.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)] [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, Jos� M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy)] [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)] [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)
A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition
NASA Astrophysics Data System (ADS)
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.
Sidler, Rolf; Carcione, Jos� M.; Holliger, Klaus
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.
Kaul, Upender K.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 � 106 spatial cells and 1 � 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Pon�ot, Ang�lique; Ramet, Pierre
An Efficient Means of Adaptive Refinement Within Systems of Overset Grids
NASA Technical Reports Server (NTRS)
An efficient means of adaptive refinement within systems of overset grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend only a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian grids of varying levels of refinement. a novel off-body grid generation and management scheme provides the mechanism for carrying out adaptive refinement of off-body flow dynamics and solid body motion. The scheme allows for very efficient use of memory resources, and flow solvers and domain connectivity routines that can exploit the structure inherent to uniform Cartesian grids.
Meakin, Robert L.
A Hybrid Solar Wind Model of the CESE+HLL Method with a Yin-Yang Overset Grid and an AMR Grid
NASA Astrophysics Data System (ADS)
A hybrid three-dimensional (3D) MHD model for solar wind study is proposed in the present paper with combined grid systems and solvers. The computational domain from the Sun to Earth space is decomposed into the near-Sun and off-Sun domains, which are respectively constructed with a Yin-Yang overset grid system and a Cartesian adaptive mesh refinement (AMR) grid system and coupled with a domain connection interface in the overlapping region between the near-Sun and off-Sun domains. The space-time conservation element and solution element method is used in the near-Sun domain, while the Harten-Lax-Leer method is employed in the off-Sun domain. The Yin-Yang overset grid can avoid well-known singularity and polar grid convergence problems and its body-fitting property helps achieve high-quality resolution near the solar surface. The block structured AMR Cartesian grid can automatically capture far-field plasma flow features, such as heliospheric current sheets and shock waves, and at the same time, it can save significant computational resources compared to the uniformly structured Cartesian grid. A numerical study of the solar wind structure for Carrington rotation 2069 shows that the newly developed hybrid MHD solar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by comparisons with multiple solar and interplanetary observations.
Feng, Xueshang; Zhang, Shaohua; Xiang, Changqing; Yang, Liping; Jiang, Chaowei; Wu, S. T.
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Liu, Yen; Vinokur, Marcel
Constructing the ASCI computational grid
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.
A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: part I--theoretical formulation.
In this paper, we present a versatile mathematical formulation of a newly developed 3-D locally conformal Finite Difference (FD) thermal algorithm developed specificallyfor coupled electromagnetic (EM) and heat diffusion simulations utilizing Overlapping Grids (OGFD) in the Cartesian and cylindrical coordinate systems. The motivation for this research arises from an attempt to characterize the dominant thermal transport phenomena typically encountered during the process cycle of a high-power, microwave-assisted material processing system employing a geometrically composite cylindrical multimode heating furnace. The cylindrical FD scheme is only applied to the outer shell of the housing cavity whereas the Cartesian FD scheme is used to advance the temperature elsewhere including top and bottom walls, and most of the inner region of the cavity volume. The temperature dependency of the EM constitutive and thermo-physical parameters of the material being processed is readily accommodated into the OGFD update equations. The time increment, which satisfies the stability constraint of the explicit OGFD time-marching scheme, is derived. In a departure from prior work, the salient features of the proposed algorithm are first, the locally conformal discretization scheme accurately describes the diffusion of heat and second, significant heat-loss mechanisms usually encountered in microwave heating problems at the interfacial boundary temperature nodes have been considered. These include convection and radiation between the surface of the workload and air inside the cavity, heat convection and radiation between the inner cavity walls and interior cavity volume, and free cooling of the outermost cavity walls. PMID:16673831
Al-Rizzo, Hussain M; Tranquilla, Jim M; Feng, Ma
Tracking algorithms using log-polar mapped image coordinates
NASA Technical Reports Server (NTRS)
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.
Weiman, Carl F. R.; Juday, Richard D.
TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide
NASA Technical Reports Server (NTRS)
A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.
Miller, David P.
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
NASA Astrophysics Data System (ADS)
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.
Mignone, A.
Multiscale geometric modeling of macromolecules I: Cartesian representation
NASA Astrophysics Data System (ADS)
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites.
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
NASA Technical Reports Server (NTRS)
Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.
Seki, Rycichi
Basic equations of horizontal two dimensional debris flow analysis in general coordinate system
NASA Astrophysics Data System (ADS)
Horizontal two dimensional debris flow models are developed by many researchers and all of those equations are written in Cartesian coordinate system. Basic equations in Cartesian coordinate system are simple and are easy to be used. However, numerical frictions are happened at the side edges of the debris flow when the channel geometry is not a straight channel. We can find many meandering channels in mountainous rivers and, in general, width-depth ration is smaller in the mountainous rivers. Hence, the numerical frictions at the side edge of the debris affect on the flow characteristics of debris flow very well and basic equations in the boundary fitted coordinate system can reduce the numerical friction at the side edge of the debris flow in meandering channels. In this study, basic equations of horizontal two dimensional debris flow analysis are written in general coordinate system and simulate the debris flow in the meandering channels by use of the basic equations of horizontal two dimensional debris flow analysis in general coordinate system. Furthermore, the debris flow in the meandering channels is simulated by use of the basic equations in Cartesian coordinate system and the difference of the flow velocity and flow depth between them discussed. Results show that the depth and the velocity of the debris flow simulated by use of the basic equations in general coordinate system is smaller and faster than those by use of the basic equations in Cartesian coordinate system, respectively. Underestimation of the flow velocity indicates that the underestimation of fluid power of debris flow on the river structures, houses and son. Furthermore, the escape time of people tends to be overestimated, when the basic equations in Cartesian coordinate system are used.
Takebayashi, Hiroshi; Fujita, Masaharu
Visual analytics for power grid contingency analysis.
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. PMID:24808167
Pak Chung Wong; Zhenyu Huang; Yousu Chen; Mackey, Patrick; Shuangshuang Jin
Simulation of disk-disk encounters with co-moving polar grids
NASA Technical Reports Server (NTRS)
The two-grid simulation method combining advantages of both polar and Cartesian mesh-codes is described. In addition to the stellar component reacting solely to gravitational forces, the gas component is included with dissipatively colliding particles. This allows fairly realistic simulation of planar encounters where both systems contain star plus gas disks.
Salo, Heikki
PSG: Peer-to-Peer semantic grid framework architecture
The grid vision, of sharing diverse resources in a flexible, coordinated and secure manner, strongly depends on metadata. Currently, grid metadata is generated and used in an ad-hoc fashion, much of it buried in the grid middleware code libraries and database schemas. This ad-hoc expression and use of metadata causes chronic dependency on human intervention during the operation of grid
Amira Soliman; Amr Kamel; Walaa Sheta; Reem Bahgat
NSDL National Science Digital Library
Become familiar with the coordinate plane. Learn the quadrants and how to graph points and read points on a coordinate plane. You are required to do the assignment and take the quiz. The other resources are to help prepare you for the quiz and book assignment. This is a quick review of the lesson.The Coordinate Plane This is a game to practice plotting and reading points.coordinates game *Assignment: Watch Powerpoint 3.3 and fill in your ...
NASA Astrophysics Data System (ADS)
Chapter 5 describes formulas for general unidirectional transfinite interpolations. Multidirectional interpolation is defined by Boolean summation of unidirectional interpolations. Examples of various types of blending function are reviewed, in particular, the functions defined through the basic stretching coordinate transformations for singular layers described in Chap. 4. The chapter ends with a description of a procedure for generating triangular, tetrahedral, or prismatic grids through the method of transfinite interpolation.
Liseikin, Vladimir D.
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
NASA Technical Reports Server (NTRS)
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.
Coirier, William J.; Powell, Kenneth G.
In this introductory chapter, we lay the groundwork for the rest of the book by providing a more detailed picture of the expected\\u000a purpose, shape, and architecture of future grid systems. We structure the chapter in terms of six questions that we believe\\u000a are central to this discussion: Why do we need computational grids? What types of applications will grids
Ian T. Foster; Carl Kesselman
NSDL National Science Digital Library
The Equatorial Coordinates model displays the position of a star in equatorial (Right Ascension/Declination --- RA/Dec) coordinates. The horizon is shown along with the four cardinal directions (N, E, S, and W). The Latitude slider changes the latitude of the observer which is shown by the change in the (teal) celestial pole relative to the northern horizon. The position of the star can be changed by using the Right Ascension and Declination sliders. Once these coordinates are selected, pressing the play button will put the star, celestial grid, and the equatorial coordinates in motion to simulate the 23 hour and 56 minute motion of stars in the night sky. Equatorial Coordinates model is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_astronomy_EquatorialCoordinates.jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the plot and selecting "Open EJS Model" from the pop-up menu item.
Belloni, Mario; Timberlake, Todd
Random subspaces for encryption based on a private shared Cartesian frame
A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities.
Bartlett, Stephen D. [School of Physics, University of Sydney, New South Wales 2006 (Australia); Hayden, Patrick [School of Computer Science, McGill University, Montreal (Canada); Spekkens, Robert W. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada)
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.
Brislawn, K.; Brown, D.; Chesshire, G.; Henshaw, W. [and others
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen�s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries
NASA Astrophysics Data System (ADS)
An immersed boundary methodology to solve the compressible Navier-Stokes equations around complex geometries in Cartesian fluid dynamics solvers is described. The objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts. A standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended. Boundary conditions on the surface are enforced by an approach inspired by analytic continuation. Each fluid field is extended independently, constrained only by the boundary condition associated with that field. Unlike most existing methods, no jump conditions or explicit derivation of them from the boundary conditions are required in this approach. Numerical stiffness that arises when the fluid-solid interface is close to grid points of the mesh is addressed by preconditioning. In addition, the embedded geometry technique is coupled with a stable high-order adaptive discretization that is enabled around the object boundary to enhance resolution. The stencils used to transition the order of accuracy of the discretization are derived using the summation-by-parts technique that ensures stability. Applications to shock reflections, shock-ramp interactions, and supersonic and low-Mach number flows over two- and three-dimensional geometries are presented.
Uddin, H.; Kramer, R. M. J.; Pantano, C.
Structure sensitive normal coordinate analysis of metal-diethyldithiocarbamate - complexes
NASA Astrophysics Data System (ADS)
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.
Mikosch, H.; Bauer, G.; Kellner, R.; Trendafilova, N. S.; St. Nikolov, G.
ERIC Educational Resources Information Center
Proposes that narrow columns provide a flexible system of organization for designers. Notes that grids serve the content on the pages, help to develop a layout that will clearly direct the reader to information; and prevent visual monotony. Concludes when grid layouts are used, school publications look as good as professional ones. (PM)
Barrington, Linda; Carter, Jacky
Comparability of Cartesian Diver, Gilson, Warburg and Winkler methods of measuring the respiratory rates of aquatic invertebrates in ecological studies
Comparison of Cartesian Diver-Winkler measurements of respiratory rates in larvae of the damselfly Pyrrhosoma nymphula, and Cartesian Diver-Gilson comparisons in the snail Potamopyrgus jenkinsi are descibed. Measurements of oxygen uptake using these different methods do not differ significantly for the same species of animal at the same temperature. Published data likewise suggest that Warburg and Winkler measurements can give similar
J. H. Lawton; J. Richards
A method for the prediction of transonic flutter by the Euler equations on a Cartesian mesh is presented. Surface boundary conditions are applied using a perturbation of a gridless treatment in such a manner that solutions are obtained on a stationary mesh. For steady problems, the gridless method applies surface boundary conditions using a weighted average of the flow properties
D. J. Kirshman; F. Liu
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
ERIC Educational Resources Information Center
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of�
Lelwica, Michelle Mary
Relative end-effector control using Cartesian position based visual servoing
This paper presents a complete design methodology for Cartesian position based visual servo control for robots with a single camera mounted at the end-effector. Position based visual servo control requires the explicit calculation of the relative position and orientation (POSE) of the workpiece object with respect to the camera. This is accomplished using image plane measurements of a number of
William J. Wilson; Carol C. Williams Hulls; Graham S. Bell
Cartesian Meshing Impacts for PWR Assemblies in Multigroup Monte Carlo and Sn Transport
NASA Astrophysics Data System (ADS)
Hybrid methods of neutron transport have increased greatly in use, for example, in applications of using both Monte Carlo and deterministic transport to calculate quantities of interest, such as flux and eigenvalue in a nuclear reactor. Many 3D parallel Sn codes apply a Cartesian mesh, and thus for nuclear reactors the representation of curved fuels (cylinder, sphere, etc.) are impacted in the representation of proper fuel inventory (both in deviation of mass and exact geometry representation). For a PWR assembly eigenvalue problem, we explore the errors associated with this Cartesian discrete mesh representation, and perform an analysis to calculate a slope parameter that relates the pcm to the percent areal/volumetric deviation (areal corresponds to 2D and volumetric to 3D, respectively). Our initial analysis demonstrates a linear relationship between pcm change and areal/volumetric deviation using Multigroup MCNP on a PWR assembly compared to a reference exact combinatorial MCNP geometry calculation. For the same multigroup problems, we also intend to characterize this linear relationship in discrete ordinates (3D PENTRAN) and discuss issues related to transport cross-comparison. In addition, we discuss auto-conversion techniques with our 3D Cartesian mesh generation tools to allow for full generation of MCNP5 inputs (Cartesian mesh and Multigroup XS) from a basis PENTRAN Sn model.
Manalo, K.; Chin, M.; Sjoden, G.
Investigating the Effects of Density and Volume of a Cartesian Diver
NSDL National Science Digital Library
This activity is an inquiry investigation where students gather data on why the Cartesian diver sinks or floats. They then develop a new question and then conduct a new investigation by changing one variable and repeat the altered experiment and record their conclusions.
Lee Anne Garhofer Ames Elementary School St. Paul, MN 55106
Development of a New Two-Dimensional Cartesian Geometry Nodal Multigroup Discrete-Ordinates Method.
National Technical Information Service (NTIS)
The purpose of this work is the development and testing of a new family of methods for calculating the spatial dependence of the neutron density in nuclear systems described in two-dimensional Cartesian geometry. The energy and angular dependence of the n...
R. E. Pevey
A mixed volume grid approach for the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
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.
Coirier, William J.; Jorgenson, Philip C. E.
C[squared] = Creative Coordinates
ERIC Educational Resources Information Center
"C[squared] = Creative Coordinates" is an engaging group of tasks that fosters the integration of mathematics and art to create meaningful understanding. The project lets students illustrate of find an image, then plot points to map their design on a grid. The project usually takes about a week to complete. When it is finished, students who are�
McHugh, Shelley R.
Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian�Eulerian hydrodynamics in 2D rz � Cylindrical coordinates
NASA Astrophysics Data System (ADS)
We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its �Cartesian� form with a special definition of �planar� masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of �planar� subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.
Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail
Numerical solution of the full potential equation using a chimera grid approach
NASA Technical Reports Server (NTRS)
A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.
Holst, Terry L.
An assessment of unstructured grid technology for timely CFD analysis
NASA Technical Reports Server (NTRS)
An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.
Kinard, Tom A.; Schabowski, Deanne M.
The National Grid Project: A system overview
NASA Technical Reports Server (NTRS)
The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.
Gaither, Adam; Gaither, Kelly; Jean, Brian; Remotigue, Michael; Whitmire, John; Soni, Bharat; Thompson, Joe; Dannenhoffer,, John; Weatherill, Nigel
Thin Wire Modeling for FDTD Electromagnetic Calculations in the Two-Dimensional Cylindrical Coordinate System
NASA Astrophysics Data System (ADS)
In this paper, the equivalent radius of a thin wire represented using the FDTD method in the two-dimensional (2D) cylindrical coordinate system is identified as 0.135?r, where ?r is the lateral side length of the rectangular cells, while that of a thin wire represented in the 3D Cartesian coordinate system is known to be 0.230?r. Furthermore, it is shown that the technique proposed by Noda and Yokoyama to represent a thin wire having an arbitrary radius in the 3D Cartesian coordinate system can be applied successfully to representing such a thin wire in the 2D cylindrical coordinate system if 0.135?r is used for the equivalent radius instead of 0.230?r.
Taniguchi, Yohei; Baba, Yoshihiro; Nagaoka, Naoto; Ametani, Akihiro
The ``best approximation'' of Planetary Ephemeris: Comparison between different coordinate systems
NASA Astrophysics Data System (ADS)
Our goal is to supply users with fast evaluation of Planetary Ephemeris maintaining the same precision of the Efemerides Astronomicas and The Astronomical Almanac. Both almanacs are constructed using the Jet Propulsion Laboratory data base DE200/LE200. Fast evaluation is provided by using polynomial approximations. In order to ensure the desired boundary for the error we compute the ``best approximation'' in the Chebyshev sense. In this work we compute polynomial approximations to the ephemeris of solar system bodies in different coordinate systems, namely: cartesian coordinates, instantaneous orbital elements and equatorial coordinates. For the Moon we found that be st results are reached when using cartesian coordinates: with polynomials of degree 29 valid for 31 days we get the same precision as ``Daily Polynomials for Right Ascension, Declination and Horizontal Parallax'', included in Efemerides Astronomicas and The Astronomical Almanac. We also present results for other bodies, where much better compression is reached.
Coma, J. C.; Lara, M.; Lopez-Moratalla, T. J.
Trajectory Coordinate Constraints in Multibody Railroad Vehicle Systems
NASA Astrophysics Data System (ADS)
In this investigation, the formulation of trajectory coordinate constraints in terms of the absolute coordinates is developed for the use in the computer simulations of railroad vehicle system applications. Examples of trajectory coordinate constraints are the specified forward velocity of a vehicle or a wheelset along a curved track or specified yaw angle of a vehicle or a wheelset with respect to a body trajectory coordinate system. The relationship between the trajectory coordinates and the absolute coordinates is defined and then used to write the trajectory constraints in terms of the absolute coordinates at the position, velocity, and acceleration levels. The motion of the trajectory coordinate system can be uniquely defined in the track body coordinate system using the arc-length coordinate defined along the space curve. It is demonstrated that the use of the trajectory coordinates leads to simple linear constraint equations, while the trajectory constraint equations become highly nonlinear functions of the absolute coordinates. This is mainly due to the nature of the nonlinear relationship between the absolute Cartesian and trajectory coordinates. A numerical example is presented in order to demonstrate the use of the proposed formulations in the analysis of multibody railroad vehicle systems.
Sugiyama, Hiroyuki; Shabana, Ahmed A.
NASA Technical Reports Server (NTRS)
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.
Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.
Unstructured Grid Generation Techniques and Software
NASA Technical Reports Server (NTRS)
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.
Posenau, Mary-Anne K. (editor)
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 formulae for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudo-harmonic (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. PMID:22508904
Li, Xian-Ying; Hu, Shi-Min
Information services for smart grids
Interconnected and integrated electrical power systems, by their very dynamic nature are complex. These multifaceted systems are subject to a host of challenges - aging infrastructure, generation availability near load centers, transmission expansion to meet growing demands, distributed resources, dynamic reactive compensation, congestion management, grid ownership vs. system operation, reliability coordination, supply and cost of natural resources for generation, etc.
Roger L. King
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.
Flach, G.; Smith, F.
NSDL National Science Digital Library
The celestial coordinate system is a projection of earth's coordinate system into the celestial sphere. Being just like Earth's system it contains an "equator", lines of "latitude" and "longitude", and even poles. (Though we don't use the same words for it.) One suggestion one might have would be to just extend the Earth's latitude, longitude, and equator out into the night sky, but the Earth is constantly spinning. For the Celestial coordinates, we have to pick some fixed reference to go by.
Joiner, David; The Shodor Education Foundation, Inc.
Easing The Calculation Of Bolt-Circle Coordinates
NASA Technical Reports Server (NTRS)
Bolt Circle Calculation (BOLT-CALC) computer program used to reduce significant time consumed in manually computing trigonometry of rectangular Cartesian coordinates of holes in bolt circle as shown on blueprint or drawing. Eliminates risk of computational errors, particularly in cases involving many holes or in cases in which coordinates expressed to many significant digits. Program assists in many practical situations arising in machine shops. Written in BASIC. Also successfully compiled and implemented by use of Microsoft's QuickBasic v4.0.
Burley, Richard K.
NSDL National Science Digital Library
This interactive Java applet lets users explore the coordinate plane through the use of a Geoboard. The user places bands on the board where each peg is at an integer coordinate. Once a band has been placed, the applet outputs the perimeter and area of the shape or, if bands are placed as line segments, the applet outputs the distance and slope of the segment.
Solving Partial Differential Equations on Overlapping Grids
We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solution of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.
Henshaw, W D
Coordinated Checkpointing Without Direct Coordination.
National Technical Information Service (NTIS)
Coordinated checkpointing is a well known method to achieve fault tolerance in distributed systems. Long running parallel applications and high availability applications are two potential users of checkpointing, although with different requirements. Paral...
N. Neves W. K. Fuchs
Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors
NASA Astrophysics Data System (ADS)
The relativistic time-dependent multipole expansion for electromagnetism and linearized gravity in the region outside a spatially compact source has been obtained directly using the formalism of irreducible Cartesian (i.e., symmetric trace-free) tensors. In the electromagnetic case, our results confirm the validity of the results obtained earlier by Campbell, Macek, and Morgan using the Debye potential formalism. However, in the more complicated linearized gravity case, the greater algebraic transparence of the Cartesian multipole approach has allowed us to obtain, for the first time, fully correct closed-form expressions for the time-dependent mass and spin multipole moments (the results of Campbell et al. for the mass moments turning out to be incorrect). The first two terms in the slow-motion expansion of the gravitational moments are explicitly calculated and shown to be equivalent to earlier results by Thorne and by Blanchet and Damour.
Damour, T.; Iyer, B. R.
Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction
NASA Astrophysics Data System (ADS)
The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when multidimensional datasets are involved. The main focus of this work is to design an NUFFT algorithm with minimal memory demands. Specifically, we introduce an analytical expression for the expected mean square error in the NUFFT approximation based on our earlier work. We then introduce an iterative algorithm to design the interpolator and scale factors. Experimental comparisons show that the proposed optimized NUFFT scheme provides considerably lower approximation errors than the previous designs [1] that rely on worst case error metrics. The improved approximations are also seen to considerably reduce the errors and artifacts in non-Cartesian MRI reconstruction.
Yang, Zhili; Jacob, Mathews
Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction.
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. PMID:24637054
Yang, Zhili; Jacob, Mathews
Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry
NASA Technical Reports Server (NTRS)
The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design
NASA Technical Reports Server (NTRS)
Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors
The relativistic time-dependent multipole expansion for electromagnetism and linearized gravity in the region outside a spatially compact source has been obtained directly using the formalism of irreducible Cartesian (i.e., symmetric trace-free) tensors. In the electromagnetic case, our results confirm the validity of the results obtained earlier by Campbell, Macek, and Morgan using the Debye potential formalism. However, in the more complicated linearized gravity case, the greater algebraic transparence of the Cartesian multipole approach has allowed us to obtain, for the first time, fully correct closed-form expressions for the time-dependent mass and spin multipole moments (the results of Campbell {ital et} {ital al}. for the mass moments turning out to be incorrect). The first two terms in the slow-motion expansion of the gravitational moments are explicitly calculated and shown to be equivalent to earlier results by Thorne and by Blanchet and Damour.
Damour, T.; Iyer, B.R. (Institut des Hautes Etudes Scientifiques 91440 Bures sur Yvette, France Departement d'Astrophysique Relativiste et de Cosmologie, Centre National de la Recherche Scientifique-Observatoire de Paris, 92195 Meudon CEDEX, France (FR))
Electric vehicle requirements for operation in smart grids
Several European projects on smart grids are considering Electric Vehicles (EVs) as active element in future power systems. Both battery-powered vehicles and plug-in hybrid vehicles are expected to interact with the grid, sharing their energy storage capacity. Different coordination concepts for EVs are being investigated, in which vehicles can be intelligently charged or discharged feeding power back to the grid
Francesco Marra; Dario Sacchetti; Chresten Traeholt; Esben Larsen
Interactive grid generation program for CAP-TSD
NASA Technical Reports Server (NTRS)
A grid generation program for use with the CAP-TSD transonic small disturbance code is described. The program runs interactively in FORTRAN on the Sun Workstation. A fifth-degree polynomial is used to map the grid index onto the computational coordinate. The grid is plotted to aid in the assessment of its quality and may be saved on file in NAMELIST format.
Bland, Samuel R.
Plasticity of intermediate mechanics students� coordinate system choice
NSDL National Science Digital Library
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.
Sayre, Eleanor C.; Wittmann, Michael C.
Grid systems for Earth radiation budget experiment applications
NASA Technical Reports Server (NTRS)
Spatial coordinate transformations are developed for several global grid systems of interest to the Earth Radiation Budget Experiment. The grid boxes are defined in terms of a regional identifier and longitude-latitude indexes. The transformations associate longitude with a particular grid box. The reverse transformations identify the center location of a given grid box. Transformations are given to relate the rotating (Earth-based) grid systems to solar position expressed in an inertial (nonrotating) coordinate system. The FORTRAN implementations of the transformations are given, along with sample input and output.
Brooks, D. R.
NSDL National Science Digital Library
With this interactive Shockwave applet students practice recognizing various types of numbers, including factors, multiples, and prime numbers. Each level presents several grids of numbers, each with a specific rule. Users select all numbers in the grid that satisfy the rule. Level 1 involves parity (odd/even) and multiplication facts of 2, 3, 4, 5 and 10. Level 2 includes multiplication facts up to 10 x 10, primes, and square numbers. Level 3 also covers powers of 2, triangle numbers less than 100, and lower cube numbers. A Key Ideas window explains each type of number. Cross Number puzzle printouts are available for further practice.
Measurement of guard-cell respiration rates using Cartesian-diver technique
Dark respiration rates of guard-cell protoplasts of Commelina communis L. were measured over a temperature range (15�30� C) using a Cartesian-diver microrespirometry technique. Measurements were made using a few microliters of suspension medium containing between 400 and 3 700 protoplasts. Respiration rates were approximately linear for at least 1 h at all temperatures. Respiration rates increased rapidly between 20 and
K. Birkenhead; J. Laybourn-Parry; C. Willmer
Nonlinear response of a flexible Cartesian manipulator with�payload and pulsating axial force
In this present work, the nonlinear response of a single-link flexible Cartesian manipulator with payload subjected to a pulsating\\u000a axial load is determined. The nonlinear temporal equation of motion is derived using D�Alembert�s principle and generalised\\u000a Galerkin�s method. Due to large transverse deflection of the manipulator, the equation of motion contains cubic geometric\\u000a and inertial types of nonlinearities along with
Barun Pratiher; Santosha Kumar Dwivedy
A methodology for Cartesian braiding of three-dimensional shapes and special structures
Cartesian three-dimensional braiding as a method of preforming has been investigated. The design of complex and unusual 3-D braids was studied in three parts. These are the grouping of yarns, the fabrication of braids with a complex cross-section, and braids with surrogate material (replacing fibrous tows) added or removed. The grouping of yarns to potentially form hybrid composites was studied
T. D. Kostar; Tsu-Wei Chou
�Mens Sana in Corpore Sano�: Cartesian dualism and the marginalisation of sex education
Cartesian dualism has left a heavy legacy in terms of how we think about ourselves, so that we treat humans as minds within bodies rather than mind\\/body unities. This has far?reaching effects on our conceptualisation of the sex\\/gender distinction and on the relationship between bodies and identities. Related to this is a dualism that is embedded in how we think
Carrie Paechter
High-order Non-reflecting Boundary Conditions for Dispersive Waves in Cartesian, Cylindrical and Spherical Coordinate Systems
NASA Astrophysics Data System (ADS)
Among the many areas of research that Professor Kawahara has been active in is the subject of open boundaries in which linear time-dependent dispersive waves are considered in an unbounded domain. The infinite domain is truncated via an artificial boundary B on which an open boundary condition (OBC) is imposed. In this paper, Higdon OBCs and Hagstrom-Hariharan (HH) OBCs are considered. Higdon-type conditions, originally implemented as low-order OBCs, are made accessible for any desired order via a new scheme. The higher-order Higdon OBC is then reformulated using auxiliary variables and made compatible for use with finite element (FE) methods. Methodologies for selecting Higdon parameters are also proposed. The performances of these schemes are demonstrated in two numerical examples. This is followed by a discussion of the HH OBC, which is applicable to non-dispersive media on cylindrical and spherical geometries. The paper extends this OBC to the "slightly dispersive" case.
van Joolen*, Vince; Givoli, Dan; Neta, Beny
A computer program for converting rectangular coordinates to latitude-longitude coordinates
A computer program was developed for converting the coordinates of any rectangular grid on a map to coordinates on a grid that is parallel to lines of equal latitude and longitude. Using this program in conjunction with groundwater flow models, the user can extract data and results from models with varying grid orientations and place these data into grid structure that is oriented parallel to lines of equal latitude and longitude. All cells in the rectangular grid must have equal dimensions, and all cells in the latitude-longitude grid measure one minute by one minute. This program is applicable if the map used shows lines of equal latitude as arcs and lines of equal longitude as straight lines and assumes that the Earth 's surface can be approximated as a sphere. The program user enters the row number , column number, and latitude and longitude of the midpoint of the cell for three test cells on the rectangular grid. The latitude and longitude of boundaries of the rectangular grid also are entered. By solving sets of simultaneous linear equations, the program calculates coefficients that are used for making the conversion. As an option in the program, the user may build a groundwater model file based on a grid that is parallel to lines of equal latitude and longitude. The program reads a data file based on the rectangular coordinates and automatically forms the new data file. (USGS)
Rutledge, A. T.
NASA Technical Reports Server (NTRS)
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.
Smith, R. E.
Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
NASA Technical Reports Server (NTRS)
A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.
Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel
An analysis of a collision situation in polar coordinates
NASA Astrophysics Data System (ADS)
Avoiding collisions with other vessels and natural or artificial navigational obstructions is an important element of navigation safety. This problem is automatically solved in anti-collision ARPA systems, or geometrically as radar plots. In both cases we use radar measurements: bearing (or relative bearing) on the target position and distance, both naturally localized in the polar coordinates system with the origin at the radar antenna. We convert original measurements to an ortho-Cartesian coordinate system. Then we solve a collision avoiding problem in the new system, and then transform the results to the polar coordinate system. This article presents a method for an analysis of a collision situation performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation.
Wolski, Adam; Banachowicz, Andrzej
P1G-8 Diagonally Staggered Grid for Elastodynamic Analysis Using the Finite-Difference Time-Domain Method
A new diagonally staggered grid configuration is proposed for the finite-difference time-domain (FDTD) analysis of elastic wave fields. The structure of the grid is the same as a standard staggered grid, but the diagonals of the standard grid lie parallel to the coordinate axes of the field of analysis in this new configuration. Adopting this grid configuration allows a natural
Masahiro Sato
NSDL National Science Digital Library
5th Grade Math State core Standard 3, Objective 2a: Locate points defined by ordered pairs of integers. Congratulations for earning a game day in the computer lab! Remember that even though it is game day I expect you to stay on task and follow directions. We have been talking in math about graphing integers on the coordinate plane. The games for today require that ...
Zilles, Miss
NASA Technical Reports Server (NTRS)
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 access from outside of NASA centers. A SAFE enabled IPG can enable IPG capabilities to be available to NASA mission design teams across different NASA center and partner company firewalls. This paper will first discuss some of the potential security issues for IPG to work across NASA center firewalls. We will then present the SAFE federated security model. Finally we will present the concept of the architecture of a SAFE enabled IPG and how it can benefit NASA mission development.
Chow, Edward T.; Stewart, Helen; Korsmeyer, David (Technical Monitor)
Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates
Wind-driven spin-up of the four-layer, quasi-isopycnic, eddy-resolving primitive equation model of Bleck and Boudra (1981) is compared with that obtained with a (numerically dissimilar) ``pure'' isopycnic coordinate model and an isobaric (i.e., quasi-Cartesian) coordinate model. In particular, the onset of hydrodynamic instabilities in the flow forced by a double-gyre wind stress pattern is studied. The spin-up processes associated with the
Rainer Bleck; Douglas Boudra
Grid welding fixture for a spacer grid
A modular grid welding fixture for a spacer grid that facilitates full grid laser welding of a spacer grid in one setup is disclosed. The modular design allows for partial implementation of each weld type. A base plate is used for mounting to the positioning\\/rotational plate of the welding system. A removable sub-plate received in the base plate is used
M. W. Anderson; J. S. Whitt
System Wide Joint Position Sensor Fault Tolerance in Robot Systems Using Cartesian Accelerometers
NASA Technical Reports Server (NTRS)
Joint position sensors are necessary for most robot control systems. A single position sensor failure in a normal robot system can greatly degrade performance. This paper presents a method to obtain position information from Cartesian accelerometers without integration. Depending on the number and location of the accelerometers. the proposed system can tolerate the loss of multiple position sensors. A solution technique suitable for real-time implementation is presented. Simulations were conducted using 5 triaxial accelerometers to recover from the loss of up to 4 joint position sensors on a 7 degree of freedom robot moving in general three dimensional space. The simulations show good estimation performance using non-ideal accelerometer measurements.
Aldridge, Hal A.; Juang, Jer-Nan
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.
Nemec, Marian; Aftosmis,Michael J.
Analysis of local anharmonicity using Gaussian model potentials and cartesian oscillator basis sets: example, HCN.
This paper examines local anharmonic vibrations in molecules using an analysis that starts with an ab initio potential energy surface, fits a model potential constructed of Gaussian basis functions, and proceeds to a quantum mechanical analysis of the anharmonic modes using Cartesian harmonic oscillator basis functions in a variational calculation. The objective of this work is to suggest methods, with origins in nuclear and molecular (electronic) quantum mechanics, that should be useful for the accurate analysis of the local anharmonic motions of hydrogen, and perhaps other atoms or small molecular fragments, residing in molecularly complicated but otherwise harmonic environments. PMID:16354032
Schmidt, P P
Parallel adaptive Cartesian upwind methods for shock-driven multiphysics simulation
The multiphysics fluid-structure interaction simulation of shock-loaded thin-walled structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. By combining a Cartesian embedded boundary approach with dynamic mesh adaptation a generic software framework for such flow solvers has been constructed that allows easy exchange of the specific hydrodynamic finite volume upwind scheme and coupling to various explicit finite element solid dynamics solvers. The paper gives an overview of the computational approach and presents first simulations that couple the software to the general purpose solid dynamics code DYNA3D.
Deiterding, Ralf [ORNL
CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method
NASA Technical Reports Server (NTRS)
A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.
Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.
An adaptively-refined Cartesian mesh solver for the Euler equations
NASA Technical Reports Server (NTRS)
A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann solver. Solution-adaptive refinement of the mesh is then applied to resolve high-gradient regions of the flow. The numerical results presented show the flexibility of this approach and the accuracy attainable by solution-based refinement.
De Zeeuw, Darren; Powell, Kenneth G.
The NCRC Grid Scheduling Environment
In support of the NCRC, a joint computing center between NOAA and ORNL, a grid-based scheduling infrastructure was designed to allow geographically separate computing resources to be used as production resources in climate and weather research workflows. These workflows require job coordination between the two centers in order to provide a complete workflow of data staging, computation, post-analysis and archival. This paper details the design, implementation and initial production phase of the infrastructure and lessons learned from the process.
Indiviglio, Frank M [ORNL; Maxwell, Don E [ORNL
A Vertical Grid Module for Baroclinic Models of the Atmosphere
The vertical grid of an atmospheric model assigns dynamic and thermo- dynamic variables to grid locations. The vertical coordinate is typically not height but one of a class of meteorological variables that vary with atmo- spheric conditions. The grid system is chosen to further numerical approx- imations of the boundary conditions so that the system is terrain following at the surface. Lagrangian vertical coordinates are useful in reducing the numerical errors from advection processes. That the choices will effect the numercial properties and accuracy is explored in this report. A MATLAB class for Lorentz vertical grids is described and applied to the vertical struc- ture equation and baroclinic atmospheric circulation. A generalized meteo- rolgoical coordinate system is developed which can support ?, isentropic ? vertical coordinate, or Lagrangian vertical coordinates. The vertical atmo- spheric column is a MATLAB class that includes the kinematic and ther- modynamic variables along with methods for computing geopoentials and terms relevant to a 3D baroclinc atmospheric model.
Drake, John B [ORNL
NSDL National Science Digital Library
The class forms a "Presidential Task Force" for a week, empowered by the president to find answers and make recommendations concerning the future of the national power grid. Task force members conduct daily debriefings with their research team and prepare a report and presentation of their findings for the president, using an actual policy document as a guide. Although this activity is geared towards fifth-grade and older students and Internet research capabilities are required, some portions may be appropriate for younger students.
Integrated Teaching And Learning Program
NSDL National Science Digital Library
Commodity Grid (CoG) Kits allow Grid users, Grid application developers, and Grid administrators to use, program, and administer Grids from a higher-level framework. The Java and Python CoG Kits are good examples. These kits allow for easy and rapid Grid application development. They encourage collaborative code reuse and avoid the duplication of effort among problem solving environments, science portals, Grid middleware, and collaboratory pilots.
Von Laszewski, Gregor
Integrating Wireless Sensor Networks with Computational Grids
Wireless sensor networks (WSNs) have been greatly developed and emerged their significance in a wide range of important applications\\u000a such as ac quisition and process in formation from the physical world. The evolvement of Grid computing has been based on\\u000a coordination of distributed and shared re sources. A Sensor Grid network can integrate these two leading technologies enabling\\u000a real-time sensor
Nikolaos Preve
A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: part II--numerical results and experimental evaluation.
In this paper, we present numerical results obtained from a robust, locally conformal 3-D Orthogonal Grid Finite Difference (OGFD) thermal algorithm introduced in Part I of our current investigation [Al-Rizzo et al., 2006] integrated with an Orthogonal Grid Finite-Difference Time Domain (OGFDTD) scheme [Al-Rizzo et al., 2000], which accurately models the volumetric electromagnetic (EM) power deposition pattern. A unified meshing scheme, which utilizes identical overlapping grids in Cartesian and cylindrical coordinates, is employed within the load zone in the OGFDTD and OGFD models. Local temperature profiles excited by the absorbed microwave energy were measured at seven locations within the sample as a function of heating time. In order to benchmark, or validate our model, an alternative analysis of the coupled EM and thermal simulations was performed using state-of-the-art, Finite Element Method-based Ansoft's High Frequency Structure Simulator (HFSS) and the coupled thermal/stress analysis tool ePHYSICS (http://www.ansoft.com). Additionally, we compare our numerical simulations against measured dynamic temperature profiles induced within a mineral ore sample maintained for exposure period of 28.5 minutes inside a cylindrical multimode heating furnace energized at 915 MHz with a microwave source power of 12.5 kW and accompanied with significant temperature elevation. A combination of convective and radiation thermal boundary conditions are considered at the interfaces between the cavity walls, air, and sample. There is a general agreement between simulated and measured spatial and temporal temperature profiles, which validates the proposed model. Results indicate that inevitable fluctuations in the frequency spectrum and output power of the magnetron, non-uniformity of sample packing, and heat released by uncontrolled exothermic chemical reactions have a significant effect on the comparisons between measured and computed temperature patterns. PMID:17278792
Al-Rizzo, Hussain M; Adada, Rami; Tranquilla, Jim M; Ma, Feng; Ionescu, Bogdan C
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.
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. PMID:12132936
Hou, Hongwei; Meng, Xiangru; Song, Yinglin; Fan, Yaoting; Zhu, Yu; Lu, Huijie; Du, Chenxia; Shao, Weihua
Calculation of rigid-body conformational changes using restraint-driven Cartesian transformations.
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.
Sompornpisut, P; Liu, Y S; Perozo, E
caGrid 1.0: An Enterprise Grid Infrastructure for Biomedical Research
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.
Oster, Scott; Langella, Stephen; Hastings, Shannon; Ervin, David; Madduri, Ravi; Phillips, Joshua; Kurc, Tahsin; Siebenlist, Frank; Covitz, Peter; Shanbhag, Krishnakant; Foster, Ian; Saltz, Joel
Accurate computation of Zernike moments in polar coordinates.
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. PMID:17269651
Xin, Yongqing; Pawlak, Miroslaw; Liao, Simon
caGrid 1.0 : an enterprise Grid infrastructure for biomedical research.
To develop software infrastructure that will provide support for discovery, characterization, integrated access, and management of diverse and disparate collections of information sources, analysis methods, and applications in biomedical research. Design: An enterprise Grid software infrastructure, called caGrid version 1.0 (caGrid 1.0), has been developed as the core Grid architecture of the NCI-sponsored cancer Biomedical Informatics Grid (caBIG{trademark}) program. It is designed to support a wide range of use cases in basic, translational, and clinical research, including (1) discovery, (2) integrated and large-scale data analysis, and (3) coordinated study. Measurements: The caGrid is built as a Grid software infrastructure and leverages Grid computing technologies and the Web Services Resource Framework standards. It provides a set of core services, toolkits for the development and deployment of new community provided services, and application programming interfaces for building client applications. Results: The caGrid 1.0 was released to the caBIG community in December 2006. It is built on open source components and caGrid source code is publicly and freely available under a liberal open source license. The core software, associated tools, and documentation can be downloaded from the following URL:
Oster, S.; Langella, S.; Hastings, S.; Ervin, D.; Madduri, R.; Phillips, J.; Kurc, T.; Siebenlist, F.; Covitz, P.; Shanbhag, K.; Foster, I.; Saltz, J.; Mathematics and Computer Science; The Ohio State Univ.; National Cancer Inst. Centerfor Bioinformatics; SemanticBits
Building on both Grid and Web services technologies, the Open Grid Services Architecture (OGSA) defines mechanisms for creating, managing, and exchanging information among entities called Grid services. Succinctly, a Grid service is a Web service that conforms to a set of conventions (interfaces and behaviors) that define how a client interacts with a Grid service. These conventions, and other OGSA
Steven Tuecke; Karl Czajkowski; Ian Foster; Jeffrey Frey; Steve Graham; Carl Kesselman
A Moving Grid Capability for NPARC
NASA Technical Reports Server (NTRS)
Version 3.1 of the NPARC computational fluid dynamics flow solver introduces a capability to solve unsteady flow on moving multi-block, structured grids with nominally second-order time accuracy. The grid motion is due to segments of the boundary grid that translate and rotate in a rigid-body manner or deform. The grid is regenerated at each time step to accommodate the boundary grid motion. The flow equations and computational models sense the moving grid through the grid velocities, which are computed from a time-difference of the grids at two consecutive time levels. For three-dimensional flow domains, it is assumed that the grid retains a planar character with respect to one coordinate. The application and accuracy of NPARC v3.1 is demonstrated for flow about a flying wedge, rotating flap, a collapsing bump in a duct, and the upstart / restart flow in a variable-geometry inlet. The results compare well with analytic and experimental results.
Slater, John W.
Numerical grid generation in computational field simulations. Volume 1
To enhance the CFS technology to its next level of applicability (i.e., to create acceptance of CFS in an integrated product and process development involving multidisciplinary optimization) the basic requirements are: rapid turn-around time, reliable and accurate simulation, affordability and appropriate linkage to other engineering disciplines. In response to this demand, there has been a considerable growth in the grid generation related research activities involving automization, parallel processing, linkage with the CAD-CAM systems, CFS with dynamic motion and moving boundaries, strategies and algorithms associated with multi-block structured, unstructured, hybrid, hexahedral, and Cartesian grids, along with its applicability to various disciplines including biomedical, semiconductor, geophysical, ocean modeling, and multidisciplinary optimization.
Soni, B.K.; Thompson, J.F.; Haeuser, J.; Eiseman, P.R. [eds.
Reversible, fast, and high-quality grid conversions.
A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations. PMID:18390374
Condat, Laurent; Van De Ville, Dimitri; Forster-Heinlein, Brigitte
National Technical Information Service (NTIS)
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 experim...
R. Pordes
Performance testing framework for smart grid communication network
NASA Astrophysics Data System (ADS)
Smart grid communication network is comprised of different communication mediums and technologies. Performance evaluation is one of the main concerns in smart grid communication system. In any smart grid communication implementation, to determine the performance factor of the network, a testing of an end-to-end process flow is required. Therefore, an effective and coordinated testing procedure plays a crucial role in evaluating the performance of smart grid communications. In this paper, a testing framework is proposed as a guideline to analyze and assess the performance of smart grid communication network.
Quang, D. N.; See, O. H.; Chee, L. L.; Xuen, C. Y.; Karuppiah, S.
Elliptic Surface Grid Generation in Three-Dimensional Space.
National Technical Information Service (NTIS)
A methodology for surface grid generation in three dimensional space is described. The method solves a Poisson equation for each coordinate on arbitrary surfaces using successive line over-relaxation. The complete surface curvature terms were discretized ...
L. Kania
Coordinate registration by automated crater recognition
An algorithm for the automatic recognition of impact craters is presented, based on Hough transforms and accounting for both the circularity of the crater rim and the presence of the internal depression. The algorithm is applied to adjust a catalogue of crater coordinates originally measured in the context of the USGS 1:2M controlled photomosaic to the more precise geodetic grid
G. G. Michael
Investigation of Radar Propagation in Buildings: A 10 Billion Element Cartesian-Mesh FETD Simulation
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.
Stowell, M L; Fasenfest, B J; White, D A
Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method
NASA Technical Reports Server (NTRS)
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.
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
Cartesian coupled coherent states simulations: NenBr2 dissociation as a test case
NASA Astrophysics Data System (ADS)
In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br2(?) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br2 vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported.
Reed, Stewart K.; Gonz�lez-Mart�nez, Maykel L.; Rubayo-Soneira, Jes�s; Shalashilin, Dmitrii V.
DOMINO: A fast 3D cartesian discrete ordinates solver for reference PWR simulations and SPN validation
As part of its activity, EDF R and D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SPN) method to compute the neutron flux inside the core for eigenvalue calculations. In order to assess the accuracy of SPN calculations, we have developed DOMINO, a new 3D Cartesian SN solver. The parallel implementation of DOMINO is very efficient and allows to complete an eigenvalue calculation involving around 300 x 10{sup 9} degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S{sub 8} 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP{sub 5} DIABOLO fission production rate is lower than 0.2% compared to the S{sub 8} DOMINO reference for this 3D PWR core model. (authors)
Courau, T.; Moustafa, S.; Plagne, L.; Poncot, A. [EDF R and D, 1, Av du General de Gaulle, F92141 Clamart cedex (France)] [EDF R and D, 1, Av du General de Gaulle, F92141 Clamart cedex (France)
Studies of charge neutral FCC Lattice Gas with Yukawa Interaction and Accelerated Cartesian Expansion method
NASA Astrophysics Data System (ADS)
In this thesis, I present the results of studies of the structural properties and phase transition of a charge neutral FCC Lattice Gas with Yukawa Interaction and discuss a novel fast calculation algorithm---Accelerated Cartesian Expansion (ACE) method. In the first part of my thesis, I discuss the results of Monte Carlo simulations carried out to understand the finite temperature (phase transition) properties and the ground state structure of a Yukawa Lattice Gas (YLG) model. In this model the ions interact via the potential q iqjexp(-kappar> ij)/rij where qi,j are the charges of the ions located at the lattice sites i and j with position vectors R i and Rj; rij = Ri-Rj, kappa is a measure of the range of the interaction and is called the screening parameter. This model approximates an interesting quaternary system of great current thermoelectric interest called LAST-m, AgSbPbmTem+2. I have also developed rapid calculation methods for the potential energy calculation in a lattice gas system with periodic boundary condition bases on the Ewald summation method and coded the algorithm to compute the energies in MC simulation. Some of the interesting results of the MC simulations are: (i) how the nature and strength of the phase transition depend on the range of interaction (Yukawa screening parameter kappa) (ii) what is the degeneracy of the ground state for different values of the concentration of charges, and (iii) what is the nature of two-stage disordering transition seen for certain values of x. In addition, based on the analysis of the surface energy of different nano-clusters formed near the transition temperature, the solidification process and the rate of production of these nano-clusters have been studied. In the second part of my thesis, we have developed two methods for rapidly computing potentials of the form R-nu. Both these methods are founded on addition theorems based on Taylor expansions. Taylor's series has a couple of inherent advantages: (i) it forms a natural framework for developing addition theorem based computational schemes for a range of potentials; (ii) only Cartesian tensors (or products of Cartesian quantities) are used as opposed to special functions. This makes creating a fast scheme possible for potential of the form R-nu . Indeed, it is also possible to generalize the proposed methods to several potentials that are important in mathematical physics. An interesting consequence of the approach has been the demonstration of the equivalence of FMMs that are based on traceless Cartesian tensors to those based on spherical expansions for nu = 1. Two methods are introduced; the first relies on exact translation of the origin of the multipole whereas the second relies on cascaded Taylor's approximations. Finally, we have shown the application of this methodology to computing Coulombic, Lennard-Jones, Yukawa potentials and etc. We have also demonstrated the efficacy of this scheme for other (non-integer) potential functions.
Huang, He
This study was made in response to screen measurements which indicated an emittance growth of nearly a factor of two within the North RTL or linac girder-1. Betatron oscillations are induced at the beginning of the North RTL to search for gross geometric aberrations arising within the RTL or sector-2 of the linac. The oscillations are induced horizontally and vertically with two X or two Y dipole correctors stepped in a nested loop fashion. In both cases the full set of RTL and first girder sector-2 linac beam position monitors (BPMs) are sampled in X and Y for each corrector setting. Horizontal (or vertical) data from pairs of BPMs are then transformed to phase space coordinates by the linear transformation constructed assuming the transport optics between the BPMs is known. A second transformation is then made to normalized phase space coordinates by using Twiss parameters consistent with the assumed transport optics. By careful choice of initial Twiss parameters the initial grid can be made square for convenience in graphical interpretation. A linear ''grid'' is then fitted to the transformed data points for each pair of BPMs. The area of each grid is calculated and linearity qualitatively evaluated. Furthermore, although not the focus of this study, the beta match at each BPM can be quantified.
Emma, P.; /SLAC
A Passivity based Cartesian Impedance Controller for Flexible Joint Robots - Part I: Torque Feedback and Gravity Compensation
Abstract� In this paper a novel approach to the Cartesian Impedance Control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent
Christian Ott; Alin Albu-sch�ffer; Andreas Kugi; Stefano Stramigioli; Gerd Hirzinger
Comparing the overflow of dense water in isopycnic and cartesian models with tracer observations in the eastern Mediterranean
Isopycnic and cartesian model simulations for the overflow and spreading of dense water are compared with each other and with independent transient-tracer observations. This case study is performed for Adriatic dense water overflowing into the deep eastern Mediterranean with chlorofluoromethane (CFC-12) observations used to test the model simulations. The realism of both types of model simulation depends on the representation
Vassil M. Roussenov; Richard G. Williams; Wolfgang Roether
A gridless boundary condition method for the solution of the Euler equations on embedded Cartesian meshes with multigrid
The solution of the Euler equations using a �gridless� boundary condition treatment on a patched, embedded Cartesian field mesh is described. 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 body. The method allows for accurate treatment of the surface boundary
D. J. Kirshman; F. Liu
Coordinate-dependent diffusion in protein folding
Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.
Best, Robert B.; Hummer, Gerhard
Implementing a Web Services Architecture Framework in a Grid Infrastructure
A major paradigm shift in distributed computing technologies has led during recent years towards two most notably solutions that are represented by grid computing principles and web services technologies and are converging versus a common framework. The grid model focus on large-scale heterogene- ous resource sharing in distributed system in a flexible, secure and coordination fashion, while interoperability, integration and
Serena Pastore
Web application security in a crossing boundaries grid system
The grid problem is how to enable coordinated resources sharing and problem solving in dynamic, multi-institutional cross organizations called Virtual Organizations (VOs) that collect a large number of nodes grouped into grid sites. An overlay of policies governs access within a collaboration that is granted to users by a VO and by a site to VOs, nodes and users through
Serena Pastore
XML-Based Workflow Description Language for Grid Applications
\\u000a In Grid computing PSE is essential for developing parallel and distributed applications in various computation intensive areas.\\u000a The workflow-based PSE supports the coordinated execution of multiple application tasks on distributed Grid resources by enabling\\u000a users to describe a workflow by composing many existing grid services or new functions. In this paper, we propose a new workflow\\u000a model which consists of
Yong-won Kwon; So-hyun Ryu; Chang-sung Jeong
Reliability Modeling for the Advanced Electric Power Grid
The advanced electric power grid promises a self-healing infrastructure using distributed, coordinated, power electronics\\u000a control. One promising power electronics device, the Flexible AC Transmission System (FACTS), can modify power flow locally\\u000a within a grid. Embedded computers within the FACTS devices, along with the links connecting them, form a communication and\\u000a control network that can dynamically change the power grid to
Ayman Z. Faza; Sahra Sedigh; Bruce M. Mcmillin
Neighborhood Sequences in the Diamond Grid - Algorithms with Four Neighbors
In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used. In this\\u000a paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal. This grid\\u000a can be described by four coordinate values using axes of the directions of atomic bonds. In this way the sum of the
Benedek Nagy; Robin Strand
Numerical relativity in spherical polar coordinates: Evolution calculations with the BSSN formulation
NASA Astrophysics Data System (ADS)
In the absence of symmetry assumptions most numerical relativity simulations adopt Cartesian coordinates. While Cartesian coordinates have some desirable properties, spherical polar coordinates appear better suited for certain applications, including gravitational collapse and supernova simulations. Development of numerical relativity codes in spherical polar coordinates has been hampered by the need to handle the coordinate singularities at the origin and on the axis, for example by careful regularization of the appropriate variables. Assuming spherical symmetry and adopting a covariant version of the Baumgarte-Shapiro-Shibata-Nakamura equations, Montero and Cordero-Carri�n recently demonstrated that such a regularization is not necessary when a partially implicit Runge-Kutta method is used for the time evolution of the gravitational fields. Here we report on an implementation of the Baumgarte-Shapiro-Shibata-Nakamura equations in spherical polar coordinates without any symmetry assumptions. Using a partially implicit Runge-Kutta method we obtain stable simulations in three spatial dimensions without the need to regularize the origin or the axis. We perform and discuss a number of tests to assess the stability, accuracy and convergence of the code, namely weak gravitational waves, �hydro-without-hydro� evolutions of spherical and rotating relativistic stars in equilibrium, and single black holes.
Baumgarte, Thomas W.; Montero, Pedro J.; Cordero-Carri�n, Isabel; M�ller, Ewald
Anharmonic state counts and partition functions for molecules via classical phase space integrals in curvilinear coordinates.
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. PMID:23697411
Kamarchik, Eugene; Jasper, Ahren W
Embedding planar graphs on the grid
We show that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-2 grid. This embedding is computable in time O(n). A nice feature of the vertex-coordinates is that they have a purely combinatorial meaning.
Walter Schnyder
Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates.
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. PMID:20922005
Baddour, Natalie
NASA Astrophysics Data System (ADS)
An approach is presented for the generation of two-dimensional, structured, dynamic grids utilizing grid speeds computed from the time differentiation of a set of grid equations. In application for the computation of unsteady, inviscid flows, it is shown that the approach is more efficient and accurate than an approach in which the grid speeds are computed using a finite difference of the grid with respect to time.
Slater, J. W.; Liou, M. S.; Hindman, R. G.
Development of Mathematical Concepts of Two-Dimensional Space in Grid Environments: An Exploratory Study.
ERIC Educational Resources Information Center
Investigated the development among fourth-graders of two-dimensional space concepts within a mathematics unit on grids, coordinates, and rectangles. Found that students' knowledge of grid and coordinate systems related to levels of competence in number sense, spatial-geometric relationships, and the ability to discriminate and integrate the two�
Sarama, Julie; Clements, Douglas H.; Swaminathan, Sudha; McMillen, Sue; Gonzalez Gomez, Rosa M.
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
NASA Technical Reports Server (NTRS)
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.
Nemec, Marian; Aftosmis, Michael J.
Visual SLAM Using Variance Grid Maps
NASA Technical Reports Server (NTRS)
An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance maps are much better for representing the structure of vegetated or rocky terrain.
Howard, Andrew B.; Marks, Tim K.
Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks
We present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or three-dimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target at a grid point at any instant in time. We first present an integer linear
Krishnendu Chakrabarty; S. Sitharama Iyengar; Hairong Qi; Eungchun Cho
Geo-spatial grid-based transformations of precipitation estimates using spatial interpolation methods
NASA Astrophysics Data System (ADS)
Geo-spatial interpolation methods are often necessary in instances where the precipitation estimates available from multisensor source data on a specific spatial grid need to be transformed to another grid with a different spatial grid or orientation. The study involves development and evaluation of spatial interpolation or weighting methods for transforming hourly multisensor precipitation estimates (MPE) available in the form of 4�4 km2 HRAP (hydrologic rainfall analysis project) grid to a Cartesian 2�2 km2 radar (NEXt generation RADar:NEXRAD) grid. Six spatial interpolation weighting methods are developed and evaluated to assess their suitability for transformation of precipitation estimates in space and time. The methods use distances and areal extents of intersection segments of the grids as weights in the interpolation schemes. These methods were applied to transform precipitation estimates from HRAP to NEXRAD grids in the South Florida Water Management District (SFWMD) region in South Florida, United States. A total of 192 rain gauges are used as ground truth to assess the quality of precipitation estimates obtained from these interpolation methods. The rain gauge data in the SFWMD region were also used for radar data bias correction procedures. To help in the assessment, several error measures are calculated and appropriate weighting functions are developed to select the most accurate method for the transformation. Three local interpolation methods out of six methods were found to be competitive and inverse distance based on four nearest neighbors (grids) was found to be the best for the transformation of data.
Teegavarapu, Ramesh S. V.; Meskele, Tadesse; Pathak, Chandra S.
Implementation of the radiative transfer equation on block-structured grids for modeling fluorescence light propagation in tissue with arbitrary shape
NASA Astrophysics Data System (ADS)
We developed a method for solving the fluorescence equation of radiative transfer in the frequency domain on blockstructured grids. In this way fluorescence light propagation in arbitrarily shaped tissue can be modeled with high accuracy without compromising on the convergence speed of these codes. The block-structure grid generator is developed as a multi-purpose tool that can be used with many numerical schemes. We present results from numerical studies that show that it is possible to resolve curved boundaries with grids that maintain much of the intrinsic structure of Cartesian grids. The natural ordering of this grid allows for simplified algorithms. In simulation studies we found that we can reduce the error in boundary fluence by a factor of five by using a two-level block structured grid. The increase in computational cost is only two-fold. We compare benchmark solutions to results with various levels of refinement, boundary conditions, and different geometries.
Montejo, Ludguier D.; Klose, Alexander D.; Hielscher, Andreas H.
Representation of protein 3D structures in spherical (?, ?, ?) coordinates and two of its potential applications.
Three-dimensional objects can be represented using cartesian, spherical or cylindrical coordinate systems, among many others. Currently all protein 3D structures in the PDB are in cartesian coordinates. We wanted to explore the possibility that protein 3D structures, especially the globular type (spheroproteins), when represented in spherical coordinates might find useful novel applications. A Fortran program was written to transform protein 3D structure files in cartesian coordinates (x,y,z) to spherical coordinates (?, ?, ?), with the centroid of the protein molecule as origin. We present here two applications, namely, (1) separation of the protein outer layer (OL) from the inner core (IC); and (2) identifying protrusions and invaginations on the protein surface. In the first application, ? and ? were partitioned into suitable intervals and the point with maximum ? in each such '?-? bin' was determined. A suitable cutoff value for ? is adopted, and for each ?-? bin, all points with ? values less than the cutoff are considered part of the IC, and those with ? values equal to or greater than the cutoff are considered part of the OL. We show that this separation procedure is successful as it gives rise to an OL that is significantly more enriched in hydrophilic amino acid residues, and an IC that is significantly more enriched in hydrophobic amino acid residues, as expected. In the second application, the point with maximum ? in each ?-? bin are sequestered and their frequency distribution constructed (i.e., maximum ?'s sorted from lowest to highest, collected into 1.50�-intervals, and the frequency in each interval plotted). We show in such plots that invaginations on the protein surface give rise to subpeaks or shoulders on the lagging side of the main peak, while protrusions give rise to similar subpeaks or shoulders, but on the leading side of the main peak. We used the dataset of Laskowski et al. (1996) to demonstrate both applications. PMID:21956738
Reyes, Vicente M
Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.
Omar, Mohamed A.
Efficient procedure for the numerical calculation of harmonic vibrational frequencies based on internal coordinates.
We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson's GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N - 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. In all cases the frequencies based on internal coordinates differ on average by <1 cm(-1) from those obtained from Cartesian coordinates. PMID:23406376
Miliordos, Evangelos; Xantheas, Sotiris S
Growing string method with interpolation and optimization in internal coordinates: Method and examples
NASA Astrophysics Data System (ADS)
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.
Zimmerman, Paul M.
Growing string method with interpolation and optimization in internal coordinates: method and examples.
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method. PMID:23676024
Zimmerman, Paul M
Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732
Omar, Mohamed A
Cross-sectional optoacoustic tomographic reconstructions in a polar grid
NASA Astrophysics Data System (ADS)
Some commonly employed optoacoustic (photoacoustic) tomographic configurations make use of an array of cylindrically-focused transducers located around the imaging sample to selectively acquire the optoacoustic signals generated in the imaging plane. Thereby, the feasibility of simultaneous acquisition of signals leads to important advantages such as high-throughput performance or real-time imaging capacity. For this particular geometry, two-dimensional model-based reconstruction has showcased good performance in terms of imaging accuracy and flexibility to account for various transducer-related effects and acoustic propagation phenomena. The forward model is expressed as a linear operator (model-matrix) that maps the optical absorption in a grid containing the sample to the resulting wavefield at the sensor positions. The standard approach, however, may lead to excessive memory requirements for the storage of the model-matrix. Herein, an optoacoustic model based on a discretization of the time-domain equation in a polar grid is introduced. Due to the rotational symmetry of the acquisition geometry and the discretization grid, only the part of the model-matrix directly corresponding to one transducer position (projection) needs to be stored. As a result, inversion of the model-matrix can be done in a memory efficient manner. Performance of the method was tested in numerical simulations and experimental measurements, attaining results equivalent to Cartesian-based grids but using a much more computationally efficient implementation.
De�n-Ben, X. Lu�s.; Lutzweiler, Christian; Razansky, Daniel
Efficient parallel seismic simulations including topography and 3-D material heterogeneities on locally refined composite grids
NASA Astrophysics Data System (ADS)
The finite difference method on a uniform Cartesian grid is a highly efficient and easy to implement technique for solving the elastic wave equation in seismic applications. However, the spacing in a uniform Cartesian grid is fixed throughout the computational domain, whereas the resolution requirements in realistic seismic simulations usually are higher near the surface than at depth. This can be seen from the well-known formula h ? L-P which relates the grid spacing h to the wave length L, and the required number of grid points per wavelength P for obtaining an accurate solution. The compressional and shear wave lengths in the earth generally increase with depth and are often a factor of ten larger below the Moho discontinuity (at about 30 km depth), than in sedimentary basins near the surface. A uniform grid must have a grid spacing based on the small wave lengths near the surface, which results in over-resolving the solution at depth. As a result, the number of points in a uniform grid is unnecessarily large. In the wave propagation project (WPP) code, we address the over-resolution-at-depth issue by generalizing our previously developed single grid finite difference scheme to work on a composite grid consisting of a set of structured rectangular grids of different spacings, with hanging nodes on the grid refinement interfaces. The computational domain in a regional seismic simulation often extends to depth 40-50 km. Hence, using a refinement ratio of two, we need about three grid refinements from the bottom of the computational domain to the surface, to keep the local grid size in approximate parity with the local wave lengths. The challenge of the composite grid approach is to find a stable and accurate method for coupling the solution across the grid refinement interface. Of particular importance is the treatment of the solution at the hanging nodes, i.e., the fine grid points which are located in between coarse grid points. WPP implements a new, energy conserving, coupling procedure for the elastic wave equation at grid refinement interfaces. When used together with our single grid finite difference scheme, it results in a method which is provably stable, without artificial dissipation, for arbitrary heterogeneous isotropic elastic materials. The new coupling procedure is based on satisfying the summation-by-parts principle across refinement interfaces. From a practical standpoint, an important advantage of the proposed method is the absence of tunable numerical parameters, which seldom are appreciated by application experts. In WPP, the composite grid discretization is combined with a curvilinear grid approach that enables accurate modeling of free surfaces on realistic (non-planar) topography. The overall method satisfies the summation-by-parts principle and is stable under a CFL time step restriction. A feature of great practical importance is that WPP automatically generates the composite grid based on the user provided topography and the depths of the grid refinement interfaces. The WPP code has been verified extensively, for example using the method of manufactured solutions, by solving Lamb's problem, by solving various layer over half- space problems and comparing to semi-analytic (FK) results, and by simulating scenario earthquakes where results from other seismic simulation codes are available. WPP has also been validated against seismographic recordings of moderate earthquakes. WPP performs well on large parallel computers and has been run on up to 32,768 processors using about 26 Billion grid points (78 Billion DOF) and 41,000 time steps. WPP is an open source code that is available under the Gnu general public license.
Petersson, Anders; Rodgers, Arthur
An image space approach to Cartesian based parallel MR imaging with total variation regularization.
The Cartesian parallel magnetic imaging problem is formulated variationally using a high-order penalty for coil sensitivities and a total variation like penalty for the reconstructed image. Then the optimality system is derived and numerically discretized. The objective function used is non-convex, but it possesses a bilinear structure that allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing a pre-estimated norm of the reconstructed image. Since the objective function is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the objective function is minimized with respect to one variable after the other using an inner generalized Newton iteration. Computational results for in vivo MR imaging data show that a significant improvement in reconstruction quality can be obtained by using the proposed regularization methods in relation to alternative approaches. PMID:21852180
Keeling, Stephen L; Clason, Christian; Hinterm�ller, Michael; Knoll, Florian; Laurain, Antoine; von Winckel, Gregory
Non-cartesian MRI reconstruction with automatic regularization Via Monte-Carlo SURE.
Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate [based on the principle of Stein's unbiased risk estimate (SURE)] of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the l1-norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction. PMID:23591478
Ramani, Sathish; Weller, Daniel S; Nielsen, Jon-Fredrik; Fessler, Jeffrey A
On the Use of CAD and Cartesian Methods for Aerodynamic Optimization
NASA Technical Reports Server (NTRS)
The objective for this paper is to present the development of an optimization capability for Curt3D, a Cartesian inviscid-flow analysis package. We present the construction of a new optimization framework and we focus on the following issues: 1) Component-based geometry parameterization approach using parametric-CAD models and CAPRI. A novel geometry server is introduced that addresses the issue of parallel efficiency while only sparingly consuming CAD resources; 2) The use of genetic and gradient-based algorithms for three-dimensional aerodynamic design problems. The influence of noise on the optimization methods is studied. Our goal is to create a responsive and automated framework that efficiently identifies design modifications that result in substantial performance improvements. In addition, we examine the architectural issues associated with the deployment of a CAD-based approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute engines. We demonstrate the effectiveness of the framework for a design problem that features topology changes and complex geometry.
Nemec, M.; Aftosmis, M. J.; Pulliam, T. H.
A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions
NASA Technical Reports Server (NTRS)
The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions 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.
Constantinescu, G.S.; Lele, S. K.
Advancing Smart Grid Interoperability and Implementing NIST's Interoperability Roadmap
The IEEE American National Standards project P2030TM addressing smart grid interoperability and the IEEE 1547 series of standards addressing distributed resources interconnection with the grid have been identified in priority action plans in the Report to NIST on the Smart Grid Interoperability Standards Roadmap. This paper presents the status of the IEEE P2030 development, the IEEE 1547 series of standards publications and drafts, and provides insight on systems integration and grid infrastructure. The P2030 and 1547 series of standards are sponsored by IEEE Standards Coordinating Committee 21.
Basso,T.; DeBlasio, R.
This patent describes an improved floating spacer grid in combination with a nuclear fuel assembly of the type having parallel fuel rods and at least one guide tube maintained in a laterally spaced array by axially spaced spacer grids. The fuel rods and guide tube extend through the spacer grids. The guide tube has a uniform circular outer surface, the spacer grids are movably mounted to the guide tube to permit axial displacement of the spacer grids relative the guide tube. Saddles form from and within the spacer grids at top and bottom edges of the grids, a spacer sleeve positioned concentrically about the guide tube intermediate the adjacent ones of the axially-spaced spacer grids for limiting axial displacement of the spacer grids, and the spacer sleeve has opposite ends closely spaced from the edges of the adjacent spacer grids to define a displacement space. The improvement comprises in combination; tubular inserts, each insert mounted to the guide tube within each of the spacer grids. Each insert includes a tubular portion positioned by the saddles to circumscribe the guide tube within the spacer grid and a circular flange portion at one end of the tubular portion. The flange portion is positioned in the displacement space and abutted to the edge of the spacer grid on the saddles, intermediate the spacer grid and spacer sleeve, and the circular flange portion has substantially the same outer diameter as the spacer sleeve thus precluding direct contact of the spacer sleeve with the spacer grid. The inserts carry all axial through-grid loads and prevent a horizontal vector force component applied against the grids.
King, R.A.; Larson, J.G.; Walton, L.A.
Interactive algebraic grid-generation technique
NASA Technical Reports Server (NTRS)
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.
Smith, R. E.; Wiese, M. R.
Large-Eddy Simulation of a Neutral Boundary Layer on a Nested Grid Using Explicit Filtering and Reconstruction
NASA Astrophysics Data System (ADS)
Large-eddy simulation (LES) is a popular technique for studying the atmospheric boundary layer (ABL) on small domains. ABL simulations often use structured nested grids to scale the solution from the mesoscale to local scales, but using LES on non-uniform grids generates additional errors. The grid refinement interfaces in nested grids can reflect resolved energy and create interpolation errors. This study investigates the use of explicit filtering and reconstruction to mitigate grid interface errors in LES of a neutral boundary layer. The domain is split in the streamwise direction into two equally sized structured grids, one fine and one coarse, with periodic boundaries in the streamwise and spanwise directions. This simply nested, idealized test case allows observation of the effects of the grid interfaces. Explicit filtering is found to reduce accumulation of resolved energy at the fine-to-coarse interface and improve the shape of coherent structures, compared to basic LES. Additional reconstruction of the subfilter velocity is shown to further the improvements of explicit filtering. These results inform the use of LES to simulate the ABL on block-structured non-uniform grids, from typical nested grids to more complex cartesian AMR grids for urban boundary layers.
Goodfriend, L.; Chow, F. K.; Vanella, M.; Balaras, E.
A breakthrough in neuroscience needs a "Nebulous Cartesian System" Oscillations, quantum dynamics and chaos in the brain and vegetative system.
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the metaphor of "finding the walking path in a cloudy or foggy day". This is meant by stating "The Nebulous Cartesian System" (NCS). Descartes, at his time undertaking his genius step, did not possess the knowledge of today's physiology and modern physics; we think that the time has come to consider such a New Cartesian System. To deal with this, we propose the utilization of the Heisenberg S-Matrix and a modified version of the Feynman Diagrams which we call "Brain Feynman Diagrams". Another metaphor to consider within the oscillatory approach of the NCS is the "string theory". We also emphasize that fundamental steps should be undertaken in order to create the own dynamical framework of the brain-body-mind incorporation; suggestions or metaphors from physics and mathematics are useful; however, the grammar of the brains intrinsic language must be understood with the help of a new biologically founded, adaptive-probabilistic Cartesian system. This new Cartesian System will undergo mutations and transcend to the philosophy of Henri Bergson in parallel to the Evolution theory of Charles Darwin to open gateways for approaching the brain-body-mind problem. PMID:17049654
Ba?ar, Erol; G�ntekin, Bahar
Solution Adapative Grid Generation with Curvature Control
NASA Astrophysics Data System (ADS)
The numerical grid generation is introduced within the framework of elliptic generation, and a method of curvature control via uniformalization is developed and implemented with the solution-adaptive capability. Uniformalization is accomplished by seeking the uniform distribution of points in terms of the coordinate curve arc-length in each curvilinear coordinate direction. The method is automatic with virtually no ad-hoc adjustment by the users, and the global arc-length uniformity can be attained. The solution adaptive method based on elliptic generation is activated with the user's specified control in the number of clustering grid points. An octree searching technique is applied to locate the near-neighbors, and the data transfer calculation is done with barycentric approximation. An octree searching increases the speed of the searching process at the expense of the storage size. The data transfer is found to be sufficiently accurate. The analytic and approximated weight calculations produce figures of nearly identical grid distribution. A comparison is given between two grids: one generated with the smoother and adaptivity and the other with the smoother, curvature control and adaptivity combined. The experiment shows significant difference between two cases in the distribution of points near curved boundary. The solution adaptivity and background distribution by uniformalization are integrated and balanced so as to generate a grid that is smooth, curvature -controlled and adaptive.
Takahashi, Satoshi
Cartesian Impedance Control on Five-Finger Dexterous Robot Hand DLR-HIT II with Flexible Joint
\\u000a This paper presents an impedance controller for five-finger dexterous robot hand DLR-HIT II, which is derived in Cartesian\\u000a space. By considering flexibility in finger joints and strong mechanical couplings in differential gear-box, modeling and\\u000a control of the robot hand are described in this paper. The model-based friction estimation and velocity observer are carried\\u000a out with an extended Kalman filter, which
Zhaopeng Chen; Neal Y. Lii; Minghe Jin; Shaowei Fan; Hong Liu
Grid Computing Portals Lecture
NSDL National Science Digital Library
Grid Computing Lecture~~Grid portals: purpose, application-based portals, historical examples, GPDK, Gridport, etc., OGCE2/gridsphere portal, portal implementation, portlets, JSR 168, portlet source and deployment files.
Ferner, Clayton; Wilkinson, Barry
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.
Barnette, Daniel W. (Veguita, NM)
NSDL National Science Digital Library
This video segment adapted from NOVA scienceNOW provides an overview of the existing United States power grid, and envisions a smart power grid that would prevent problems, such as blackouts, and reduce energy waste and pollution.
Foundation, Wgbh E.
caGrid: design and implementation of the core architecture of the cancer biomedical informatics grid
Motivation: The complexity of cancer is prompting researchers to find new ways to synthesize information from diverse data sources and to carry out coordinated research efforts that span multiple institutions. There is a need for standard applications, common data models, and softwareinfrastructuretoenablemoreefficientaccesstoandsharingof distributedcomputationalresourcesincancerresearch.Toaddressthis need the National Cancer Institute (NCI) has initiated a national-scale effort, called the cancer Biomedical Informatics Grid
Joel H. Saltz; Scott Oster; Shannon Hastings; Stephen Langella; Tahsin M. Kur�; William Sanchez; Manav Kher; Arumani Manisundaram; Krishnakant Shanbhag; Peter A. Covitz
NASA Technical Reports Server (NTRS)
Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.
Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert
In this paper we present a linear algorithm to draw triconnected planar graphs of degree 3 planar on a linear-sized hexagonal grid such that in at most one edge are bends. This algorithm can be used to draw this class of graphs planar with straight lines on a n\\/2 � n\\/2 grid, improving the best known grid bounds by a
Goos Kant
National Technical Information Service (NTIS)
An approach is presented for the generation of two-dimensional, structured, dynamic grids. The grid motion may be due to the motion of the boundaries of the computational domain or to the adaptation of the grid to the transient, physical solution. A time-...
J. W. Slater M. Liou R. G. Hindman
This patent describes an improved floating spacer grid in combination with a nuclear fuel assembly of the type having parallel fuel rods and at least one guide tube maintained in a laterally spaced array by axially spaced spacer grids. The fuel rods and guide tube extend through the spacer grids. The guide tube has a uniform circular outer surface, the
R. A. King; J. G. Larson; L. A. Walton
A General Procedure for Introducing Structured Nonorthogonal Discretization Grids Into High-Order Finite-Difference Time-Domain Methods
This paper describes a general procedure for introducing structured nonorthogonal discretization grids into any high-order finite-difference time-domain method originally formulated on a uniform rectangular grid. The proposed procedure employs a coordinate transformation to map a conformal grid-a grid where all cells conform to the material boundaries of the given problem-onto a uniform rectangular grid where any high-order finite-difference scheme can
Roberto B. Armenta; Costas D. Sarris
Grid welding fixture for a spacer grid
A modular grid welding fixture for a spacer grid that facilitates full grid laser welding of a spacer grid in one setup is disclosed. The modular design allows for partial implementation of each weld type. A base plate is used for mounting to the positioning/rotational plate of the welding system. A removable sub-plate received in the base plate is used to position the grid strips for proper location for welding. A top fixture plate is aligned with the base plate and provides for mounting of a second sub-plate if required. Side plates with spring loaded pressure pads that are hinged to the top fixture plate apply uniform pressure to the outer grid strips during processing. The base plate, top plate, side plate, and pressure pads are provided with a plurality of through holes to allow access of the laser beam for welding. Corner clips are used to insure contact of the overlapping sections of the outer grid strips for proper corner welding. 4 figs.
Anderson, M.W.; Whitt, J.S.
Grid Computing Lecture - Globus 4.0 grid services
NSDL National Science Digital Library
Grid Computing Lecture~~Globus 4.0 grid services: Using Web services for grid computing, stateful web services, Grid computing standards, Open Grid Services Architecture (OGSA), Web Services Resource Framework (WSRF), programming GT 4.0 grid services, GT 4.0 container.
Ferner, Clayton; Wilkinson, Barry
Local DER driven grid support by coordinated operation of devices
In the traditional operation of electricity networks the system operator has a number of ancillary services available for preservation of system balance. These services are called upon near real-time, after the planning phase. Ancillary services consist of regulating power, reserve capacity and emergency capacity, each with their own characteristics. Regulating power is deployed via load frequency control. Reserve capacity is
C. J. Warmer; M. P. F. Hommelberg; J. K. Kok; I. G. Kamphuis
Coordinated monitoring, forecasting and control in interconnected electric power grids
The trends in expansion of electric power systems (EPSs) and changes in the conditions of their operation have led to considerable transformations in their structure and operation. Joint operation of power interconnections of regions or countries within an extended super power interconnection, practical impossibility to visualize information on its current state, various principles of control and different software applied in
N. I. Voropai; C. Rehtanz; O. A. Soukhanov
NASA Astrophysics Data System (ADS)
The third chapter discusses very important issues of grid generation, connected with a description of grid quality measures in forms suitable for formulating grid techniques. The definitions of the grid quality measures are based on the metric tensors and on the relations between the metric elements considered in Chap. 2. Special attention is paid to the invariants of the metric tensors, which are the basic elements for the definition of many important grid quality measures. Clear algebraic and geometric interpretations of the invariants are presented.
Liseikin, Vladimir D.
A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics
NASA Technical Reports Server (NTRS)
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.
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
Dynamic fisheye grids for binary black hole simulations
NASA Astrophysics Data System (ADS)
We present a new warped gridding scheme adapted to simulating gas dynamics in binary black hole spacetimes. The grid concentrates grid points in the vicinity of each black hole to resolve the smaller scale structures there, and rarefies grid points away from each black hole to keep the overall problem size at a practical level. In this respect, our system can be thought of as a �double� version of the fisheye coordinate system, used before in numerical relativity codes for evolving binary black holes. The gridding scheme is constructed as a mapping between a uniform coordinate system�in which the equations of motion are solved�to the distorted system representing the spatial locations of our grid points. Since we are motivated to eventually use this system for circumbinary disc calculations, we demonstrate how the distorted system can be constructed to asymptote to the typical spherical polar coordinate system, amenable to efficiently simulating orbiting gas flows about central objects with little numerical diffusion. We discuss its implementation in the Harm3d code, tailored to evolve the magnetohydrodynamics equations in curved spacetimes. We evaluate the performance of the system�s implementation in Harm3d with a series of tests, such as the advected magnetic field loop test, magnetized Bondi accretion, and evolutions of hydrodynamic discs about a single black hole and about a binary black hole. Like we have done with Harm3d, this gridding scheme can be implemented in other unigrid codes as a (possibly) simpler alternative to adaptive mesh refinement.
Zilh�o, Miguel; Noble, Scott C.
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 providers involved in the Smart Grid and provides profiles on them including contact information, company overviews, technology reviews, and key Smart Grid activities.
Navigation in Grid Space with the NAS Grid Benchmarks
NASA Technical Reports Server (NTRS)
We present a navigational tool for computational grids. The navigational process is based on measuring the grid characteristics with the NAS Grid Benchmarks (NGB) and using the measurements to assign tasks of a grid application to the grid machines. The tool allows the user to explore the grid space and to navigate the execution at a grid application to minimize its turnaround time. We introduce the notion of gridscape as a user view of the grid and show how it can be me assured by NGB, Then we demonstrate how the gridscape can be used with two different schedulers to navigate a grid application through a rudimentary grid.
Frumkin, Michael; Hood, Robert; Biegel, Bryan A. (Technical Monitor)
Grid enabled Service Support Environment - SSE Grid
NASA Astrophysics Data System (ADS)
The SSEGrid project is an ESA/ESRIN project which started in 2009 and is executed by two Belgian companies, Spacebel and VITO, and one Dutch company, Dutch Space. The main project objectives are the introduction of a Grid-based processing on demand infrastructure at the Image Processing Centre for earth observation products at VITO and the inclusion of Grid processing services in the Service Support Environment (SSE) at ESRIN. The Grid-based processing on demand infrastructure is meant to support a Grid processing on demand model for Principal Investigators (PI) and allow the design and execution of multi-sensor applications with geographically spread data while minimising the transfer of huge volumes of data. In the first scenario, 'support a Grid processing on demand model for Principal Investigators', we aim to provide processing power close to the EO-data at the processing and archiving centres. We will allow a PI (non-Grid expert user) to upload his own algorithm, as a process, and his own auxiliary data from the SSE Portal and use them in an earth observation workflow on the SSEGrid Infrastructure. The PI can design and submit workflows using his own processes, processes made available by VITO/ESRIN and possibly processes from other users that are available on the Grid. These activities must be user-friendly and not requiring detailed knowledge about the underlying Grid middleware. In the second scenario we aim to design, implement and demonstrate a methodology to set up an earth observation processing facility, which uses large volumes of data from various geographically spread sensors. The aim is to provide solutions for problems that we face today, like wasting bandwidth by copying large volumes of data to one location. We will avoid this by processing the data where they are. The multi-mission Grid-based processing on demand infrastructure will allow developing and executing complex and massive multi-sensor data (re-)processing applications more efficiently. A workflow can be built and submitted for execution on multiple loosely coupled Grids (e.g. at VITO and at ESRIN). It is ensured that the data are processed where they are located. For this purpose the project aims to upgrade the Service Support Environment (SSE) to integrate multi-Grid processing services to be used by the PI for the systematic processing or reprocessing of EO data. For both scenarios described above, two processing modes will be available. In near real-time (NRT), or 'subscription mode', processing, the execution of a workflow is started but suspended a certain step where the workflow waits until certain data are present on the Grid. As soon as the data become available from the sensors, the execution is resumed automatically. In 'historical mode' it is assumed that the data are already present. An other main objective of the SSEGrid project is to propose new or amended versions of 'Web Processing Service' protocols that may be able to bridge geo-spatial Service Oriented Architectures and Open Grid Services Architectures. In this context we will propose the Grid Web Processing Service as an extension of the OGC WPS service to allow for the dynamic deployment of user processes (workflows or Grid processes) and auxiliary data, for the discovery of user auxiliary data, for the query of process status and process audit (execution trace, log file) and for the notification of process completion or failure.
Goor, Erwin; Paepen, Martine
Securing smart grid technology
NASA Astrophysics Data System (ADS)
In the developing countries electrical energy is very important for its all-round improvement by saving thousands of dollars and investing them in other sector for development. For Growing needs of power existing hierarchical, centrally controlled grid of the 20th Century is not sufficient. To produce and utilize effective power supply for industries or people we should have Smarter Electrical grids that address the challenges of the existing power grid. The Smart grid can be considered as a modern electric power grid infrastructure for enhanced efficiency and reliability through automated control, high-power converters, modern communications infrastructure along with modern IT services, sensing and metering technologies, and modern energy management techniques based on the optimization of demand, energy and network availability and so on. The main objective of this paper is to provide a contemporary look at the current state of the art in smart grid communications as well as critical issues on smart grid technologies primarily in terms of information and communication technology (ICT) issues like security, efficiency to communications layer field. In this paper we propose new model for security in Smart Grid Technology that contains Security Module(SM) along with DEM which will enhance security in Grid. It is expected that this paper will provide a better understanding of the technologies, potential advantages and research challenges of the smart grid and provoke interest among the research community to further explore this promising research area.
Chaitanya Krishna, E.; Kosaleswara Reddy, T.; Reddy, M. YogaTeja; Reddy G. M., Sreerama; Madhusudhan, E.; AlMuhteb, Sulaiman
ARGOT: accelerated radiative transfer on grids using oct-tree
NASA Astrophysics Data System (ADS)
We present two types of numerical prescriptions that accelerate the radiative transfer calculation around point sources within a three-dimensional Cartesian grid by using the oct-tree structure for the distribution of radiation sources. In one prescription, distant radiation sources are grouped as a bright extended source when the group's angular size, ?s, is smaller than a critical value, ?crit, and radiative transfer is solved on supermeshes whose angular size is similar to that of the group of sources. The supermesh structure is constructed by coarse-graining the mesh structure. With this method, the computational time scales with Nmlog (Nm)log (Ns), where Nm and Ns are the number of meshes and that of radiation sources, respectively. While this method is very efficient, it inevitably overestimates the optical depth when a group of sources acts as an extended powerful radiation source and affects distant meshes. In the other prescription, a distant group of sources is treated as a bright point source ignoring the spatial extent of the group, and the radiative transfer is solved on the meshes rather than the supermeshes. This prescription is simply a grid-based version of START by Hasegawa & Umemura and yields better results in general with slightly more computational cost [?] than the supermesh prescription. Our methods can easily be implemented to any grid-based hydrodynamic codes and are well suited to adaptive mesh refinement methods.
Okamoto, Takashi; Yoshikawa, Kohji; Umemura, Masayuki
Coordination of Client Services.
ERIC Educational Resources Information Center
Case coordination is an important social work activity with roots in the earliest objectives and functions of the profession. This article outlines the theoretical framework of case coordination and describes the tasks, skills, and knowledge essential to it. (Author)
Bertsche, Anne Vandeberg; Horejsi, Charles R.
Muscular Dystrophy Coordinating Committee
The Muscular Dystrophy Community Assistance, Research, and Education Amendments of 2001 ("MD-CARE Act"; P.L. 107-84) authorized the establishment of the Muscular Dystrophy Coordinating Committee (MDCC) to coordinate activities across NIH ...
NSDL National Science Digital Library
Become familiar with the coordinate plane. Learn the quadrants and how to graph points and read points on a coordinate plane. You are required to do the assignment and take the quiz. The other resources are to help prepare you for the quiz and book assignment. This is a quick review of the lesson.The Coordinate Plane This is a game to practice plotting and reading points.coordinates game *Assignment: Watch Powerpoint 3.3 and fill in your ...
Cook, Miss
NASA Astrophysics Data System (ADS)
SpaceGRID is an ESA study aimed at identifying the potential benefits of "Grids" to the ESA community and defining a road map for the implementation of this technol- ogy within ESA. Grid technology is an emerging computing infrastructure that is intended to provide uniform access to a set of distributed, networked resources that would otherwise be incompatible. Depending on the Grid application, the resources may be large-scale computational systems, data-archives or shared facilities constituting a collaborative working environment. The SpaceGRID study spans a broad range of domains including Earth Observation, various aspects of spacecraft engineering and Solar System research (solar, STP and planetary). In this presentation we provide an overview of the aims of the SpaceGRID study and report on the requirements analysis for the Solar System research field.
Perry, C. H.; Dunkin, S.; Grande, M.; Pike, C. D.; Stewart, B.; Beco, S.; SpaceGRID Consortium
NSDL National Science Digital Library
Hosted by IBM, the World Community Grid is an ambitious public-computing network developed to bolster humanitarian research around the world. The Grid gains its power through a vast network of computers, all contributing small pieces to large research projects while they are idle. At present the Grid is supporting the Institute for Systems Biology's Human Proteome Folding Project, which will ultimately contribute to disease prevention by developing a greater understanding of the shapes of human proteins. In addition to information about this ongoing project, the Grid website contains downloadable Request for Proposals documents, and a section for Project Archives. The site also provides simple instructions for joining the Grid; several online forums; and Grid statistics including current member totals.
Natural frequencies of arbitrarily shaped plates using the Rayleigh-Ritz method together with natural co-ordinate regions and normalized characteristic orthogonal polynomials
NASA Astrophysics Data System (ADS)
A Rayleigh-Ritz method mapping arbitrarily shaped plates on to a natural co-ordinate plane using serendipity functions is presented. The displacement function uses normalized beam characteristic orthogonal polynomials. The kinetic and strain energy equations are mapped from Cartesian co-ordinates to natural co-ordinates and the Rayleigh coefficient is minimized. Flexural free vibration analyses of various shaped plates is performed. Results are in excellent agreement with those found in the literature. This paper corrects the theory previously presented on this topic.
Geannakakes, G. N.
Processing Coordination Ambiguity
ERIC Educational Resources Information Center
We examined temporarily ambiguous coordination structures such as "put the butter in the bowl and the pan on the towel." Minimal Attachment predicts that the ambiguous noun phrase "the pan" will be interpreted as a noun-phrase coordination structure because it is syntactically simpler than clausal coordination. Constraint-based theories assume�
Engelhardt, Paul E.; Ferreira, Fernanda
LCLS Undulator Coordinate System
This note defines the LCLS undulator coordinate system and relates that coordinate system to the linear accelerator coordinate system. The slight downward pitch of the SLAC linac and the finite radius of the Earth necessitate some choices and definitions for the undulator layout which is described here. The layout described is consistent with the LCLS optics MAD file ''LCLS13APR04''.
Bong, E.
A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions. Appendix A
NASA Technical Reports Server (NTRS)
Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.
Constantinescu, George S.; Lele, S. K.
A nonhydrostatic model with a generalized vertical coordinate
NASA Astrophysics Data System (ADS)
The advantages of a hybrid coordinate representation which is isentropic in the free atmosphere are that it dynamically provides high resolution near the tropopause and fronts, and that truncation error of vertical advection terms virtually vanishes in the adiabatic limit. A complete set of compressible and nonhydrostatic equations framed in generalized vertical coordinates are introduced. The hybrid coordinate is implemented by prescribing the vertical velocity in the coordinate space subject to the conditions that its associated grid locations generally follow isentropic surfaces, and that the grid locations always vary monotonically in z. In this respect, the current set of equations represents a nonhydrostatic generalization of the hybrid isentropic system used with success in hydrostatic models. The numerical system has been tested using a series of two-dimensional mountain wave simulations. In the case of steep and tall mountains; it is found that the system is flexible and robust enough to simulate nonlinear flow phenomena, such as rotors, which represent serious obstacles to traditional entropy-related coordinate models. In addition, a three-dimensional dry baroclinic simulation has been used to compare the hybrid coordinate model with a traditional z coordinate model. It is found that the hybrid coordinate model has slight advantages over the z coordinate model in prediction of upper-level PV gradient near the tropopause and fronts.
He, Zuwen
Automatic unstructured grid generators
A review of automatic unstructured grid generators is given. These types of grids have found widespread use in computational fluid dynamics, computational structural dynamics, computational electro-magnetics and computational thermodynamics. The following topics are treated: the methods most commonly used, the specification of desired element size\\/shape and surface definition\\/meshing. Finally, the use of automatic grid generators as an enabling technology for
Rainald L�hner
Unstructured surface grid generation
NASA Technical Reports Server (NTRS)
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.
Samareh-Abolhassani, Jamshid
Grid Computing Security Lecture
NSDL National Science Digital Library
Grid Computing Lecture~~Security: secure connection, authentication and authorization, password authentication, symmetric (secret) and asymmetric (public/private) key cyptography, RSA algorithm.
Ferner, Clayton; Wilkinson, Barry
Challenges facing production grids
Today's global communities of users expect quality of service from distributed Grid systems equivalent to that their local data centers. This must be coupled to ubiquitous access to the ensemble of processing and storage resources across multiple Grid infrastructures. We are still facing significant challenges in meeting these expectations, especially in the underlying security, a sustainable and successful economic model, and smoothing the boundaries between administrative and technical domains. Using the Open Science Grid as an example, I examine the status and challenges of Grids operating in production today.
Pordes, Ruth; /Fermilab
A typical embodiment of the invention provides structural support for the grids in a nuclear reactor fuel assembly. Illustratively, the external surfaces of water rods or instrument tubes in a fuel assembly are provided with annular recesses. A spacer grid retainer is engaged within the recesses by means of spring loaded fingers on the retainer, in which the spring loading forces are greater than anticipated vibration forces to reduce fretting corrosion. Notches formed in the retainer secure the grid to the retainer, all in a manner that simplifies fuel assembly construction and restricts grid movement at lower cost.
Christiansen, D.W.
Design of a Vector-Vorticity Dynamical Core on a Hexagonal Grid (Hex-VVDC)
NASA Astrophysics Data System (ADS)
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.
Konor, C. S.; Heikes, R. P.; Jung, J.; Randall, D.; Arakawa, A.
PML-FDTD in cylindrical and spherical grids
Perfectly matched layers (PMLs) are derived for cylindrical and spherical finite-difference time-domain (FDTD) grids. The formulation relies on the complex coordinate stretching approach. Two-dimensional (2-D) cylindrical and three-dimensional (3-D) spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation by showing very good agreement between the perfectly matched layer-finite-difference time-domain (FDTD)
F. L. Teixeira; W. C. Chew
NASA Technical Reports Server (NTRS)
SAGE, Self Adaptive Grid codE, is a flexible tool for adapting and restructuring both 2D and 3D grids. Solution-adaptive grid methods are useful tools for efficient and accurate flow predictions. In supersonic and hypersonic flows, strong gradient regions such as shocks, contact discontinuities, shear layers, etc., require careful distribution of grid points to minimize grid error and produce accurate flow-field predictions. SAGE helps the user obtain more accurate solutions by intelligently redistributing (i.e. adapting) the original grid points based on an initial or interim flow-field solution. The user then computes a new solution using the adapted grid as input to the flow solver. The adaptive-grid methodology poses the problem in an algebraic, unidirectional manner for multi-dimensional adaptations. The procedure is analogous to applying tension and torsion spring forces proportional to the local flow gradient at every grid point and finding the equilibrium position of the resulting system of grid points. The multi-dimensional problem of grid adaption is split into a series of one-dimensional problems along the computational coordinate lines. The reduced one dimensional problem then requires a tridiagonal solver to find the location of grid points along a coordinate line. Multi-directional adaption is achieved by the sequential application of the method in each coordinate direction. The tension forces direct the redistribution of points to the strong gradient region. To maintain smoothness and a measure of orthogonality of grid lines, torsional forces are introduced that relate information between the family of lines adjacent to one another. The smoothness and orthogonality constraints are direction-dependent, since they relate only the coordinate lines that are being adapted to the neighboring lines that have already been adapted. Therefore the solutions are non-unique and depend on the order and direction of adaption. Non-uniqueness of the adapted grid is acceptable since it makes possible an overall and local error reduction through grid redistribution. SAGE includes the ability to modify the adaption techniques in boundary regions, which substantially improves the flexibility of the adaptive scheme. The vectorial approach used in the analysis also provides flexibility. The user has complete choice of adaption direction and order of sequential adaptions without concern for the computational data structure. Multiple passes are available with no restraint on stepping directions; for each adaptive pass the user can choose a completely new set of adaptive parameters. This facility, combined with the capability of edge boundary control, enables the code to individually adapt multi-dimensional multiple grids. Zonal grids can be adapted while maintaining continuity along the common boundaries. For patched grids, the multiple-pass capability enables complete adaption. SAGE is written in FORTRAN 77 and is intended to be machine independent; however, it requires a FORTRAN compiler which supports NAMELIST input. It has been successfully implemented on Sun series computers, SGI IRIS's, DEC MicroVAX computers, HP series computers, the Cray YMP, and IBM PC compatibles. Source code is provided, but no sample input and output files are provided. The code reads three datafiles: one that contains the initial grid coordinates (x,y,z), one that contains corresponding flow-field variables, and one that contains the user control parameters. It is assumed that the first two datasets are formatted as defined in the plotting software package PLOT3D. Several machine versions of PLOT3D are available from COSMIC. The amount of main memory is dependent on the size of the matrix. The standard distribution medium for SAGE is a 5.25 inch 360K MS-DOS format diskette. It is also available on a .25 inch streaming magnetic tape cartridge in UNIX tar format or on a 9-track 1600 BPI ASCII CARD IMAGE format magnetic tape. SAGE was developed in 1989, first released as a 2D version in 1991 and updated to 3D in 1993.
Davies, C. B.
Bipolar coordinates for computation of transition duct flows
NASA Technical Reports Server (NTRS)
Numerical simulation techniques for flows in jet-engine transition ducts with changing cross sections are developed and demonstrated. The boundary-conforming grids required are generated using bipolar coordinates, and the singularities arising at the no-slip boundaries are treated as described by de Vahl Davis (1979) and Tsai and Levy (1987). Grids for several typical configurations are employed in computations with the three-dimensional laminar/turbulent viscous-flow solver of Levy et al. (1983), and the results are presented graphically. The scheme used to deal with singularities is shown to be robust, suggesting that the bipolar grids may be applicable to Navier-Stokes computations.
Madabhushi, R. K.; Levy, R.
GridMAT-MD: a grid-based membrane analysis tool for use with molecular dynamics.
GridMAT-MD is a new program developed to aid in the analysis of lipid bilayers from molecular dynamics simulations. It reads a GROMACS coordinate file and generates two types of data: a two-dimensional contour plot depicting membrane thickness, and a polygon-based tessellation of the individual lipid headgroups. GridMAT-MD can also account for proteins or small molecules within the headgroups of the lipids, closely approximating their occupied lateral area. The program requires no installation, is fast, and is freely available. PMID:19090582
Allen, William J; Lemkul, Justin A; Bevan, David R
Construction of Pierced Hemispherical Grids.
National Technical Information Service (NTIS)
This report describes an easy way to construct hemispherical grids and a procedure to cut holes of any shape through the grids without distorting the grid itself. The grid material may be either stainless steel or tungsten. The grid is made from a high tr...
P. A. Taylor
Construction of Pierced Hemispherical Grids.
National Technical Information Service (NTIS)
This reprint describes an easy way to construct hemispherical grids and a procedure to cut holes of any shape through the grids without distorting the grid itself. Such grids may be used as filters/or accelerators. The use of high-transparency grids in th...
P. A. Taylor
I have to admit a great measure of sympathy for the IT populace at large, when it is confronted by the barrage of hype around grid technology, particularly within the enterprise. Individual vendors have attempted to plant their flags in the notionally virgin technological territory and proclaim it as their own, using terms such as grid, autonomic, self-healing, self-managing, adaptive,
Paul Strong
National Technical Information Service (NTIS)
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...
T. Hinke
Smart Grid security technology
The security of the United States and the way of life of its citizens is dependant on the availability of the North American power grid. Much of the technology currently in use by the grid is outdated and in many cases unreliable. There have been three major blackouts in the past nine years. Further, the reliance on old technology leads
Anthony R. Metke; Randy L. Ekl
NASA Technical Reports Server (NTRS)
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Ives, David
Compressing Electrical Power Grids
In this paper we apply the Singular Value Decomposition (SVD) analysis to examining the coupling structure of an electrical power grid in order to highlight opportunities for reducing the network traffic, by identifying what are the salient data that need to be communicated between parts of the infrastructure to apply a control action. Our main finding is that typical grid
Zhifang Wang; Anna Scaglione; Robert J. Thomas
On composite overlapping grids
The fundamental principles, implementation, and applications of CMPGRD are reviewed; CMPGRD is a software package developed by Brown et al. (1988) to generate two- and three-dimensional curvilinear composite overlapping grids for flow computations. Particular attention is given to the numerical solution of partial differential equations (PDEs) on composite grids: discretization, interpolation, FDM convergence rates, and the treatment of elliptic and
David L. Brown; William D. Henshaw; Heinz-Otto Kreiss; Geoffrey Chesshire
ERIC Educational Resources Information Center
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)
Simco, Greg
Securing a Grid environment presents a distinctive set of challenges. This paper groups the activities that need to be secured into four categories: naming and authentication; secure communication; trust, policy, and authorization; and enforcement of access control. It examines the current state of the art in securing these processes and introduces new technologies that promise to meet the security requirements of Grids more completely.
Humphrey, Marty; Thompson, Mary R.; Jackson, Keith R.
Flexible Residential Smart Grid Simulation Framework
NASA Astrophysics Data System (ADS)
Different scheduling and coordination algorithms controlling household appliances' operations can potentially lead to energy consumption reduction and/or load balancing in conjunction with different electricity pricing methods used in smart grid programs. In order to easily implement different algorithms and evaluate their efficiency against other ideas, a flexible simulation framework is desirable in both research and business fields. However, such a platform is currently lacking or underdeveloped. In this thesis, we provide a simulation framework to focus on demand side residential energy consumption coordination in response to different pricing methods. This simulation framework, equipped with an appliance consumption library using realistic values, aims to closely represent the average usage of different types of appliances. The simulation results of traditional usage yield close matching values compared to surveyed real life consumption records. Several sample coordination algorithms, pricing schemes, and communication scenarios are also implemented to illustrate the use of the simulation framework.
Xiang, Wang
Optimal mass transport for higher dimensional adaptive grid generation
NASA Astrophysics Data System (ADS)
In this work, we describe an approach for higher dimensional adaptive grid generation based on solving the L2 Monge-Kantorovich problem (MKP) which is a special case of the classical optimal mass transportation problem. Two methods are developed for computing the coordinate transformation used to define the grid adaptation. For the first method, the transformation is determined by solving a parabolic Monge-Amp�re equation for a steady state solution. For the second method, the grid movement is determined from the velocity field obtained by solving a fluid dynamics formulation of the L2 MKP. Several numerical experiments are presented to demonstrate the performance of the MKP methods and to compare them with some related adaptive grid methods. The experimental results demonstrate that the MKP methods show promise as effective and reliable methods for higher dimensional adaptive grid generation.
Sulman, Mohamed; Williams, J. F.; Russell, R. D.
Gravity inversion in spherical coordinates using tesseroids
NASA Astrophysics Data System (ADS)
Satellite observations of the gravity field have provided geophysicists with exceptionally dense and uniform coverage of data over vast areas. This enables regional or global scale high resolution geophysical investigations. Techniques like forward modeling and inversion of gravity anomalies are routinely used to investigate large geologic structures, such as large igneous provinces, suture zones, intracratonic basins, and the Moho. Accurately modeling such large structures requires taking the sphericity of the Earth into account. A reasonable approximation is to assume a spherical Earth and use spherical coordinates. In recent years, efforts have been made to advance forward modeling in spherical coordinates using tesseroids, particularly with respect to speed and accuracy. Conversely, traditional space domain inverse modeling methods have not yet been adapted to use spherical coordinates and tesseroids. In the literature there are a range of inversion methods that have been developed for Cartesian coordinates and right rectangular prisms. These include methods for estimating the relief of an interface, like the Moho or the basement of a sedimentary basin. Another category includes methods to estimate the density distribution in a medium. The latter apply many algorithms to solve the inverse problem, ranging from analytic solutions to random search methods as well as systematic search methods. We present an adaptation for tesseroids of the systematic search method of "planting anomalous densities". This method can be used to estimate the geometry of geologic structures. As prior information, it requires knowledge of the approximate densities and positions of the structures. The main advantage of this method is its computational efficiency, requiring little computer memory and processing time. We demonstrate the shortcomings and capabilities of this approach using applications to synthetic and field data. Performing the inversion of gravity and gravity gradient data, simultaneously or separately, is straight forward and requires no changes to the existing algorithm. Such feature makes it ideal for inverting the multicomponent gravity gradient data from the GOCE satellite. An implementation of our adaptation is freely available in the open-source modeling and inversion package Fatiando a Terra (http://www.fatiando.org).
Uieda, Leonardo; Barbosa, Valeria C. F.
Characterizing and Correcting Gradient Errors in Non-Cartesian Imaging: Are Gradient Errors Linear-Time-Invariant?
Non-Cartesian and rapid imaging sequences are more sensitive to scanner imperfections such as gradient delays and eddy currents. These imperfections vary between scanners and over time and can be a significant impediment towards successful implementation and eventual adoption of non-Cartesian techniques by scanner manufacturers. Differences between the k-space trajectory desired and the trajectory actually acquired lead to misregistration and reduction in image quality. While early calibration methods required considerable scan time, more recent methods can work more quickly by making certain approximations. We examine a rapid gradient calibration procedure applied to multi-echo 3DPR acquisitions where the calibration runs as part of every scan. After measuring the trajectories traversed for excitations on each of the orthogonal gradient axes, trajectories for the oblique projections actually acquired during the scan are synthesized as linear combinations of these measurements. The ability to do rapid calibration depends on the assumption that gradient errors are linear and time-invariant. This work examines the validity of these assumptions and shows that the assumption of linearity is reasonable, but that gradient errors can vary over short time periods (due to changes in gradient coil temperature) and thus it is important to use calibration data matched to the scan data.
Brodsky, Ethan K.; Samsonov, Alexey A.; Block, Walter F.
Parallel grid library for rapid and flexible simulation development
NASA Astrophysics Data System (ADS)
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as cell data. The amount of data in grid cells can vary both in space and time allowing dccrg to be used in very different types of simulations, for example in fluid and particle codes. Dccrg transfers the data between neighboring cells on different processes transparently and asynchronously allowing one to overlap computation and communication. This enables excellent scalability at least up to 32 k cores in magnetohydrodynamic tests depending on the problem and hardware. In the version of dccrg presented here part of the mesh metadata is replicated between MPI processes reducing the scalability of adaptive mesh refinement (AMR) to between 200 and 600 processes. Dccrg is free software that anyone can use, study and modify and is available at https://gitorious.org/dccrg. Users are also kindly requested to cite this work when publishing results obtained with dccrg. Program summaryProgram title: DCCRG Catalogue identifier: AEOM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 54975 No. of bytes in distributed program, including test data, etc.: 974015 Distribution format: tar.gz Programming language: C++. Computer: PC, cluster, supercomputer. Operating system: POSIX. The code has been parallelized using MPI and tested with 1-32768 processes RAM: 10 MB-10 GB per process Classification: 4.12, 4.14, 6.5, 19.3, 19.10, 20. External routines: MPI-2 [1], boost [2], Zoltan [3], sfc++ [4] Nature of problem: Grid library supporting arbitrary data in grid cells, parallel adaptive mesh refinement, transparent remote neighbor data updates and load balancing. Solution method: The simulation grid is represented by an adjacency list (graph) with vertices stored into a hash table and edges into contiguous arrays. Message Passing Interface standard is used for parallelization. Cell data is given as a template parameter when instantiating the grid. Restrictions: Logically cartesian grid. Running time: Running time depends on the hardware, problem and the solution method. Small problems can be solved in under a minute and very large problems can take weeks. The examples and tests provided with the package take less than about one minute using default options. In the version of dccrg presented here the speed of adaptive mesh refinement is at most of the order of 106 total created cells per second.
Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.
Tax Coordination and Unemployment
This paper analyses the implications of unemployment for fiscal competition and tax coordination among small open economies.\\u000a Unemployment is modeled as resulting from wage bargaining. The analysis focuses on the effect of labour and capital tax coordination\\u000a on welfare. We show that, while coordinated capital and labour tax increases unambiguously raise welfare if labour markets\\u000a are competitive, different results emerge
Clemens Fuest; Bernd Huber
A unified formulation for the three-dimensional shallow water equations using orthogonal co-ordinates: theory and application
NASA Astrophysics Data System (ADS)
In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a ?-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50-100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains acceptable for very large model domains.
Kernkamp, Herman W. J.; Petit, Henri A. H.; Gerritsen, Herman; de Goede, Erik D.
On Multigrid for Overlapping Grids
We describe various aspects of solving elliptic boundary value problems on overlapping grids. We describe the Overlapping-Grid-MultiGrid-solver, Ogmg, that can be used to obtain solutions to elliptic boundary value problems. Ogmg solves problems in two and three space dimensions on composite overlapping grids. Second and fourth-order accurate approximations are supported. Given an overlapping grid generated from the Ogen grid generator,
William D. Henshaw