Science.gov

Sample records for algebraic mesh quality

  1. Algebraic surface design and finite element meshes

    NASA Technical Reports Server (NTRS)

    Bajaj, Chandrajit L.

    1992-01-01

    Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.

  2. Mesh Quality Improvement Toolkit

    2002-11-15

    MESQUITE is a linkable software library to be used by simulation and mesh generation tools to improve the quality of meshes. Mesh quality is improved by node movement and/or local topological modifications. Various aspects of mesh quality such as smoothness, element shape, size, and orientation are controlled by choosing the appropriate mesh qualtiy metric, and objective function tempate, and a numerical optimization solver to optimize the quality of meshes, MESQUITE uses the TSTT mesh interfacemore » specification to provide an interoperable toolkit that can be used by applications which adopt the standard. A flexible code design makes it easy for meshing researchers to add additional mesh quality metrics, templates, and solvers to develop new quality improvement algorithms by making use of the MESQUITE infrastructure.« less

  3. Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix

    NASA Technical Reports Server (NTRS)

    Kerlick, G. D.; Klopfer, G. H.

    1982-01-01

    An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.

  4. A Linear Algebra Measure of Cluster Quality.

    ERIC Educational Resources Information Center

    Mather, Laura A.

    2000-01-01

    Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)

  5. Quality Mesh Smoothing via Local Surface Fitting and Optimum Projection

    PubMed Central

    Wang, Jun; Yu, Zeyun

    2011-01-01

    The smoothness and angle quality of a surface mesh are two important indicators of the “goodness” of the mesh for downstream applications such as visualization and numerical simulation. We present in this paper a novel surface mesh processing method not only to reduce mesh noise but to improve angle quality as well. Our approach is based on the local surface fitting around each vertex using the least square minimization technique. The new position of the vertex is obtained by finding the maximum inscribed circle (MIC) of the surrounding polygon and projecting the circle’s center onto the analytically fitted surface. The procedure above repeats until the maximal vertex displacement is less than a pre-defined threshold. The mesh smoothness is improved by a combined idea of surface fitting and projection, while the angle quality is achieved by utilizing the MIC-based projection scheme. Results on a variety of geometric mesh models have demonstrated the effectiveness of our method. PMID:21686314

  6. Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.

    PubMed

    Gao, Zhanheng; Yu, Zeyun; Holst, Michael

    2012-12-01

    Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.

  7. A structured multi-block solution-adaptive mesh algorithm with mesh quality assessment

    NASA Technical Reports Server (NTRS)

    Ingram, Clint L.; Laflin, Kelly R.; Mcrae, D. Scott

    1995-01-01

    The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.

  8. Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality.

    PubMed

    Bronson, Jonathan R; Levine, Joshua A; Whitaker, Ross T

    2013-01-01

    We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

  9. Quality metrics for high order meshes: analysis of the mechanical simulation of the heart beat.

    PubMed

    Lamata, Pablo; Roy, Ishani; Blazevic, Bojan; Crozier, Andrew; Land, Sander; Niederer, Steven A; Hose, D Rod; Smith, Nicolas P

    2013-01-01

    The quality of a computational mesh is an important characteristic for stable and accurate simulations. Quality depends on the regularity of the initial mesh, and in mechanical simulations it evolves in time, with deformations causing changes in volume and distortion of mesh elements. Mesh quality metrics are therefore relevant for both mesh personalization and the monitoring of the simulation process. This work evaluates the significance, in meshes with high order interpolation, of four quality metrics described in the literature, applying them to analyse the stability of the simulation of the heart beat. It also investigates how image registration and mesh warping parameters affect the quality and stability of meshes. Jacobian-based metrics outperformed or matched the results of coarse geometrical metrics of aspect ratio or orthogonality, although they are more expensive computationally. The stability of simulations of a complete heart cycle was best predicted with a specificity of 61%, sensitivity of 85%, and only nominal differences were found changing the intra-element and per-element combination of quality values. A compromise between fitting accuracy and mesh stability and quality was found. Generic geometrical quality metrics have a limited success predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.

  10. Quality Partitioned Meshing of Multi-Material Objects

    PubMed Central

    Zhang, Qin; Cha, Deukhyun; Bajaj, Chandrajit

    2016-01-01

    We present a simple but effective algorithm for generating topologically and geometrically consistent quality triangular surface meshing of compactly packed multiple heterogeneous domains in R3. By compact packing we imply that adjacent homogeneous domains or materials share some 0, 1, and/or 2 dimensional boundary. Such packed multiple material (or multi-material) solids arise naturally from classification/partitioning/segmentation of homogeneous domains in R3 into different sub-regions. The multi-materials may also represent separate functionally classified sections or just be multiple component copies tightly fused together as perhaps by layered manufacturing processes. The input to our algorithm is a geometric representation of the entire multi-material solid, and a volumetric classification map identifying the individual materials. As output, each individual material region is represented by a triangulated 2-manifold boundary, with adjacent material regions having shared boundaries. Our algorithm has been implemented, and applied to different multi-material solids, and the results are additionally presented with quantitative analysis of detection and cure of non-manifold interfaces as well as spurious small components. These meshes are useful for combined boundary element analysis, however these simulation results are not presented. PMID:27563367

  11. Production-quality Tools for Adaptive Mesh RefinementVisualization

    SciTech Connect

    Weber, Gunther H.; Childs, Hank; Bonnell, Kathleen; Meredith,Jeremy; Miller, Mark; Whitlock, Brad; Bethel, E. Wes

    2007-10-25

    Adaptive Mesh Refinement (AMR) is a highly effectivesimulation method for spanning a large range of spatiotemporal scales,such as astrophysical simulations that must accommodate ranges frominterstellar to sub-planetary. Most mainstream visualization tools stilllack support for AMR as a first class data type and AMR code teams usecustom built applications for AMR visualization. The Department ofEnergy's (DOE's) Science Discovery through Advanced Computing (SciDAC)Visualization and Analytics Center for Enabling Technologies (VACET) isextending and deploying VisIt, an open source visualization tool thataccommodates AMR as a first-class data type, for use asproduction-quality, parallel-capable AMR visual data analysisinfrastructure. This effort will help science teams that use AMR-basedsimulations and who develop their own AMR visual data analysis softwareto realize cost and labor savings.

  12. New high quality adaptive mesh generator utilized in modelling plasma streamer propagation at atmospheric pressures

    NASA Astrophysics Data System (ADS)

    Papadakis, A. P.; Georghiou, G. E.; Metaxas, A. C.

    2008-12-01

    A new adaptive mesh generator has been developed and used in the analysis of high-pressure gas discharges, such as avalanches and streamers, reducing computational times and computer memory needs significantly. The new adaptive mesh generator developed, uses normalized error indicators, varying from 0 to 1, to guarantee optimal mesh resolution for all carriers involved in the analysis. Furthermore, it uses h- and r-refinement techniques such as mesh jiggling, edge swapping and node addition/removal to develop an element quality improvement algorithm that improves the mesh quality significantly and a fast and accurate algorithm for interpolation between meshes. Finally, the mesh generator is applied in the characterization of the transition from a single electron to the avalanche and streamer discharges in high-voltage, high-pressure gas discharges for dc 1 mm gaps, RF 1 cm point-plane gaps and parallel-plate 40 MHz configurations, in ambient atmospheric air.

  13. Application of Quaternions for Mesh

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    2002-01-01

    A new three dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

  14. A universal algorithm for an improved finite element mesh generation Mesh quality assessment in comparison to former automated mesh-generators and an analytic model.

    PubMed

    Kaminsky, Jan; Rodt, Thomas; Gharabaghi, Alireza; Forster, Jan; Brand, Gerd; Samii, Madjid

    2005-06-01

    The FE-modeling of complex anatomical structures is not solved satisfyingly so far. Voxel-based as opposed to contour-based algorithms allow an automated mesh generation based on the image data. Nonetheless their geometric precision is limited. We developed an automated mesh-generator that combines the advantages of voxel-based generation with improved representation of the geometry by displacement of nodes on the object-surface. Models of an artificial 3D-pipe-section and a skullbase were generated with different mesh-densities using the newly developed geometric, unsmoothed and smoothed voxel generators. Compared to the analytic calculation of the 3D-pipe-section model the normalized RMS error of the surface stress was 0.173-0.647 for the unsmoothed voxel models, 0.111-0.616 for the smoothed voxel models with small volume error and 0.126-0.273 for the geometric models. The highest element-energy error as a criterion for the mesh quality was 2.61x10(-2) N mm, 2.46x10(-2) N mm and 1.81x10(-2) N mm for unsmoothed, smoothed and geometric voxel models, respectively. The geometric model of the 3D-skullbase resulted in the lowest element-energy error and volume error. This algorithm also allowed the best representation of anatomical details. The presented geometric mesh-generator is universally applicable and allows an automated and accurate modeling by combining the advantages of the voxel-technique and of improved surface-modeling.

  15. Application of Quaternions for Mesh Deformation

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    2002-01-01

    A new three-dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

  16. A priori mesh quality metrics for three-dimensional hybrid grids

    SciTech Connect

    Kallinderis, Y. Fotia, S.

    2015-01-01

    Use of general hybrid grids to attain complex-geometry field simulations poses a challenge on estimation of their quality. Apart from the typical problems of non-uniformity and non-orthogonality, the change in element topology is an extra issue to address. The present work derives and evaluates an a priori mesh quality indicator for structured, unstructured, as well as hybrid grids consisting of hexahedra, prisms, tetrahedra, and pyramids. Emphasis is placed on deriving a direct relation between the quality measure and mesh distortion. The work is based on use of the Finite Volume discretization for evaluation of first order spatial derivatives. The analytic form of the truncation error is derived and applied to elementary types of mesh distortion including typical hybrid grid interfaces. The corresponding analytic expressions provide relations between the truncation error and the degree of stretching, skewness, shearing, torsion, expansion, as well as the type of grid interface.

  17. Local meshing plane analysis as a source of information about the gear quality

    NASA Astrophysics Data System (ADS)

    Mączak, Jędrzej

    2013-07-01

    In the paper the application of the local meshing plane concept is discussed and applied for detecting of tooth degradation due to fatigue, and for overall gear quality assessment. Knowing the kinematic properties of the machine (i.e. gear tooth numbers) it is possible to modify the diagnostic signal in such a manner that its fragments will be linked to different rotating parts. This allows for presentation of either raw or processed gearbox signal in a form of three dimensional map on the plane "pinion teeth×gear teeth", called local meshing plane. The meshing plane in Cartesian coordinates z1×z2 allows for precise location and assessment of gear faults in terms of meshing quality of consecutive tooth pairs. Although the method was applied to simulated signals generated by the gearbox model, similar results were obtained for the measurement signals recorded during the back-to-back test stand experiment. The described method could be used for assessing the manufacturing quality of gears, the assembly quality as well as for the gear failure evaluation during normal exploitation.

  18. Automatic MeSH term assignment and quality assessment.

    PubMed Central

    Kim, W.; Aronson, A. R.; Wilbur, W. J.

    2001-01-01

    For computational purposes documents or other objects are most often represented by a collection of individual attributes that may be strings or numbers. Such attributes are often called features and success in solving a given problem can depend critically on the nature of the features selected to represent documents. Feature selection has received considerable attention in the machine learning literature. In the area of document retrieval we refer to feature selection as indexing. Indexing has not traditionally been evaluated by the same methods used in machine learning feature selection. Here we show how indexing quality may be evaluated in a machine learning setting and apply this methodology to results of the Indexing Initiative at the National Library of Medicine. PMID:11825203

  19. Instructional Quality and Student Learning in Higher Education: Evidence from Developmental Algebra Courses

    ERIC Educational Resources Information Center

    Chingos, Matthew M.

    2016-01-01

    Little is known about the importance of instructional quality in American higher education because few recent studies have had access to direct measures of student learning that are comparable across sections of the same course. Using data from two developmental algebra courses at a large community college, I found that student learning varies…

  20. High-quality conforming hexahedral meshes of patient-specific abdominal aortic aneurysms including their intraluminal thrombi.

    PubMed

    Tarjuelo-Gutierrez, J; Rodriguez-Vila, B; Pierce, D M; Fastl, T E; Verbrugghe, P; Fourneau, I; Maleux, G; Herijgers, P; Holzapfel, G A; Gomez, E J

    2014-02-01

    In order to perform finite element (FE) analyses of patient-specific abdominal aortic aneurysms, geometries derived from medical images must be meshed with suitable elements. We propose a semi-automatic method for generating conforming hexahedral meshes directly from contours segmented from medical images. Magnetic resonance images are generated using a protocol developed to give the abdominal aorta high contrast against the surrounding soft tissue. These data allow us to distinguish between the different structures of interest. We build novel quadrilateral meshes for each surface of the sectioned geometry and generate conforming hexahedral meshes by combining the quadrilateral meshes. The three-layered morphology of both the arterial wall and thrombus is incorporated using parameters determined from experiments. We demonstrate the quality of our patient-specific meshes using the element Scaled Jacobian. The method efficiently generates high-quality elements suitable for FE analysis, even in the bifurcation region of the aorta into the iliac arteries. For example, hexahedral meshes of up to 125,000 elements are generated in less than 130 s, with 94.8 % of elements well suited for FE analysis. We provide novel input for simulations by independently meshing both the arterial wall and intraluminal thrombus of the aneurysm, and their respective layered morphologies.

  1. Spherical geodesic mesh generation

    SciTech Connect

    Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich

    2015-02-27

    In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.

  2. A Program to Improve the Triangulated Surface Mesh Quality Along Aircraft Component Intersections

    NASA Technical Reports Server (NTRS)

    Cliff, Susan E.

    2005-01-01

    A computer program has been developed for improving the quality of unstructured triangulated surface meshes in the vicinity of component intersections. The method relies solely on point removal and edge swapping for improving the triangulations. It can be applied to any lifting surface component such as a wing, canard or horizontal tail component intersected with a fuselage, or it can be applied to a pylon that is intersected with a wing, fuselage or nacelle. The lifting surfaces or pylon are assumed to be aligned in the axial direction with closed trailing edges. The method currently maintains salient edges only at leading and trailing edges of the wing or pylon component. This method should work well for any shape of fuselage that is free of salient edges at the intersection. The method has been successfully demonstrated on a total of 125 different test cases that include both blunt and sharp wing leading edges. The code is targeted for use in the automated environment of numerical optimization where geometric perturbations to individual components can be critical to the aerodynamic performance of a vehicle. Histograms of triangle aspect ratios are reported to assess the quality of the triangles attached to the intersection curves before and after application of the program. Large improvements to the quality of the triangulations were obtained for the 125 test cases; the quality was sufficient for use with an automated tetrahedral mesh generation program that is used as part of an aerodynamic shape optimization method.

  3. Influence of different mesh filter module configurations on effluent quality and long-term filtration performance.

    PubMed

    Loderer, Christian; Wörle, Anna; Fuchs, Werner

    2012-04-01

    Recently, a new type of wastewater treatment system became the focus of scientific research: the mesh filter activated sludge system. It is a modification of the membrane bioreactor (MBR), in which a membrane filtration process serves for sludge separation. The main difference is that a mesh filter is used instead of the membrane. The effluent is not of the same excellent quality as with membrane bioreactors due to the much lager pore sizes of the mesh. Nevertheless, it still resembles the quality of currently used standard treatment system, the activated sludge process. The new process shows high future potential as an alternative where a small footprint of these plants is required (3 times lower footprint than conventional activated sludge systems because of neglecting the secondary clarifier and reducing the biological stage). However, so far only limited information on this innovative process is available. In this study, the effect of different pore sizes and different mesh module configurations on the effluent quality was investigated varying the parameters cross-flow velocity (CFV) and flux rate. Furthermore the long-term filtration performance was studied in a pilot reactor system and results were compared to the full-scale conventional activated sludge process established at the same site. The results demonstrate that the configuration of the filter module has little impact on effluent quality and is only of importance with regard to engineering aspects. Most important for a successful operation are the hydrodynamic conditions within the filter module. The statement "the higher the pore size the higher the effluent turbidity" was verified. Excellent effluent quality with suspended solids between 5 and 15 mg L(-1) and high biological elimination rates (chemical oxygen demand (COD) 90-95%, biological oxygen demand (BOD5) 94-98%, total nitrogen (TN) 70-80%, and ammonium nitrogen (NH(4)-N) 95-99%) were achieved and also compared to those of conventional

  4. Influence of different mesh filter module configurations on effluent quality and long-term filtration performance.

    PubMed

    Loderer, Christian; Wörle, Anna; Fuchs, Werner

    2012-04-01

    Recently, a new type of wastewater treatment system became the focus of scientific research: the mesh filter activated sludge system. It is a modification of the membrane bioreactor (MBR), in which a membrane filtration process serves for sludge separation. The main difference is that a mesh filter is used instead of the membrane. The effluent is not of the same excellent quality as with membrane bioreactors due to the much lager pore sizes of the mesh. Nevertheless, it still resembles the quality of currently used standard treatment system, the activated sludge process. The new process shows high future potential as an alternative where a small footprint of these plants is required (3 times lower footprint than conventional activated sludge systems because of neglecting the secondary clarifier and reducing the biological stage). However, so far only limited information on this innovative process is available. In this study, the effect of different pore sizes and different mesh module configurations on the effluent quality was investigated varying the parameters cross-flow velocity (CFV) and flux rate. Furthermore the long-term filtration performance was studied in a pilot reactor system and results were compared to the full-scale conventional activated sludge process established at the same site. The results demonstrate that the configuration of the filter module has little impact on effluent quality and is only of importance with regard to engineering aspects. Most important for a successful operation are the hydrodynamic conditions within the filter module. The statement "the higher the pore size the higher the effluent turbidity" was verified. Excellent effluent quality with suspended solids between 5 and 15 mg L(-1) and high biological elimination rates (chemical oxygen demand (COD) 90-95%, biological oxygen demand (BOD5) 94-98%, total nitrogen (TN) 70-80%, and ammonium nitrogen (NH(4)-N) 95-99%) were achieved and also compared to those of conventional

  5. Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

    NASA Technical Reports Server (NTRS)

    Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

    2013-01-01

    Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

  6. Matrix Norms and the Condition Number: A General Framework to Improve Mesh Quality via Node-Movement

    SciTech Connect

    KNUPP,PATRICK

    1999-09-27

    Objective functions for unstructured hexahedral and tetrahedral mesh optimization are analyzed using matrices and matrix norms. Mesh untangling objective functions that create valid meshes are used to initialize the optimization process. Several new objective functions to achieve element invertibility and quality are investigated, the most promising being the ''condition number''. The condition number of the Jacobian matrix of an element forms the basis of a barrier-based objective function that measures the distance to the set of singular matrices and has the ideal matrix as a stationary point. The method was implemented in the Cubit code, with promising results.

  7. Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

    NASA Technical Reports Server (NTRS)

    Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

    1992-01-01

    Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

  8. Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography

    NASA Astrophysics Data System (ADS)

    Jermyn, Michael; Ghadyani, Hamid; Mastanduno, Michael A.; Turner, Wes; Davis, Scott C.; Dehghani, Hamid; Pogue, Brian W.

    2013-08-01

    Multimodal approaches that combine near-infrared (NIR) and conventional imaging modalities have been shown to improve optical parameter estimation dramatically and thus represent a prevailing trend in NIR imaging. These approaches typically involve applying anatomical templates from magnetic resonance imaging/computed tomography/ultrasound images to guide the recovery of optical parameters. However, merging these data sets using current technology requires multiple software packages, substantial expertise, significant time-commitment, and often results in unacceptably poor mesh quality for optical image reconstruction, a reality that represents a significant roadblock for translational research of multimodal NIR imaging. This work addresses these challenges directly by introducing automated digital imaging and communications in medicine image stack segmentation and a new one-click three-dimensional mesh generator optimized for multimodal NIR imaging, and combining these capabilities into a single software package (available for free download) with a streamlined workflow. Image processing time and mesh quality benchmarks were examined for four common multimodal NIR use-cases (breast, brain, pancreas, and small animal) and were compared to a commercial image processing package. Applying these tools resulted in a fivefold decrease in image processing time and 62% improvement in minimum mesh quality, in the absence of extra mesh postprocessing. These capabilities represent a significant step toward enabling translational multimodal NIR research for both expert and nonexpert users in an open-source platform.

  9. Dubai 3d Textuerd Mesh Using High Quality Resolution Vertical/oblique Aerial Imagery

    NASA Astrophysics Data System (ADS)

    Tayeb Madani, Adib; Ziad Ahmad, Abdullateef; Christoph, Lueken; Hammadi, Zamzam; Manal Abdullah Sabeal, Manal Abdullah x.

    2016-06-01

    Providing high quality 3D data with reasonable quality and cost were always essential, affording the core data and foundation for developing an information-based decision-making tool of urban environments with the capability of providing decision makers, stakeholders, professionals, and public users with 3D views and 3D analysis tools of spatial information that enables real-world views. Helps and assist in improving users' orientation and also increase their efficiency in performing their tasks related to city planning, Inspection, infrastructures, roads, and cadastre management. In this paper, the capability of multi-view Vexcel UltraCam Osprey camera images is examined to provide a 3D model of building façades using an efficient image-based modeling workflow adopted by commercial software's. The main steps of this work include: Specification, point cloud generation, and 3D modeling. After improving the initial values of interior and exterior parameters at first step, an efficient image matching technique such as Semi Global Matching (SGM) is applied on the images to generate point cloud. Then, a mesh model of points is calculated using and refined to obtain an accurate model of buildings. Finally, a texture is assigned to mesh in order to create a realistic 3D model. The resulting model has provided enough LoD2 details of the building based on visual assessment. The objective of this paper is neither comparing nor promoting a specific technique over the other and does not mean to promote a sensor-based system over another systems or mechanism presented in existing or previous paper. The idea is to share experience.

  10. Quality-of-service-based protection in MPLS control WDM mesh networks

    NASA Astrophysics Data System (ADS)

    Wen, Wushao; Mukherjee, Biswanath; Yoo, S. J. B.

    2001-10-01

    Intelligent methods for automatic protection and restoration are critical in optical transport mesh networks. This paper discusses the problem of quality of service (QoS)-based protection in term of the protection-switching time and availability for end-to-end lightpaths in a WDM mesh network. We analyze the backup lightpath-sharing problem in such networks and study the correlation of the working lightpaths and its impact to the sharing of their backup lightpaths. We present a multi-protocol-label-switching (MPLS) control-based fully distributed algorithm to solve the protection problem. The proposed algorithm includes intelligent and fully automatic procedures to set up, take down, activate, restore, and manage backup lightpaths. It greatly reduces the required resources for protection by allowing the sharing of network resources by multiple backup lightpaths. At the same time, it guarantees, if possible, to satisfy the availability requirement even with resource sharing by taking the correlation of working lightpaths into consideration when deciding backup lightpaths. A simple analysis of the proposed algorithm in terms of computation, time, and message complexity indicates that the implementation of the algorithm is practical. The illustrative studies that compare the performance of 1:1, unlimited sharing, and QoS-based sharing backup algorithms indicates that QoS-based sharing achieves comparable performance as unlimited sharing, which is much better than the 1:1 backup scheme in terms of connection blocking probability, average number of connections in the network for a given offered load, and network-resource utilization.

  11. Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Part II - A Framework for Volume Mesh Optimization and the Condition Number of the Jacobian Matrix

    SciTech Connect

    Knupp, P.M.

    1999-03-26

    Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices. significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equivalence in two-dimensions of the Smoothness and Condition Number of the Jacobian matrix objective functions does not extend to three dimensions and further. that the equivalence of the Oddy and Condition Number of the Metric Tensor objective functions in two-dimensions also fails to extend to three-dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ''whisker-weaved'' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure.

  12. Excellence through Mathematics Communication and Collaboration (E = mc[squared]): A New Approach to Quality in College Algebra

    ERIC Educational Resources Information Center

    Marshall, Gerald L.; Riedel, Herbert H. J.

    2005-01-01

    Within the context of traditional quality management principles, a program designed to enhance soft skills of College Algebra students was piloted in fall 2001. Results of the pilot project include increased retention, persistence, note-taking ability, and positive responses concerning course expectations. Quality enhancement efforts in this…

  13. Multigrid techniques for unstructured meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.

    1995-01-01

    An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

  14. NON-CONFORMING FINITE ELEMENTS; MESH GENERATION, ADAPTIVITY AND RELATED ALGEBRAIC MULTIGRID AND DOMAIN DECOMPOSITION METHODS IN MASSIVELY PARALLEL COMPUTING ENVIRONMENT

    SciTech Connect

    Lazarov, R; Pasciak, J; Jones, J

    2002-02-01

    Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.

  15. Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)

    NASA Astrophysics Data System (ADS)

    Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.

    2015-10-01

    An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

  16. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  17. Examining the Relationship of QualityCore[R] Implementation and Student Achievement in Algebra I. ACT Research Report Series, 2012 (4)

    ERIC Educational Resources Information Center

    Ndum, Edwin; Allen, Jeff; Fisher, Teri

    2012-01-01

    We assessed the relationship of level of QualityCore[R] implementation and student achievement in Algebra I. The study is based on 1,291 9th grade students in three large metropolitan school districts who took EXPLORE in the fall and the QualityCore Algebra I end-of-course assessment (EOC) in the spring. During the same period, the students' 41…

  18. A prospective randomised controlled trial comparing chronic groin pain and quality of life in lightweight versus heavyweight polypropylene mesh in laparoscopic inguinal hernia repair

    PubMed Central

    Prakash, Pradeep; Bansal, Virinder Kumar; Misra, Mahesh Chandra; Babu, Divya; Sagar, Rajesh; Krishna, Asuri; Kumar, Subodh; Rewari, Vimi; Subramaniam, Rajeshwari

    2016-01-01

    BACKGROUND: The aim of our study was to compare chronic groin pain and quality of life (QOL) after laparoscopic lightweight (LW) and heavyweight (HW) mesh repair for groin hernia. MATERIALS AND METHODS: One hundred and forty adult patients with uncomplicated inguinal hernia were randomised into HW mesh group or LW mesh group. Return to activity, chronic groin pain and recurrence rates were assessed. Short form-36 v2 health survey was used for QOL analysis. RESULTS: One hundred and thirty-one completed follow-up of 3 months, 66 in HW mesh group and 65 in LW mesh group. Early post-operative convalescence was better in LW mesh group in terms of early return to walking (P = 0.01) and driving (P = 0.05). The incidence of early post-operative pain, chronic groin pain and QOL and recurrences were comparable. CONCLUSION: Outcomes following laparoscopic inguinal hernia repair using HW and LW mesh are comparable in the short-term as well as long-term. PMID:27073309

  19. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  20. Color postprocessing for 3-dimensional finite element mesh quality evaluation and evolving graphical workstation

    NASA Technical Reports Server (NTRS)

    Panthaki, Malcolm J.

    1987-01-01

    Three general tasks on general-purpose, interactive color graphics postprocessing for three-dimensional computational mechanics were accomplished. First, the existing program (POSTPRO3D) is ported to a high-resolution device. In the course of this transfer, numerous enhancements are implemented in the program. The performance of the hardware was evaluated from the point of view of engineering postprocessing, and the characteristics of future hardware were discussed. Second, interactive graphical tools implemented to facilitate qualitative mesh evaluation from a single analysis. The literature was surveyed and a bibliography compiled. Qualitative mesh sensors were examined, and the use of two-dimensional plots of unaveraged responses on the surface of three-dimensional continua was emphasized in an interactive color raster graphics environment. Finally, a postprocessing environment was designed for state-of-the-art workstation technology. Modularity, personalization of the environment, integration of the engineering design processes, and the development and use of high-level graphics tools are some of the features of the intended environment.

  1. Acquire High Quality Meshes of Scale Models for AN Automatic Modelling Process

    NASA Astrophysics Data System (ADS)

    Giraud, F.; Jacquot, K.; Chevrier, C.; Halin, G.

    2013-07-01

    Urban scale models depicting whole towns such as the hundred-scale model collection known as plans-reliefs are a valuable source of information of cities and their surroundings. These physical representations of French strongholds from the 17th through the 19th century suffer from many problems that are, among other things, wear and tear or the lack of visibility and accessibility. A virtual collection would allow remote accessibility for visitors as well as history researchers. Moreover, it may also be linked to other digital collections and therefore, promote the collection to make people come to the museums to see the physical scale models. We also work on other physical town scale models like Epinal for which the scale is a bit higher. In a first part, we define a protocol for acquiring 3D meshes of town scale models from both photogrammetric and scanning methods. Then we compare the results of both methods The photogrammetric protocol has been elaborated by choosing the most accurate software, 123DCatch, which asks for about 60 pictures, and defining the settings needed to obtain exploitable photographs. In the same way, we defined the devices and settings needed for the laser scan acquisition method. In a second part, we segment the 3D meshes in planes by using Geomagic, which has been chosen between several programs, for its accurate resulting geometry.

  2. A search tool based on 'encapsulated' MeSH thesaurus to retrieve quality health resources on the internet.

    PubMed

    Darmoni, S J; Thirion, B; Leroyt, J P; Douyère, M; Lacoste, B; Godard, C; Rigolle, I; Brisou, M; Videau, S; Goupyt, E; Piott, J; Quéré, M; Ouazir, S; Abdulrab, H

    2001-01-01

    In the year 2001, the Internet has become a major source of health information for the health professional and the Netizen. The objective of Doc' CISMeF (D'C) was to create a powerful generic search tool based on a structured information model which 'encapsulates' the MeSH thesaurus to index and retrieve quality health resources on the Internet. To index resources, D'C uses four sections in its information model: 'meta-term', keyword, subheading, and resource type. Two search options are available: simple and advanced. The simple search requires the end-user to input a single term or expression. If this term belongs to the D'C information structure model, it will be exploded. If not, a full-text search is performed. In the advanced search, complex searches are possible combining Boolean operators with meta-terms, keywords, subheadings and resource types. D'C uses two standard tools for organising information: the MeSH thesaurus and the Dublin Core metadata format. Resources included in D'C are described according to the following elements: title, author or creator, subject and keywords, description, publishers, date, resource type, format, identifier, and language.

  3. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

  4. Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

    PubMed

    Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

    2016-01-01

    A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively. PMID:27186457

  5. Computer Algebra.

    ERIC Educational Resources Information Center

    Pavelle, Richard; And Others

    1981-01-01

    Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)

  6. Iterative methods for elliptic finite element equations on general meshes

    NASA Technical Reports Server (NTRS)

    Nicolaides, R. A.; Choudhury, Shenaz

    1986-01-01

    Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

  7. Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.

    1997-01-01

    An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.

  8. Cubit Adaptive Meshing Algorithm Library

    2004-09-01

    CAMAL (Cubit adaptive meshing algorithm library) is a software component library for mesh generation. CAMAL 2.0 includes components for triangle, quad and tetrahedral meshing. A simple Application Programmers Interface (API) takes a discrete boundary definition and CAMAL computes a quality interior unstructured grid. The triangle and quad algorithms may also import a geometric definition of a surface on which to define the grid. CAMAL’s triangle meshing uses a 3D space advancing front method, the quadmore » meshing algorithm is based upon Sandia’s patented paving algorithm and the tetrahedral meshing algorithm employs the GHS3D-Tetmesh component developed by INRIA, France.« less

  9. Enhancing the MeSH thesaurus to retrieve French online health resources in a quality-controlled gateway.

    PubMed

    Douyère, Magaly; Soualmia, Lina F; Névéol, Aurélie; Rogozan, Alexandrina; Dahamna, Badisse; Leroy, Jean-Philippe; Thirion, Benoît; Darmoni, Stefan J

    2004-12-01

    The amount of health information available on the Internet is considerable. In this context, several health gateways have been developed. Among them, CISMeF (Catalogue and Index of Health Resources in French) was designed to catalogue and index health resources in French. The goal of this article is to describe the various enhancements to the MeSH thesaurus developed by the CISMeF team to adapt this terminology to the broader field of health Internet resources instead of scientific articles for the medline bibliographic database. CISMeF uses two standard tools for organizing information: the MeSH thesaurus and several metadata element sets, in particular the Dublin Core metadata format. The heterogeneity of Internet health resources led the CISMeF team to enhance the MeSH thesaurus with the introduction of two new concepts, respectively, resource types and metaterms. CISMeF resource types are a generalization of the publication types of medline. A resource type describes the nature of the resource and MeSH keyword/qualifier pairs describe the subject of the resource. A metaterm is generally a medical specialty or a biological science, which has semantic links with one or more MeSH keywords, qualifiers and resource types. The CISMeF terminology is exploited for several tasks: resource indexing performed manually, resource categorization performed automatically, visualization and navigation through the concept hierarchies and information retrieval using the Doc'CISMeF search engine. The CISMeF health gateway uses several MeSH thesaurus enhancements to optimize information retrieval, hierarchy navigation and automatic indexing.

  10. Metrics and visualization tools for surface mesh comparison

    NASA Astrophysics Data System (ADS)

    Zhou, Laixin; Pang, Alex

    2001-05-01

    This paper describes a system for comparing surface meshes using different distance metrics and mapping the results to different visual presentations. Hierarchical and multi- resolution (HMR) methods produce meshes with different levels of details. Different HMR methods produce meshes with varying quality. The surface mesh comparison system presented here allows the user to qualitatively compare and investigate the merits of the meshes produced by different HMR algorithms as well as how different resolution meshes degrade as they are simplified.

  11. Adaptive and Unstructured Mesh Cleaving

    PubMed Central

    Bronson, Jonathan R.; Sastry, Shankar P.; Levine, Joshua A.; Whitaker, Ross T.

    2015-01-01

    We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or “cleave”, these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes. PMID:26137171

  12. Earth Algebra.

    ERIC Educational Resources Information Center

    Schaufele, Christopher; Zumoff, Nancy

    Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

  13. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  14. MeshKit

    SciTech Connect

    2010-10-05

    MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact with iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.

  15. MeshKit

    2010-10-05

    MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact withmore » iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.« less

  16. Local, Optimization-based Simplicial Mesh Smoothing

    1999-12-09

    OPT-MS is a C software package for the improvement and untangling of simplicial meshes (triangles in 2D, tetrahedra in 3D). Overall mesh quality is improved by iterating over the mesh vertices and adjusting their position to optimize some measure of mesh quality, such as element angle or aspect ratio. Several solution techniques (including Laplacian smoothing, "Smart" Laplacian smoothing, optimization-based smoothing and several combinations thereof) and objective functions (for example, element angle, sin (angle), and aspectmore » ratio) are available to the user for both two and three-dimensional meshes. If the mesh contains invalid elements (those with negative area) a different optimization algorithm for mesh untangling is provided.« less

  17. 6th International Meshing Roundtable '97

    SciTech Connect

    White, D.

    1997-09-01

    The goal of the 6th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the pas~ the Roundtable has enjoyed significant participation born each of these groups from a wide variety of countries. The Roundtable will consist of technical presentations from contributed papers and abstracts, two invited speakers, and two invited panels of experts discussing topics related to the development and use of automatic mesh generation tools. In addition, this year we will feature a "Bring Your Best Mesh" competition and poster session to encourage discussion and participation from a wide variety of mesh generation tool users. The schedule and evening social events are designed to provide numerous opportunities for informal dialog. A proceedings will be published by Sandia National Laboratories and distributed at the Roundtable. In addition, papers of exceptionally high quaIity will be submitted to a special issue of the International Journal of Computational Geometry and Applications. Papers and one page abstracts were sought that present original results on the meshing process. Potential topics include but are got limited to: Unstructured triangular and tetrahedral mesh generation Unstructured quadrilateral and hexahedral mesh generation Automated blocking and structured mesh generation Mixed element meshing Surface mesh generation Geometry decomposition and clean-up techniques Geometry modification techniques related to meshing Adaptive mesh refinement and mesh quality control Mesh visualization Special purpose meshing algorithms for particular applications Theoretical or novel ideas with practical potential Technical presentations from industrial researchers.

  18. Automated subject-specific, hexahedral mesh generation via image registration

    PubMed Central

    Ji, Songbai; Ford, James C.; Greenwald, Richard M.; Beckwith, Jonathan G.; Paulsen, Keith D.; Flashman, Laura A.; McAllister, Thomas W.

    2011-01-01

    Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods “morph” an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique’s performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields. PMID:21731153

  19. Scalar energy fluctuations in Large-Eddy Simulation of turbulent flames: Statistical budgets and mesh quality criterion

    SciTech Connect

    Vervisch, Luc; Domingo, Pascale; Lodato, Guido; Veynante, Denis

    2010-04-15

    Large-Eddy Simulation (LES) provides space-filtered quantities to compare with measurements, which usually have been obtained using a different filtering operation; hence, numerical and experimental results can be examined side-by-side in a statistical sense only. Instantaneous, space-filtered and statistically time-averaged signals feature different characteristic length-scales, which can be combined in dimensionless ratios. From two canonical manufactured turbulent solutions, a turbulent flame and a passive scalar turbulent mixing layer, the critical values of these ratios under which measured and computed variances (resolved plus sub-grid scale) can be compared without resorting to additional residual terms are first determined. It is shown that actual Direct Numerical Simulation can hardly accommodate a sufficiently large range of length-scales to perform statistical studies of LES filtered reactive scalar-fields energy budget based on sub-grid scale variances; an estimation of the minimum Reynolds number allowing for such DNS studies is given. From these developments, a reliability mesh criterion emerges for scalar LES and scaling for scalar sub-grid scale energy is discussed. (author)

  20. Some Aspects of Multigrid Methods on Non-Structured Meshes

    NASA Technical Reports Server (NTRS)

    Guillard, H.; Marco, N.

    1996-01-01

    To solve a given fine mesh problem, the design of a multigrid method requires the definition of coarse levels, associated coarse grid operators and inter-grid transfer operators. For non-structured simplified meshes, these definitions can rely on the use of non-nested triangulations. These definitions can also be founded on agglomeration/aggregation techniques in a purely algebraic manner. This paper analyzes these two options, shows the connections of the volume-agglomeration method with algebraic methods and proposes a new definition of prolongation operator suitable for the application of the volume-agglomeration method to elliptic problems.

  1. Conformal refinement of unstructured quadrilateral meshes

    SciTech Connect

    Garmella, Rao

    2009-01-01

    We present a multilevel adaptive refinement technique for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are refined using templates based on 1:3 refinement of edges. We demonstrate that by careful design of the refinement and coarsening strategy, we can maintain high quality elements in the refined mesh. We demonstrate the method on a number of examples with dynamically changing refinement regions.

  2. Mesh for prolapse surgery: Why the fuss?

    PubMed

    Rajshekhar, Smita; Mukhopadhyay, Sambit; Klinge, Uwe

    2015-06-01

    Pelvic organ prolapse is a common gynaecological problem. Surgical techniques to repair prolapse have been constantly evolving to reduce the recurrence of prolapse and need for reoperation. Grafts made of synthetic and biological materials became popular in the last decade as they were intended to provide extra support to native tissue repairs. However, serious complications related to use of synthetic meshes have been reported and there is increasing medico-legal concern about mesh use in prolapse surgery. Some mesh products already have been withdrawn from the market and the FDA has introduced stricter surveillance of new and existing products. Large randomized studies comparing mesh with non-mesh procedures are lacking which creates uncertainty for the surgeon and their patients.The small cohorts of the RCTs available with short follow-up periods just allow the conclusion that the mesh repair can be helpful in the short to medium term but unfortunately are not able to prove safety for all patients. In particular, current clinical reports cannot define for which indication what material may be superior compared to non-mesh repair.Quality control through long-term individual and national mesh registries is needed to keep a record of all surgeons using mesh and all devices being used, monitoring their effectiveness and safety data. Meshes with better biocompatibility designed specifically for use in vaginal surgery may provide superior clinical results, where the reduction of complications may allow a wider range of indications. PMID:25952907

  3. Mesh for prolapse surgery: Why the fuss?

    PubMed

    Rajshekhar, Smita; Mukhopadhyay, Sambit; Klinge, Uwe

    2015-06-01

    Pelvic organ prolapse is a common gynaecological problem. Surgical techniques to repair prolapse have been constantly evolving to reduce the recurrence of prolapse and need for reoperation. Grafts made of synthetic and biological materials became popular in the last decade as they were intended to provide extra support to native tissue repairs. However, serious complications related to use of synthetic meshes have been reported and there is increasing medico-legal concern about mesh use in prolapse surgery. Some mesh products already have been withdrawn from the market and the FDA has introduced stricter surveillance of new and existing products. Large randomized studies comparing mesh with non-mesh procedures are lacking which creates uncertainty for the surgeon and their patients.The small cohorts of the RCTs available with short follow-up periods just allow the conclusion that the mesh repair can be helpful in the short to medium term but unfortunately are not able to prove safety for all patients. In particular, current clinical reports cannot define for which indication what material may be superior compared to non-mesh repair.Quality control through long-term individual and national mesh registries is needed to keep a record of all surgeons using mesh and all devices being used, monitoring their effectiveness and safety data. Meshes with better biocompatibility designed specifically for use in vaginal surgery may provide superior clinical results, where the reduction of complications may allow a wider range of indications.

  4. Quality of life assessment in women after cervicosacropexy with polypropylene mesh for pelvic organ prolapse: a preliminary study

    PubMed Central

    Majkusiak, Wojciech; Tomasik, Paweł; Zwierzchowska, Aneta; Wielgoś, Mirosław; Barcz, Ewa

    2015-01-01

    Aim of the study Aim of the study was to assess the changes in the subjective perception of quality of life in patients who underwent abdominal cervicosacropexy for pelvic organ prolapse. Material and methods Forty patients with diagnosed pelvic organ prolapse (Pelvic Organ Prolapse – Quantification [POPQ] stage IV or IIIC) underwent abdominal supracervical hysterectomy and cervicosacropexy. The questionnaire concerning the quality of life was filled in before and 6 months after the surgery. Results In all patients, an accurate prolapse correction was achieved. In 42% of patients, stress urinary incontinence (SUI) was diagnosed prior to surgery, while after the surgery in 38.24% (p > 0.05). In 50% of women, symptoms of overactive bladder (OAB) occurred pre-surgery. These symptoms were reported by 17.65% of patients postoperatively (p < 0.05). Urinary retention was observed in 32.36% before and in 2.5% after the surgery (p < 0.05). The average score of the quality of sexual life was 5.75 (SD 2.52, 95% CI: 4.41-7.1) before and increased to 7.93 (SD 1.77, 95% CI: 6.9-8.95) after the procedure (p < 0.05). The mean score of the overall quality of life in relation to POP before and after the procedure was 2.77 (SD 2.39, 95% CI: 1.87-8.64) and 9.03 (SD 1.08, 95% CI: 8.66-9.43), respectively (p < 0.001). Conclusions These results show a highly significant improvement of the quality of life in patients who underwent abdominal cervicosacropexy for POP. The change in quality of their sexual life, reduced OAB and urinary retention rates, as well as improvement of the esthetic self-perception may have contributed to this positive effect. PMID:26327900

  5. Update on Development of Mesh Generation Algorithms in MeshKit

    SciTech Connect

    Jain, Rajeev; Vanderzee, Evan; Mahadevan, Vijay

    2015-09-30

    MeshKit uses a graph-based design for coding all its meshing algorithms, which includes the Reactor Geometry (and mesh) Generation (RGG) algorithms. This report highlights the developmental updates of all the algorithms, results and future work. Parallel versions of algorithms, documentation and performance results are reported. RGG GUI design was updated to incorporate new features requested by the users; boundary layer generation and parallel RGG support were added to the GUI. Key contributions to the release, upgrade and maintenance of other SIGMA1 libraries (CGM and MOAB) were made. Several fundamental meshing algorithms for creating a robust parallel meshing pipeline in MeshKit are under development. Results and current status of automated, open-source and high quality nuclear reactor assembly mesh generation algorithms such as trimesher, quadmesher, interval matching and multi-sweeper are reported.

  6. Algebraic multigrid

    NASA Technical Reports Server (NTRS)

    Ruge, J. W.; Stueben, K.

    1987-01-01

    The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

  7. Hexahedral Mesh Untangling

    SciTech Connect

    KNUPP,PATRICK

    2000-12-13

    We investigate a well-motivated mesh untangling objective function whose optimization automatically produces non-inverted elements when possible. Examples show the procedure is highly effective on simplicial meshes and on non-simplicial (e.g., hexahedral) meshes constructed via mapping or sweeping algorithms. The current whisker-weaving (WW) algorithm in CUBIT usually produces hexahedral meshes that are unsuitable for analyses due to inverted elements. The majority of these meshes cannot be untangled using the new objective function. The most likely source of the difficulty is poor mesh topology.

  8. SU-E-J-02: 4D Digital Tomosynthesis Based On Algebraic Image Reconstruction and Total-Variation Minimization for the Improvement of Image Quality

    SciTech Connect

    Kim, D; Kang, S; Kim, T; Suh, T; Kim, S

    2014-06-01

    Purpose: In this paper, we implemented the four-dimensional (4D) digital tomosynthesis (DTS) imaging based on algebraic image reconstruction technique and total-variation minimization method in order to compensate the undersampled projection data and improve the image quality. Methods: The projection data were acquired as supposed the cone-beam computed tomography system in linear accelerator by the Monte Carlo simulation and the in-house 4D digital phantom generation program. We performed 4D DTS based upon simultaneous algebraic reconstruction technique (SART) among the iterative image reconstruction technique and total-variation minimization method (TVMM). To verify the effectiveness of this reconstruction algorithm, we performed systematic simulation studies to investigate the imaging performance. Results: The 4D DTS algorithm based upon the SART and TVMM seems to give better results than that based upon the existing method, or filtered-backprojection. Conclusion: The advanced image reconstruction algorithm for the 4D DTS would be useful to validate each intra-fraction motion during radiation therapy. In addition, it will be possible to give advantage to real-time imaging for the adaptive radiation therapy. This research was supported by Leading Foreign Research Institute Recruitment Program (Grant No.2009-00420) and Basic Atomic Energy Research Institute (BAERI); (Grant No. 2009-0078390) through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP)

  9. Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching.

    PubMed

    Park, Jae-Hyeung; Yeom, Han-Ju; Kim, Hee-Jae; Zhang, HuiJun; Li, BoNi; Ji, Yeong-Min; Kim, Sang-Hoo

    2015-03-23

    Mesh-based computer generated hologram enables realistic and efficient representation of three-dimensional scene. However, the dark line artifacts on the boundary between neighboring meshes are frequently observed, degrading the quality of the reconstruction. In this paper, we propose a simple technique to remove the dark line artifacts by matching the phase on the boundary of neighboring meshes. The feasibility of the proposed method is confirmed by the numerical and optical reconstruction of the generated hologram.

  10. An Interpreted Language and System for the Visualization of Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Moran, Patrick J.; Gerald-Yamasaki, Michael (Technical Monitor)

    1998-01-01

    We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.

  11. Adaptive Hybrid Mesh Refinement for Multiphysics Applications

    SciTech Connect

    Khamayseh, Ahmed K; de Almeida, Valmor F

    2007-01-01

    The accuracy and convergence of computational solutions of mesh-based methods is strongly dependent on the quality of the mesh used. We have developed methods for optimizing meshes that are comprised of elements of arbitrary polygonal and polyhedral type. We present in this research the development of r-h hybrid adaptive meshing technology tailored to application areas relevant to multi-physics modeling and simulation. Solution-based adaptation methods are used to reposition mesh nodes (r-adaptation) or to refine the mesh cells (h-adaptation) to minimize solution error. The numerical methods perform either the r-adaptive mesh optimization or the h-adaptive mesh refinement method on the initial isotropic or anisotropic meshes to maximize the equidistribution of a weighted geometric and/or solution function. We have successfully introduced r-h adaptivity to a least-squares method with spherical harmonics basis functions for the solution of the spherical shallow atmosphere model used in climate forecasting. In addition, application of this technology also covers a wide range of disciplines in computational sciences, most notably, time-dependent multi-physics, multi-scale modeling and simulation.

  12. Compact Mesh Generator

    2007-02-02

    The CMG is a small, lightweight, structured mesh generation code. It features a simple text input parser that allows setup of various meshes via a small set of text commands. Mesh generation data can be output to text, the silo file format, or the API can be directly queried by applications. It can run serially or in parallel via MPI. The CMG includes the ability to specify varius initial conditions on a mesh via meshmore » tags.« less

  13. Meshes: The next generation

    SciTech Connect

    Christon, M.; Hardin, D.; Compton, J.; Zosel, M.

    1994-08-29

    Building complex meshes for large-scale numerical simulations presents immense difficulties in exploiting high-performance computers. Industry and research leaders will describe the current state of the art for generating meshes for such large scientific problems. This will be followed by a panel and general audience discussion of the algorithmic and architectural issues surrounding the generation of meshes with10{sup 7} to 10{sup 9} grid points. (Note: The terms ``mesh`` and ``grid`` are used interchangeably in the literature.)

  14. Choosing corners of rectangles for mapped meshing

    SciTech Connect

    Mitchell, S.A.

    1996-12-16

    Consider mapping a regular i x j quadrilateral mesh of a rectangle onto a surface. The quality of the mapped mesh of the surface depends heavily on which vertices of the surface correspond to corners of the rectangle. The authors problem is, given an n-sided surface, chose as corners four vertices such that the surface resembles a rectangle with corners at those vertices. Note that n could be quite large, and the length and width of the rectangle, i and j, are not prespecified. In general, there is either a goal number or a prescribed number of mesh edges for each bounding curve of the surface. The goals affect the quality of the mesh, and the prescribed edges may make finding a feasible set of corners difficult. The algorithm need only work for surfaces that are roughly rectangular, particular those without large reflex angles, as otherwise an unstructured meshing algorithm is used instead. The authors report on the theory and implementation of algorithms for this problem. They also given an overview of a solution to a related problem called interval assignment: given a complex of surfaces sharing curves, globally assign the number of mesh edges or intervals for each curve such that it is possible to mesh each surface according to its prescribed quadrilateral meshing algorithm, and assigned and user-prescribed boundary mesh edges and corners. They also note a practical, constructive technique that relies on interval assignment that can generate a quadrilateral mesh of a complex of surfaces such that a compatible hexahedral mesh of the enclosed volume exists.

  15. Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

    NASA Astrophysics Data System (ADS)

    Landry, Jonathan; Soulaïmani, Azzeddine; Luke, Edward; Ben Haj Ali, Amine

    2016-12-01

    A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.

  16. Turbulent flow calculations using unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1990-01-01

    A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow-field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of flow-field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with experimental data.

  17. Algebraic trigonometry

    NASA Astrophysics Data System (ADS)

    Vaninsky, Alexander

    2011-04-01

    This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.

  18. A Generic Mesh Data Structure with Parallel Applications

    ERIC Educational Resources Information Center

    Cochran, William Kenneth, Jr.

    2009-01-01

    High performance, massively-parallel multi-physics simulations are built on efficient mesh data structures. Most data structures are designed from the bottom up, focusing on the implementation of linear algebra routines. In this thesis, we explore a top-down approach to design, evaluating the various needs of many aspects of simulation, not just…

  19. A Triangle Mesh Standardization Method Based on Particle Swarm Optimization.

    PubMed

    Wang, Wuli; Duan, Liming; Bai, Yang; Wang, Haoyu; Shao, Hui; Zhong, Siyang

    2016-01-01

    To enhance the triangle quality of a reconstructed triangle mesh, a novel triangle mesh standardization method based on particle swarm optimization (PSO) is proposed. First, each vertex of the mesh and its first order vertices are fitted to a cubic curve surface by using least square method. Additionally, based on the condition that the local fitted surface is the searching region of PSO and the best average quality of the local triangles is the goal, the vertex position of the mesh is regulated. Finally, the threshold of the normal angle between the original vertex and regulated vertex is used to determine whether the vertex needs to be adjusted to preserve the detailed features of the mesh. Compared with existing methods, experimental results show that the proposed method can effectively improve the triangle quality of the mesh while preserving the geometric features and details of the original mesh. PMID:27509129

  20. A Triangle Mesh Standardization Method Based on Particle Swarm Optimization

    PubMed Central

    Duan, Liming; Bai, Yang; Wang, Haoyu; Shao, Hui; Zhong, Siyang

    2016-01-01

    To enhance the triangle quality of a reconstructed triangle mesh, a novel triangle mesh standardization method based on particle swarm optimization (PSO) is proposed. First, each vertex of the mesh and its first order vertices are fitted to a cubic curve surface by using least square method. Additionally, based on the condition that the local fitted surface is the searching region of PSO and the best average quality of the local triangles is the goal, the vertex position of the mesh is regulated. Finally, the threshold of the normal angle between the original vertex and regulated vertex is used to determine whether the vertex needs to be adjusted to preserve the detailed features of the mesh. Compared with existing methods, experimental results show that the proposed method can effectively improve the triangle quality of the mesh while preserving the geometric features and details of the original mesh. PMID:27509129

  1. Tomographic mesh generation for OSEM reconstruction of SPECT images

    NASA Astrophysics Data System (ADS)

    Lu, Yao; Yu, Bo; Vogelsang, Levon; Krol, Andrzej; Xu, Yuesheng; Hu, Xiaofei; Feiglin, David

    2009-02-01

    To improve quality of OSEM SPECT reconstruction in the mesh domain, we implemented an adaptive mesh generation method that produces tomographic mesh consisting of triangular elements with size and density commensurate with geometric detail of the objects. Node density and element size change smoothly as a function of distance from the edges and edge curvature without creation of 'bad' elements. Tomographic performance of mesh-based OSEM reconstruction is controlled by the tomographic mesh structure, i.e. node density distribution, which in turn is ruled by the number of key points on the boundaries. A greedy algorithm is used to influence the distribution of nodes on the boundaries. The relationship between tomographic mesh properties and OSEM reconstruction quality has been investigated. We conclude that by selecting adequate number of key points, one can produce a tomographic mesh with lowest number of nodes that is sufficient to provide desired quality of reconstructed images, appropriate for the imaging system properties.

  2. Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report

    SciTech Connect

    KNUPP,PATRICK; MITCHELL,SCOTT A.

    1999-11-01

    In an attempt to automatically produce high-quality all-hex meshes, we investigated a mesh improvement strategy: given an initial poor-quality all-hex mesh, we iteratively changed the element connectivity, adding and deleting elements and nodes, and optimized the node positions. We found a set of hex reconnection primitives. We improved the optimization algorithms so they can untangle a negative-Jacobian mesh, even considering Jacobians on the boundary, and subsequently optimize the condition number of elements in an untangled mesh. However, even after applying both the primitives and optimization we were unable to produce high-quality meshes in certain regions. Our experiences suggest that many boundary configurations of quadrilaterals admit no hexahedral mesh with positive Jacobians, although we have no proof of this.

  3. phdMesh

    2008-01-01

    Parallel Heterogeneous Dynamic unstructured Mesh (phdMesh) data structure library and integration testing code that performs dynamic load balancing of the data structure and parallel geometric proximity search on a contrived test problem. The phdMesh library is intended to be module within a finite element or finite volume library or code. The integration testing code is intended to provide a compact and highly portable performance evaluation code for parallel computing systems.

  4. Structured adaptive grid generation using algebraic methods

    NASA Technical Reports Server (NTRS)

    Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.

    1993-01-01

    The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration

  5. Numerical algebraic geometry and algebraic kinematics

    NASA Astrophysics Data System (ADS)

    Wampler, Charles W.; Sommese, Andrew J.

    In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

  6. Modified laparoscopic ventral mesh rectopexy.

    PubMed

    Sileri, P; Capuano, I; Franceschilli, L; Giorgi, F; Gaspari, A L

    2014-06-01

    We present a modified laparoscopic ventral mesh rectopexy procedure using biological mesh and bilateral anterior mesh fixation. The rectopexy is anterior with a minimal posterior mobilization. The rectum is symmetrically suspended to the sacral promontory through a mesorectal window.

  7. Quantization of Algebraic Reduction

    SciTech Connect

    Sniatycki, Jeodrzej

    2007-11-14

    For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.

  8. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

  9. Performance of a streaming mesh refinement algorithm.

    SciTech Connect

    Thompson, David C.; Pebay, Philippe Pierre

    2004-08-01

    In SAND report 2004-1617, we outline a method for edge-based tetrahedral subdivision that does not rely on saving state or communication to produce compatible tetrahedralizations. This report analyzes the performance of the technique by characterizing (a) mesh quality, (b) execution time, and (c) traits of the algorithm that could affect quality or execution time differently for different meshes. It also details the method used to debug the several hundred subdivision templates that the algorithm relies upon. Mesh quality is on par with other similar refinement schemes and throughput on modern hardware can exceed 600,000 output tetrahedra per second. But if you want to understand the traits of the algorithm, you have to read the report!

  10. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  11. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  12. Orientation in operator algebras

    PubMed Central

    Alfsen, Erik M.; Shultz, Frederic W.

    1998-01-01

    A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457

  13. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  14. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  15. Mesh implants: An overview of crucial mesh parameters

    PubMed Central

    Zhu, Lei-Ming; Schuster, Philipp; Klinge, Uwe

    2015-01-01

    Hernia repair is one of the most frequently performed surgical interventions that use mesh implants. This article evaluates crucial mesh parameters to facilitate selection of the most appropriate mesh implant, considering raw materials, mesh composition, structure parameters and mechanical parameters. A literature review was performed using the PubMed database. The most important mesh parameters in the selection of a mesh implant are the raw material, structural parameters and mechanical parameters, which should match the physiological conditions. The structural parameters, especially the porosity, are the most important predictors of the biocompatibility performance of synthetic meshes. Meshes with large pores exhibit less inflammatory infiltrate, connective tissue and scar bridging, which allows increased soft tissue ingrowth. The raw material and combination of raw materials of the used mesh, including potential coatings and textile design, strongly impact the inflammatory reaction to the mesh. Synthetic meshes made from innovative polymers combined with surface coating have been demonstrated to exhibit advantageous behavior in specialized fields. Monofilament, large-pore synthetic meshes exhibit advantages. The value of mesh classification based on mesh weight seems to be overestimated. Mechanical properties of meshes, such as anisotropy/isotropy, elasticity and tensile strength, are crucial parameters for predicting mesh performance after implantation. PMID:26523210

  16. Urogynecologic Surgical Mesh Implants

    MedlinePlus

    ... Boston Scientific's urogynecologic surgical mesh may contain counterfeit raw material. We are examining these allegations to determine any ... are currently not aware that the alleged counterfeit raw material contributes to adverse events associated with these products. ...

  17. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  18. Discrete Minimal Surface Algebras

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Hoppe, Jens

    2010-05-01

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  19. Airplane Mesh Development with Grid Density Studies

    NASA Technical Reports Server (NTRS)

    Cliff, Susan E.; Baker, Timothy J.; Thomas, Scott D.; Lawrence, Scott L.; Rimlinger, Mark J.

    1999-01-01

    Automatic Grid Generation Wish List Geometry handling, including CAD clean up and mesh generation, remains a major bottleneck in the application of CFD methods. There is a pressing need for greater automation in several aspects of the geometry preparation in order to reduce set up time and eliminate user intervention as much as possible. Starting from the CAD representation of a configuration, there may be holes or overlapping surfaces which require an intensive effort to establish cleanly abutting surface patches, and collections of many patches may need to be combined for more efficient use of the geometrical representation. Obtaining an accurate and suitable body conforming grid with an adequate distribution of points throughout the flow-field, for the flow conditions of interest, is often the most time consuming task for complex CFD applications. There is a need for a clean unambiguous definition of the CAD geometry. Ideally this would be carried out automatically by smart CAD clean up software. One could also define a standard piece-wise smooth surface representation suitable for use by computational methods and then create software to translate between the various CAD descriptions and the standard representation. Surface meshing remains a time consuming, user intensive procedure. There is a need for automated surface meshing, requiring only minimal user intervention to define the overall density of mesh points. The surface mesher should produce well shaped elements (triangles or quadrilaterals) whose size is determined initially according to the surface curvature with a minimum size for flat pieces, and later refined by the user in other regions if necessary. Present techniques for volume meshing all require some degree of user intervention. There is a need for fully automated and reliable volume mesh generation. In addition, it should be possible to create both surface and volume meshes that meet guaranteed measures of mesh quality (e.g. minimum and maximum

  20. Unstructured mesh generation and adaptivity

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.

    1995-01-01

    An overview of current unstructured mesh generation and adaptivity techniques is given. Basic building blocks taken from the field of computational geometry are first described. Various practical mesh generation techniques based on these algorithms are then constructed and illustrated with examples. Issues of adaptive meshing and stretched mesh generation for anisotropic problems are treated in subsequent sections. The presentation is organized in an education manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

  1. Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation.

    PubMed

    Gao, Zhanheng; Yu, Zeyun; Holst, Michael

    2013-01-01

    A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.

  2. Quality Control of Trichinella Testing at the Slaughterhouse Laboratory: Evaluation of the Use of a 400-Micrometer-Mesh-Size Sieve in the Magnetic Stirrer Method.

    PubMed

    Franssen, Frits; van Andel, Esther; Swart, Arno; van der Giessen, Joke

    2016-02-01

    The performance of a 400-μm-mesh-size sieve (sieve400) has not previously been compared with that of a 180-μm-mesh-size sieve (sieve180). Using pork samples spiked with 0 to 10 Trichinella muscle larvae and an artificial digestion method, sieve performance was evaluated for control of Trichinella in meat-producing animals. The use of a sieve400 resulted in 12% lower larval counts, 147% more debris, and 28% longer counting times compared with the use of a sieve180. Although no false-negative results were obtained, prolonged counting times with the sieve400 may have an impact on performance in a high-throughput environment such as a slaughterhouse laboratory. Based on our results, the sieve180 remains the sieve of choice for Trichinella control in meat in slaughterhouse laboratories, according to the European Union reference method (European Commission regulation 2075/2005). Furthermore, the results of the present study contribute to the discussion of harmonization of meat inspection requirements among countries. PMID:26818995

  3. Quality Control of Trichinella Testing at the Slaughterhouse Laboratory: Evaluation of the Use of a 400-Micrometer-Mesh-Size Sieve in the Magnetic Stirrer Method.

    PubMed

    Franssen, Frits; van Andel, Esther; Swart, Arno; van der Giessen, Joke

    2016-02-01

    The performance of a 400-μm-mesh-size sieve (sieve400) has not previously been compared with that of a 180-μm-mesh-size sieve (sieve180). Using pork samples spiked with 0 to 10 Trichinella muscle larvae and an artificial digestion method, sieve performance was evaluated for control of Trichinella in meat-producing animals. The use of a sieve400 resulted in 12% lower larval counts, 147% more debris, and 28% longer counting times compared with the use of a sieve180. Although no false-negative results were obtained, prolonged counting times with the sieve400 may have an impact on performance in a high-throughput environment such as a slaughterhouse laboratory. Based on our results, the sieve180 remains the sieve of choice for Trichinella control in meat in slaughterhouse laboratories, according to the European Union reference method (European Commission regulation 2075/2005). Furthermore, the results of the present study contribute to the discussion of harmonization of meat inspection requirements among countries.

  4. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…

  5. Documentation for MeshKit - Reactor Geometry (&mesh) Generator

    SciTech Connect

    Jain, Rajeev; Mahadevan, Vijay

    2015-09-30

    This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing. RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.

  6. Cosmology on a Mesh

    NASA Astrophysics Data System (ADS)

    Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.

    2003-04-01

    An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.

  7. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  8. Curved mesh generation and mesh refinement using Lagrangian solid mechanics

    SciTech Connect

    Persson, P.-O.; Peraire, J.

    2008-12-31

    We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements even for highly distorted or anisotropic initial meshes. We describe the method and the solution procedures, and we show a number of examples of two and three dimensional simplex meshes with curved boundaries. We also demonstrate how to use the technique for local refinement of non-curved meshes in the presence of curved boundaries.

  9. Element Agglomeration Algebraic Multilevel Monte-Carlo Library

    SciTech Connect

    2015-02-19

    ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizations of subsurface flow problems.

  10. Element Agglomeration Algebraic Multilevel Monte-Carlo Library

    2015-02-19

    ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizationsmore » of subsurface flow problems.« less

  11. Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.

  12. Euler and Navier-Stokes computations for two-dimensional geometries using unstructured meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.

    1990-01-01

    A general purpose unstructured mesh solver for steady-state two-dimensional inviscid and viscous flows is described. The efficiency and accuracy of the method are enhanced by the simultaneous use of adaptive meshing and an unstructured multigrid technique. A method for generating highly stretched triangulations in regions of viscous flow is outlined, and a procedure for implementing an algebraic turbulence model on unstructured meshes is described. Results are shown for external and internal inviscid flows and for turbulent viscous flow over a multi-element airfoil configuration.

  13. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  14. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…

  15. Algebraic Reasoning through Patterns

    ERIC Educational Resources Information Center

    Rivera, F. D.; Becker, Joanne Rossi

    2009-01-01

    This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

  16. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  17. Hexahedral mesh generation via the dual arrangement of surfaces

    SciTech Connect

    Mitchell, S.A.; Tautges, T.J.

    1997-12-31

    Given a general three-dimensional geometry with a prescribed quadrilateral surface mesh, the authors consider the problem of constructing a hexahedral mesh of the geometry whose boundary is exactly the prescribed surface mesh. Due to the specialized topology of hexahedra, this problem is more difficult than the analogous one for tetrahedra. Folklore has maintained that a surface mesh must have a constrained structure in order for there to exist a compatible hexahedral mesh. However, they have proof that a surface mesh need only satisfy mild parity conditions, depending on the topology of the three-dimensional geometry, for there to exist a compatible hexahedral mesh. The proof is based on the realization that a hexahedral mesh is dual to an arrangement of surfaces, and the quadrilateral surface mesh is dual to the arrangement of curves bounding these surfaces. The proof is constructive and they are currently developing an algorithm called Whisker Weaving (WW) that mirrors the proof steps. Given the bounding curves, WW builds the topological structure of an arrangement of surfaces having those curves as its boundary. WW progresses in an advancing front manner. Certain local rules are applied to avoid structures that lead to poor mesh quality. Also, after the arrangement is constructed, additional surfaces are inserted to separate features, so e.g., no two hexahedra share more than one quadrilateral face. The algorithm has generated meshes for certain non-trivial problems, but is currently unreliable. The authors are exploring strategies for consistently selecting which portion of the surface arrangement to advance based on the existence proof. This should lead us to a robust algorithm for arbitrary geometries and surface meshes.

  18. Electrical properties analysis of wire mesh for mesh reflectors

    NASA Astrophysics Data System (ADS)

    Li, Tuanjie; Su, Jinguo

    2011-07-01

    The knitted wire mesh is often used as a reflecting surface of large deployable antennas. Different weaves have different electrical properties and it is very important and necessary to research the method of analyzing the electrical properties of wire mesh. This paper has developed an effective method to address the problem. First, a periodic unit of wire model in actual complex mesh structure is converted into an equivalent strip model according to the correlation between strip width and wire diameter. The equivalent regular wire-grid unit of the strip model is derived from the equivalences between the wire-grid unit and the strip model in near and far fields. Then the regular wire-grid units are arranged to form an equivalent mesh surface with the corresponding weave pattern, so the electrical properties of the mesh surface are equivalent to those of the actual mesh structure. Through analyzing electrical properties of the mesh surface including amplitude difference, phase difference and reflecting loss, we can find out the electrical properties of the actual knitted wire mesh. The single satin mesh and a two-bar tricot mesh are used as examples to illustrate the method of electrical properties analysis of wire mesh.

  19. Mesh fistulation into the rectum after laparoscopic ventral mesh rectopexy☆

    PubMed Central

    Adeyemo, Dayo

    2013-01-01

    INTRODUCTION Laparoscopic ventral mesh rectopexy (LVMR) is an effective method of management of functional disorders of the rectum including symptomatic rectal intussusception, and obstructed defaecation. Despite the technical demands of the procedure and common use of foreign body (mesh), the incidence of mesh related severe complications of the rectum is very low. PRESENTATION OF CASE A 63 year old woman presented with recurrent pelvic sepsis following a mesh rectopexy. Investigations revealed fistulation of the mesh into the rectum. She was treated with an anterior resection. DISCUSSION The intraoperative findings and management of the complication are described. Risk factors for mesh attrition and fistulation are also discussed. CONCLUSION Chronic sepsis may lead to ‘late’ fistulation after mesh rectopexy. PMID:24566425

  20. To mesh or not to mesh: a review of pelvic organ reconstructive surgery

    PubMed Central

    Dällenbach, Patrick

    2015-01-01

    Pelvic organ prolapse (POP) is a major health issue with a lifetime risk of undergoing at least one surgical intervention estimated at close to 10%. In the 1990s, the risk of reoperation after primary standard vaginal procedure was estimated to be as high as 30% to 50%. In order to reduce the risk of relapse, gynecological surgeons started to use mesh implants in pelvic organ reconstructive surgery with the emergence of new complications. Recent studies have nevertheless shown that the risk of POP recurrence requiring reoperation is lower than previously estimated, being closer to 10% rather than 30%. The development of mesh surgery – actively promoted by the marketing industry – was tremendous during the past decade, and preceded any studies supporting its benefit for our patients. Randomized trials comparing the use of mesh to native tissue repair in POP surgery have now shown better anatomical but similar functional outcomes, and meshes are associated with more complications, in particular for transvaginal mesh implants. POP is not a life-threatening condition, but a functional problem that impairs quality of life for women. The old adage “primum non nocere” is particularly appropriate when dealing with this condition which requires no treatment when asymptomatic. It is currently admitted that a certain degree of POP is physiological with aging when situated above the landmark of the hymen. Treatment should be individualized and the use of mesh needs to be selective and appropriate. Mesh implants are probably an important tool in pelvic reconstructive surgery, but the ideal implant has yet to be found. The indications for its use still require caution and discernment. This review explores the reasons behind the introduction of mesh augmentation in POP surgery, and aims to clarify the risks, benefits, and the recognized indications for its use. PMID:25848324

  1. Optimizing triangular mesh generation from range images

    NASA Astrophysics Data System (ADS)

    Lu, Tianyu; Yun, David Y.

    2000-03-01

    An algorithm for the automatic reconstruction of triangular mesh surface model form range images is presented. The optimal piecewise linear surface approximation problem is defined as: given a set S of points uniformly sampled from a vibrate function f(x,y) on a rectangular grid of dimension W X H, find a minimum triangular mesh approximating the surface with vertices anchored at a subset S' of S, such that the deviation at any sample point is within a given bound of (epsilon) > 0. The algorithm deploys a multi- agent resource planning approach to achieve adaptive, accurate and concise piecewise linear approximation using the L-(infinity) norm. The resulting manifold triangular mesh can be directly used as 3D rendering model for visualization with controllable and guaranteed quality. Due to this dual optimality, the algorithm achieves both storage efficiency and visual quality. The error control scheme further facilitates the construction of models in multiple levels of details, which is desirable in animation and virtual reality moving scenes. Experiments with various benchmark range images form smooth functional surfaces to satellite terrain images yield succinct, accurate and visually pleasant triangular meshes. Furthermore, the independence and multiplicity of agents suggest a natural parallelism for triangulation computation, which provides a promising solution for the real-time exploration of large data sets.

  2. Prophylactic Antibiotics for Mesh Inguinal Hernioplasty

    PubMed Central

    Sanabria, Alvaro; Domínguez, Luis Carlos; Valdivieso, Eduardo; Gómez, Gabriel

    2007-01-01

    Objective: To assess the effectiveness of antibiotic prophylaxis in mesh hernioplasty. Background: Antibiotic prophylaxis use in mesh inguinal hernioplasty is controversial. Available evidence is nonconclusive because of the low number of clinical trials assessing its effectiveness. Some trials have a small sample size that could overestimate or underestimate the real effectiveness of this intervention. Meta-analysis is a good method to improve these methodological flaws. Methods: Meta-analysis intended to measure the benefits of antibiotic prophylaxis on surgical site infection rate in adult patients scheduled for mesh inguinal hernioplasty. Six randomized clinical trials were found. Quality was assessed using Cochrane Collaboration criteria. Results: A total of 2507 patients were analyzed. Surgical site infection frequency was 1.38% in the antibiotic group versus 2.89% in the control group (odds ratio = 0.48; 95% confidence interval, 0.27–0.85). There was no statistical heterogeneity. Sensitivity analysis by quality did not show differences in overall results. Conclusion: Antibiotic prophylaxis use in patients submitted to mesh inguinal hernioplasty decreased the rate of surgical site infection by almost 50%. PMID:17435546

  3. SUPERIMPOSED MESH PLOTTING IN MCNP

    SciTech Connect

    J. HENDRICKS

    2001-02-01

    The capability to plot superimposed meshes has been added to MCNP{trademark}. MCNP4C featured a superimposed mesh weight window generator which enabled users to set up geometries without having to subdivide geometric cells for variance reduction. The variance reduction was performed with weight windows on a rectangular or cylindrical mesh superimposed over the physical geometry. Experience with the new capability was favorable but also indicated that a number of enhancements would be very beneficial, particularly a means of visualizing the mesh and its values. The mathematics for plotting the mesh and its values is described here along with a description of other upgrades.

  4. Metal-Mesh Lithography

    PubMed Central

    Tang, Zhao; Wei, Qingshan; Wei, Alexander

    2011-01-01

    Metal-mesh lithography (MML) is a practical hybrid of microcontact printing and capillary force lithography that can be applied over millimeter-sized areas with a high level of uniformity. MML can be achieved by blotting various inks onto substrates through thin copper grids, relying on preferential wetting and capillary interactions between template and substrate for pattern replication. The resulting mesh patterns, which are inverted relative to those produced by stenciling or serigraphy, can be reproduced with low micrometer resolution. MML can be combined with other surface chemistry and lift-off methods to create functional microarrays for diverse applications, such as periodic islands of gold nanorods and patterned corrals for fibroblast cell cultures. PMID:22103322

  5. Metal-mesh lithography.

    PubMed

    Tang, Zhao; Wei, Qingshan; Wei, Alexander

    2011-12-01

    Metal-mesh lithography (MML) is a practical hybrid of microcontact printing and capillary force lithography that can be applied over millimeter-sized areas with a high level of uniformity. MML can be achieved by blotting various inks onto substrates through thin copper grids, relying on preferential wetting and capillary interactions between template and substrate for pattern replication. The resulting mesh patterns, which are inverted relative to those produced by stenciling or serigraphy, can be reproduced with low micrometer resolution. MML can be combined with other surface chemistry and lift-off methods to create functional microarrays for diverse applications, such as periodic islands of gold nanorods and patterned corrals for fibroblast cell cultures.

  6. Mesh2d

    2011-12-31

    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,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » 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.« less

  7. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  8. Parallel Adaptive Mesh Refinement

    SciTech Connect

    Diachin, L; Hornung, R; Plassmann, P; WIssink, A

    2005-03-04

    As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the

  9. Semirelativistic Lagrange mesh calculations

    NASA Astrophysics Data System (ADS)

    Semay, C.; Baye, D.; Hesse, M.; Silvestre-Brac, B.

    2001-07-01

    The Lagrange mesh method is a very powerful procedure to compute eigenvalues and eigenfunctions of nonrelativistic Hamiltonians. The trial eigenstates are developed in a basis of well-chosen functions and the computation of Hamiltonian matrix elements requires only the evaluation of the potential at grid points. It is shown that this method can be used to solve semirelativistic two-body eigenvalue equations. As in the nonrelativistic case, it is very accurate, fast, and very simple to implement.

  10. Particle-mesh techniques

    NASA Technical Reports Server (NTRS)

    Macneice, Peter

    1995-01-01

    This is an introduction to numerical Particle-Mesh techniques, which are commonly used to model plasmas, gravitational N-body systems, and both compressible and incompressible fluids. The theory behind this approach is presented, and its practical implementation, both for serial and parallel machines, is discussed. This document is based on a four-hour lecture course presented by the author at the NASA Summer School for High Performance Computational Physics, held at Goddard Space Flight Center.

  11. Leibniz algebras associated with representations of filiform Lie algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2015-12-01

    In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.

  12. A novel three-dimensional mesh deformation method based on sphere relaxation

    SciTech Connect

    Zhou, Xuan; Li, Shuixiang

    2015-10-01

    In our previous work (2013) [19], we developed a disk relaxation based mesh deformation method for two-dimensional mesh deformation. In this paper, the idea of the disk relaxation is extended to the sphere relaxation for three-dimensional meshes with large deformations. We develop a node based pre-displacement procedure to apply initial movements on nodes according to their layer indices. Afterwards, the nodes are moved locally by the improved sphere relaxation algorithm to transfer boundary deformations and increase the mesh quality. A three-dimensional mesh smoothing method is also adopted to prevent the occurrence of the negative volume of elements, and further improve the mesh quality. Numerical applications in three-dimension including the wing rotation, bending beam and morphing aircraft are carried out. The results demonstrate that the sphere relaxation based approach generates the deformed mesh with high quality, especially regarding complex boundaries and large deformations.

  13. Wireless mesh networks.

    PubMed

    Wang, Xinheng

    2008-01-01

    Wireless telemedicine using GSM and GPRS technologies can only provide low bandwidth connections, which makes it difficult to transmit images and video. Satellite or 3G wireless transmission provides greater bandwidth, but the running costs are high. Wireless networks (WLANs) appear promising, since they can supply high bandwidth at low cost. However, the WLAN technology has limitations, such as coverage. A new wireless networking technology named the wireless mesh network (WMN) overcomes some of the limitations of the WLAN. A WMN combines the characteristics of both a WLAN and ad hoc networks, thus forming an intelligent, large scale and broadband wireless network. These features are attractive for telemedicine and telecare because of the ability to provide data, voice and video communications over a large area. One successful wireless telemedicine project which uses wireless mesh technology is the Emergency Room Link (ER-LINK) in Tucson, Arizona, USA. There are three key characteristics of a WMN: self-organization, including self-management and self-healing; dynamic changes in network topology; and scalability. What we may now see is a shift from mobile communication and satellite systems for wireless telemedicine to the use of wireless networks based on mesh technology, since the latter are very attractive in terms of cost, reliability and speed.

  14. On Optimal Bilinear Quadrilateral Meshes

    SciTech Connect

    D'Azevedo, E.

    1998-10-26

    The novelty of this work is in presenting interesting error properties of two types of asymptotically optimal quadrilateral meshes for bilinear approximation. The first type of mesh has an error equidistributing property where the maximum interpolation error is asymptotically the same over all elements. The second type has faster than expected super-convergence property for certain saddle-shaped data functions. The super-convergent mesh may be an order of magnitude more accurate than the error equidistributing mesh. Both types of mesh are generated by a coordinate transformation of a regular mesh of squares. The coordinate transformation is derived by interpreting the Hessian matrix of a data function as a metric tensor. The insights in this work may have application in mesh design near known corner or point singularities.

  15. Mesh Algorithms for PDE with Sieve I: Mesh Distribution

    DOE PAGES

    Knepley, Matthew G.; Karpeev, Dmitry A.

    2009-01-01

    We have developed a new programming framework, called Sieve, to support parallel numerical partial differential equation(s) (PDE) algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms acting on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode notmore » only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated using the same fundamental mechanisms used to represent meshes. We present the complete description of an algorithm to encode a mesh partition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same algorithm. The use of a high level of abstraction within the Sieve leads to several benefits in terms of code reuse, simplicity, and extensibility. We discuss these benefits and compare our approach to other existing mesh libraries.« less

  16. Mesh Oriented datABase

    2004-04-01

    MOAB is a component for representing and evaluating mesh data. MOAB can store stuctured and unstructured mesh, consisting of elements in the finite element "zoo". The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh. MOAB is optimized for efficiency in space and time, based on access to mesh in chunks rather than through individual entities, while also versatile enough to support individualmore » entity access. The MOAB data model consists of a mesh interface instance, mesh entities (vertices and elements), sets, and tags. Entities are addressed through handles rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms isa powerful yet simple interface for representing metadata or application-specific data. For example, sets and tags can be used together to describe geometric topology, boundary condition, and inter-processor interface groupings in a mesh. MOAB is used in several ways in various applications. MOAB serves as the underlying mesh data representation in the VERDE mesh verification code. MOAB can also be used as a mesh input mechanism, using mesh readers induded with MOAB, or as a t’anslator between mesh formats, using readers and writers included with MOAB.« less

  17. Mesh Oriented datABase

    SciTech Connect

    Tautges, Timothy J.

    2004-04-01

    MOAB is a component for representing and evaluating mesh data. MOAB can store stuctured and unstructured mesh, consisting of elements in the finite element "zoo". The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh. MOAB is optimized for efficiency in space and time, based on access to mesh in chunks rather than through individual entities, while also versatile enough to support individual entity access. The MOAB data model consists of a mesh interface instance, mesh entities (vertices and elements), sets, and tags. Entities are addressed through handles rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms isa powerful yet simple interface for representing metadata or application-specific data. For example, sets and tags can be used together to describe geometric topology, boundary condition, and inter-processor interface groupings in a mesh. MOAB is used in several ways in various applications. MOAB serves as the underlying mesh data representation in the VERDE mesh verification code. MOAB can also be used as a mesh input mechanism, using mesh readers induded with MOAB, or as a t’anslator between mesh formats, using readers and writers included with MOAB.

  18. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.

  19. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

  20. Volume Decomposition and Feature Recognition for Hexahedral Mesh Generation

    SciTech Connect

    GADH,RAJIT; LU,YONG; TAUTGES,TIMOTHY J.

    1999-09-27

    Considerable progress has been made on automatic hexahedral mesh generation in recent years. Several automatic meshing algorithms have proven to be very reliable on certain classes of geometry. While it is always worth pursuing general algorithms viable on more general geometry, a combination of the well-established algorithms is ready to take on classes of complicated geometry. By partitioning the entire geometry into meshable pieces matched with appropriate meshing algorithm the original geometry becomes meshable and may achieve better mesh quality. Each meshable portion is recognized as a meshing feature. This paper, which is a part of the feature based meshing methodology, presents the work on shape recognition and volume decomposition to automatically decompose a CAD model into meshable volumes. There are four phases in this approach: (1) Feature Determination to extinct decomposition features, (2) Cutting Surfaces Generation to form the ''tailored'' cutting surfaces, (3) Body Decomposition to get the imprinted volumes; and (4) Meshing Algorithm Assignment to match volumes decomposed with appropriate meshing algorithms. The feature determination procedure is based on the CLoop feature recognition algorithm that is extended to be more general. Results are demonstrated over several parts with complicated topology and geometry.

  1. Tangle-Free Finite Element Mesh Motion for Ablation Problems

    NASA Technical Reports Server (NTRS)

    Droba, Justin

    2016-01-01

    In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.

  2. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863

  3. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  4. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  5. Aprepro - Algebraic Preprocessor

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  6. Geometric Algebra for Physicists

    NASA Astrophysics Data System (ADS)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  7. The Algebraic Way

    NASA Astrophysics Data System (ADS)

    Hiley, B. J.

    In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

  8. Details of tetrahedral anisotropic mesh adaptation

    NASA Astrophysics Data System (ADS)

    Jensen, Kristian Ejlebjerg; Gorman, Gerard

    2016-04-01

    We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.

  9. toolkit computational mesh conceptual model.

    SciTech Connect

    Baur, David G.; Edwards, Harold Carter; Cochran, William K.; Williams, Alan B.; Sjaardema, Gregory D.

    2010-03-01

    The Sierra Toolkit computational mesh is a software library intended to support massively parallel multi-physics computations on dynamically changing unstructured meshes. This domain of intended use is inherently complex due to distributed memory parallelism, parallel scalability, heterogeneity of physics, heterogeneous discretization of an unstructured mesh, and runtime adaptation of the mesh. Management of this inherent complexity begins with a conceptual analysis and modeling of this domain of intended use; i.e., development of a domain model. The Sierra Toolkit computational mesh software library is designed and implemented based upon this domain model. Software developers using, maintaining, or extending the Sierra Toolkit computational mesh library must be familiar with the concepts/domain model presented in this report.

  10. Adaptive Mesh Enrichment for the Poisson-Boltzmann Equation

    NASA Astrophysics Data System (ADS)

    Dyshlovenko, Pavel

    2001-09-01

    An adaptive mesh enrichment procedure for a finite-element solution of the two-dimensional Poisson-Boltzmann equation is described. The mesh adaptation is performed by subdividing the cells using information obtained in the previous step of the solution and next rearranging the mesh to be a Delaunay triangulation. The procedure allows the gradual improvement of the quality of the solution and adjustment of the geometry of the problem. The performance of the proposed approach is illustrated by applying it to the problem of two identical colloidal particles in a symmetric electrolyte.

  11. Serial and parallel dynamic adaptation of general hybrid meshes

    NASA Astrophysics Data System (ADS)

    Kavouklis, Christos

    termination detection algorithm of Dijkstra is employed for (i) parallel flagging of mesh edges, (ii) global numbering of newly created nodes, and (iii) deletion of nodes after coarsening. An inexpensive dynamic load balancing strategy is employed to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced, which yields savings in computation time and a simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) parallel flow feature detection, (ii) data migration and dynamic updates of local data structures, (iii) determination of the new interpartition boundary and (iv) determination of the communication pattern of processors after load balancing.

  12. A Decoupled Finite Element Heterogeneous Coarse Mesh Transport Method.

    SciTech Connect

    Mosher, S. W.; Rahnema, Farzad

    2005-01-01

    In a recent paper, an original finite element (FE) method was presented for solving eigenvalue transport problems on a coarse spatial mesh. The method employed a surface Green's function expansion of the angular flux trial functions, so that heterogeneous coarse-meshes could be treated with relative ease. Numerical problems were solved using the multigroup discrete ordinates approximation in one-dimensional (1-D) slab geometry. Unfortunately, difficulties were encountered in finding solutions to the algebraic finite element equations, which led to sizeable angular flux discontinuities at coarse-mesh interfaces and significant errors. For this reason, a nonvariational iterative technique was ultimately favored for converging the angular flux distribution, and was used in conjunction with a Rayleigh quotient for converging the eigenvalue. In this paper, a new derivation of finite element equations is presented, which seems to offer a remedy for at least some of the numerical ills that plagued the previous work. First, the equations are derived in terms of a generalized response function expansion. This allows a more efficient response basis to be employed and vastly reduces the overall computational effort without a substantial loss of accuracy. Second, the tight coupling between coarse-meshes in the original equations is effectively broken by assuming that an accurate estimate of the flux distribution entering a given coarse-mesh is known. With an additional assumption that an accurate eigenvalue estimate is known, an iterative approach to solving these decoupled finite element (DFE) equations is developed. The DFE method has been applied to both 1- and 2-D heterogeneous coarse-mesh problems with a far greater degree of success than the original FE method. However, some numerical difficulties remain to be overcome before the new approach can be considered robust.

  13. Risk Factors for Mesh Exposure after Transvaginal Mesh Surgery

    PubMed Central

    Niu, Ke; Lu, Yong-Xian; Shen, Wen-Jie; Zhang, Ying-Hui; Wang, Wen-Ying

    2016-01-01

    Background: Mesh exposure after surgery continues to be a clinical challenge for urogynecological surgeons. The purpose of this study was to explore the risk factors for polypropylene (PP) mesh exposure after transvaginal mesh (TVM) surgery. Methods: This study included 195 patients with advanced pelvic organ prolapse (POP), who underwent TVM from January 2004 to December 2012 at the First Affiliated Hospital of Chinese PLA General Hospital. Clinical data were evaluated including patient's demography, TVM type, concomitant procedures, operation time, blood loss, postoperative morbidity, and mesh exposure. Mesh exposure was identified through postoperative vaginal examination. Statistical analysis was performed to identify risk factors for mesh exposure. Results: Two-hundred and nine transvaginal PP meshes were placed, including 194 in the anterior wall and 15 in the posterior wall. Concomitant tension-free vaginal tape was performed in 61 cases. The mean follow-up time was 35.1 ± 23.6 months. PP mesh exposure was identified in 32 cases (16.4%), with 31 in the anterior wall and 1 in the posterior wall. Significant difference was found in operating time and concomitant procedures between exposed and nonexposed groups (F = 7.443, P = 0.007; F = 4.307, P = 0.039, respectively). Binary logistic regression revealed that the number of concomitant procedures and operation time were risk factors for mesh exposure (P = 0.001, P = 0.043). Conclusion: Concomitant procedures and increased operating time increase the risk for postoperative mesh exposure in patients undergoing TVM surgery for POP. PMID:27453227

  14. An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement.

    SciTech Connect

    Edgel, Jared; Benzley, Steven E.; Owen, Steven James

    2010-08-01

    Most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is often too coarse in some areas and over refined in other areas. Because this method generates 27 new hexes in place of a single hex, there is little control on mesh density. This paper presents an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement method. 2-refinement is based on dividing the hex to be refined into eight new hexes. This method allows a greater control on mesh density when compared to a 3-refinement procedure. This adaptive all-hexahedral meshing algorithm provides a mesh that is efficient for analysis by providing a high element density in specific locations and a reduced mesh density in other areas. In addition, this tool can be effectively used for inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, which have shown great promise in accommodating automatic all-hexahedral algorithms. This adaptive all-hexahedral grid-based meshing algorithm employs a 2-refinement insertion method. This allows greater control on mesh density when compared to 3-refinement methods. This algorithm uses a two layer transition zone to increase element quality and keeps transitions from lower to higher mesh densities smooth. Templates were introduced to allow both convex and concave refinement.

  15. Colposacropexy with Prolene mesh.

    PubMed

    Baker, K R; Beresford, J M; Campbell, C

    1990-07-01

    A retrospective analysis of 59 patients who underwent colposacropexy (CSP) using Prolene (polypropylene) mesh is presented. Fifty-eight of the patients had undergone previous surgical treatment, including either vaginal or abdominal hysterectomy. Twenty-two patients underwent CSP alone, 24 had CSP and retropubic urethropexy (RPU), eight had CSP with anterior or posterior repair, or both, and five had CSP and RPU with anterior and posterior repair. The operations were associated with a minimum of intraoperative complications and acceptable postoperative problems. A postoperative questionnaire was sent to the patients with an 89 per cent response rate. None of the patients complained of protrusion from the vagina. It is concluded that, in the hands of experienced surgeons, CSP is a safe, efficacious operative procedure that should remain the procedure of choice for vaginal vault prolapse since it restores the normal vaginal axis, maintains existing vaginal length and provides permanent care. PMID:2193414

  16. Invisible metallic mesh.

    PubMed

    Ye, Dexin; Lu, Ling; Joannopoulos, John D; Soljačić, Marin; Ran, Lixin

    2016-03-01

    A solid material possessing identical electromagnetic properties as air has yet to be found in nature. Such a medium of arbitrary shape would neither reflect nor refract light at any angle of incidence in free space. Here, we introduce nonscattering corrugated metallic wires to construct such a medium. This was accomplished by aligning the dark-state frequencies in multiple scattering channels of a single wire. Analytical solutions, full-wave simulations, and microwave measurement results on 3D printed samples show omnidirectional invisibility in any configuration. This invisible metallic mesh can improve mechanical stability, electrical conduction, and heat dissipation of a system, without disturbing the electromagnetic design. Our approach is simple, robust, and scalable to higher frequencies. PMID:26884208

  17. Invisible metallic mesh

    PubMed Central

    Ye, Dexin; Lu, Ling; Joannopoulos, John D.; Soljačić, Marin; Ran, Lixin

    2016-01-01

    A solid material possessing identical electromagnetic properties as air has yet to be found in nature. Such a medium of arbitrary shape would neither reflect nor refract light at any angle of incidence in free space. Here, we introduce nonscattering corrugated metallic wires to construct such a medium. This was accomplished by aligning the dark-state frequencies in multiple scattering channels of a single wire. Analytical solutions, full-wave simulations, and microwave measurement results on 3D printed samples show omnidirectional invisibility in any configuration. This invisible metallic mesh can improve mechanical stability, electrical conduction, and heat dissipation of a system, without disturbing the electromagnetic design. Our approach is simple, robust, and scalable to higher frequencies. PMID:26884208

  18. Quadrilateral finite element mesh coarsening

    DOEpatents

    Staten, Matthew L; Dewey, Mark W; Benzley, Steven E

    2012-10-16

    Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.

  19. Laparoscopic paracolostomy hernia mesh repair.

    PubMed

    Virzí, Giuseppe; Giuseppe, Virzí; Scaravilli, Francesco; Francesco, Scaravilli; Ragazzi, Salvatore; Salvatore, Ragazzi; Piazza, Diego; Diego, Piazza

    2007-12-01

    Paracolostomy hernia is a common occurrence, representing a late complication of stoma surgery. Different surgical techniques have been proposed to repair the wall defect, but the lowest recurrence rates are associated with the use of mesh. We present the case report of a patient in which laparoscopic paracolostomy hernia mesh repair has been successfully performed. PMID:18097321

  20. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  1. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  2. A Survey of Solver-Related Geometry and Meshing Issues

    NASA Technical Reports Server (NTRS)

    Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris

    2016-01-01

    There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.

  3. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  4. Algebra for Gifted Third Graders.

    ERIC Educational Resources Information Center

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  5. Which mesh for hernia repair?

    PubMed Central

    Brown, CN; Finch, JG

    2010-01-01

    INTRODUCTION The concept of using a mesh to repair hernias was introduced over 50 years ago. Mesh repair is now standard in most countries and widely accepted as superior to primary suture repair. As a result, there has been a rapid growth in the variety of meshes available and choosing the appropriate one can be difficult. This article outlines the general properties of meshes and factors to be considered when selecting one. MATERIALS AND METHODS We performed a search of the medical literature from 1950 to 1 May 2009, as indexed by Medline, using the PubMed search engine (). To capture all potentially relevant articles with the highest degree of sensitivity, the search terms were intentionally broad. We used the following terms: ‘mesh, pore size, strength, recurrence, complications, lightweight, properties’. We also hand-searched the bibliographies of relevant articles and product literature to identify additional pertinent reports. RESULTS AND CONCLUSIONS The most important properties of meshes were found to be the type of filament, tensile strength and porosity. These determine the weight of the mesh and its biocompatibility. The tensile strength required is much less than originally presumed and light-weight meshes are thought to be superior due to their increased flexibility and reduction in discomfort. Large pores are also associated with a reduced risk of infection and shrinkage. For meshes placed in the peritoneal cavity, consideration should also be given to the risk of adhesion formation. A variety of composite meshes have been promoted to address this, but none appears superior to the others. Finally, biomaterials such as acellular dermis have a place for use in infected fields but have yet to prove their worth in routine hernia repair. PMID:20501011

  6. Pseudo Algebraically Closed Extensions

    NASA Astrophysics Data System (ADS)

    Bary-Soroker, Lior

    2009-07-01

    This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.

  7. Assessing Elementary Algebra with STACK

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  8. Heterogeneous Wireless Mesh Network Technology Evaluation for Space Proximity and Surface Applications

    NASA Technical Reports Server (NTRS)

    DeCristofaro, Michael A.; Lansdowne, Chatwin A.; Schlesinger, Adam M.

    2014-01-01

    NASA has identified standardized wireless mesh networking as a key technology for future human and robotic space exploration. Wireless mesh networks enable rapid deployment, provide coverage in undeveloped regions. Mesh networks are also self-healing, resilient, and extensible, qualities not found in traditional infrastructure-based networks. Mesh networks can offer lower size, weight, and power (SWaP) than overlapped infrastructure-perapplication. To better understand the maturity, characteristics and capability of the technology, we developed an 802.11 mesh network consisting of a combination of heterogeneous commercial off-the-shelf devices and opensource firmware and software packages. Various streaming applications were operated over the mesh network, including voice and video, and performance measurements were made under different operating scenarios. During the testing several issues with the currently implemented mesh network technology were identified and outlined for future work.

  9. A LAGUERRE VORONOI BASED SCHEME FOR MESHING PARTICLE SYSTEMS.

    PubMed

    Bajaj, Chandrajit

    2005-06-01

    We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initial quadrilateral or an initial hexahedral scaffold conforming to individual particles. The scaffolds are subsequently refined via applications of recursive subdivision (splitting and averaging rules). Our choice of averaging rules yield a particle conforming quadrilateral/hexahedral mesh, of good quality, along with being smooth and differentiable in the limit. Extensions of the basic scheme to dynamic re-meshing in the case of addition, deletion, and moving particles are also discussed. Motivating applications of the use of these static and dynamic meshes for particle systems include the mechanics of epoxy/glass composite materials, bio-molecular force field calculations, and gas hydrodynamics simulations in cosmology.

  10. 21 CFR 878.3300 - Surgical mesh.

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... GENERAL AND PLASTIC SURGERY DEVICES Prosthetic Devices § 878.3300 Surgical mesh. (a) Identification... acetabular and cement restrictor mesh used during orthopedic surgery. (b) Classification. Class II....

  11. 21 CFR 878.3300 - Surgical mesh.

    Code of Federal Regulations, 2014 CFR

    2014-04-01

    ... GENERAL AND PLASTIC SURGERY DEVICES Prosthetic Devices § 878.3300 Surgical mesh. (a) Identification... acetabular and cement restrictor mesh used during orthopedic surgery. (b) Classification. Class II....

  12. 21 CFR 878.3300 - Surgical mesh.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... GENERAL AND PLASTIC SURGERY DEVICES Prosthetic Devices § 878.3300 Surgical mesh. (a) Identification... acetabular and cement restrictor mesh used during orthopedic surgery. (b) Classification. Class II....

  13. 21 CFR 878.3300 - Surgical mesh.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... GENERAL AND PLASTIC SURGERY DEVICES Prosthetic Devices § 878.3300 Surgical mesh. (a) Identification... acetabular and cement restrictor mesh used during orthopedic surgery. (b) Classification. Class II....

  14. 21 CFR 878.3300 - Surgical mesh.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... GENERAL AND PLASTIC SURGERY DEVICES Prosthetic Devices § 878.3300 Surgical mesh. (a) Identification... acetabular and cement restrictor mesh used during orthopedic surgery. (b) Classification. Class II....

  15. Streaming Compression of Hexahedral Meshes

    SciTech Connect

    Isenburg, M; Courbet, C

    2010-02-03

    We describe a method for streaming compression of hexahedral meshes. Given an interleaved stream of vertices and hexahedral our coder incrementally compresses the mesh in the presented order. Our coder is extremely memory efficient when the input stream documents when vertices are referenced for the last time (i.e. when it contains topological finalization tags). Our coder then continuously releases and reuses data structures that no longer contribute to compressing the remainder of the stream. This means in practice that our coder has only a small fraction of the whole mesh in memory at any time. We can therefore compress very large meshes - even meshes that do not file in memory. Compared to traditional, non-streaming approaches that load the entire mesh and globally reorder it during compression, our algorithm trades a less compact compressed representation for significant gains in speed, memory, and I/O efficiency. For example, on the 456k hexahedra 'blade' mesh, our coder is twice as fast and uses 88 times less memory (only 3.1 MB) with the compressed file increasing about 3% in size. We also present the first scheme for predictive compression of properties associated with hexahedral cells.

  16. College Algebra II.

    ERIC Educational Resources Information Center

    Benjamin, Carl; And Others

    Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…

  17. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  18. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  19. Algebraic Artful Aids.

    ERIC Educational Resources Information Center

    Glick, David

    1995-01-01

    Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

  20. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  1. Nanowire mesh solar fuels generator

    DOEpatents

    Yang, Peidong; Chan, Candace; Sun, Jianwei; Liu, Bin

    2016-05-24

    This disclosure provides systems, methods, and apparatus related to a nanowire mesh solar fuels generator. In one aspect, a nanowire mesh solar fuels generator includes (1) a photoanode configured to perform water oxidation and (2) a photocathode configured to perform water reduction. The photocathode is in electrical contact with the photoanode. The photoanode may include a high surface area network of photoanode nanowires. The photocathode may include a high surface area network of photocathode nanowires. In some embodiments, the nanowire mesh solar fuels generator may include an ion conductive polymer infiltrating the photoanode and the photocathode in the region where the photocathode is in electrical contact with the photoanode.

  2. Cu mesh for flexible transparent conductive electrodes.

    PubMed

    Kim, Won-Kyung; Lee, Seunghun; Hee Lee, Duck; Hee Park, In; Seong Bae, Jong; Woo Lee, Tae; Kim, Ji-Young; Hun Park, Ji; Chan Cho, Yong; Ryong Cho, Chae; Jeong, Se-Young

    2015-06-03

    Copper electrodes with a micromesh/nanomesh structure were fabricated on a polyimide substrate using UV lithography and wet etching to produce flexible transparent conducting electrodes (TCEs). Well-defined mesh electrodes were realized through the use of high-quality Cu thin films. The films were fabricated using radio-frequency (RF) sputtering with a single-crystal Cu target--a simple but innovative approach that overcame the low oxidation resistance of ordinary Cu. Hybrid Cu mesh electrodes were fabricated by adding a capping layer of either ZnO or Al-doped ZnO. The sheet resistance and the transmittance of the electrode with an Al-doped ZnO capping layer were 6.197 ohm/sq and 90.657%, respectively, and the figure of merit was 60.502 × 10(-3)/ohm, which remained relatively unchanged after thermal annealing at 200 °C and 1,000 cycles of bending. This fabrication technique enables the mass production of large-area flexible TCEs, and the stability and high performance of Cu mesh hybrid electrodes in harsh environments suggests they have strong potential for application in smart displays and solar cells.

  3. Cu Mesh for Flexible Transparent Conductive Electrodes

    PubMed Central

    Kim, Won-Kyung; Lee, Seunghun; Hee Lee, Duck; Hee Park, In; Seong Bae, Jong; Woo Lee, Tae; Kim, Ji-Young; Hun Park, Ji; Chan Cho, Yong; Ryong Cho, Chae; Jeong, Se-Young

    2015-01-01

    Copper electrodes with a micromesh/nanomesh structure were fabricated on a polyimide substrate using UV lithography and wet etching to produce flexible transparent conducting electrodes (TCEs). Well-defined mesh electrodes were realized through the use of high-quality Cu thin films. The films were fabricated using radio-frequency (RF) sputtering with a single-crystal Cu target—a simple but innovative approach that overcame the low oxidation resistance of ordinary Cu. Hybrid Cu mesh electrodes were fabricated by adding a capping layer of either ZnO or Al-doped ZnO. The sheet resistance and the transmittance of the electrode with an Al-doped ZnO capping layer were 6.197 ohm/sq and 90.657%, respectively, and the figure of merit was 60.502 × 10–3/ohm, which remained relatively unchanged after thermal annealing at 200 °C and 1,000 cycles of bending. This fabrication technique enables the mass production of large-area flexible TCEs, and the stability and high performance of Cu mesh hybrid electrodes in harsh environments suggests they have strong potential for application in smart displays and solar cells. PMID:26039977

  4. Parallel Adaptive Mesh Refinement Library

    NASA Technical Reports Server (NTRS)

    Mac-Neice, Peter; Olson, Kevin

    2005-01-01

    Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

  5. Final Technical Report: Global Field Aligned Mesh and Gyrokinetic Field Solver in a Tokamak Edge Geometry

    SciTech Connect

    Cummings, Julian C.

    2013-05-15

    This project was a collaboration between researchers at the California Institute of Technology and the University of California, Irvine to investigate the utility of a global field-aligned mesh and gyrokinetic field solver for simulations of the tokamak plasma edge region. Mesh generation software from UC Irvine was tested with specific tokamak edge magnetic geometry scenarios and the quality of the meshes and the solutions to the gyrokinetic Poisson equation were evaluated.

  6. Image-driven mesh optimization

    SciTech Connect

    Lindstrom, P; Turk, G

    2001-01-05

    We describe a method of improving the appearance of a low vertex count mesh in a manner that is guided by rendered images of the original, detailed mesh. This approach is motivated by the fact that greedy simplification methods often yield meshes that are poorer than what can be represented with a given number of vertices. Our approach relies on edge swaps and vertex teleports to alter the mesh connectivity, and uses the downhill simplex method to simultaneously improve vertex positions and surface attributes. Note that this is not a simplification method--the vertex count remains the same throughout the optimization. At all stages of the optimization the changes are guided by a metric that measures the differences between rendered versions of the original model and the low vertex count mesh. This method creates meshes that are geometrically faithful to the original model. Moreover, the method takes into account more subtle aspects of a model such as surface shading or whether cracks are visible between two interpenetrating parts of the model.

  7. Method and system for mesh network embedded devices

    NASA Technical Reports Server (NTRS)

    Wang, Ray (Inventor)

    2009-01-01

    A method and system for managing mesh network devices. A mesh network device with integrated features creates an N-way mesh network with a full mesh network topology or a partial mesh network topology.

  8. Parallel adaptation of general three-dimensional hybrid meshes

    SciTech Connect

    Kavouklis, Christos Kallinderis, Yannis

    2010-05-01

    A new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid grids has been developed. The meshes considered in this work are composed of four kinds of elements; tetrahedra, prisms, hexahedra and pyramids, which poses a challenge to parallel mesh adaptation. Additional complexity imposed by the presence of multiple types of elements affects especially data migration, updates of local data structures and interpartition data structures. Efficient partition of hybrid meshes has been accomplished by transforming them to suitable graphs and using serial graph partitioning algorithms. Communication among processors is based on the faces of the interpartition boundary and the termination detection algorithm of Dijkstra is employed to ensure proper flagging of edges for refinement. An inexpensive dynamic load balancing strategy is introduced to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced which yields savings in computation time and relatively simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) data migration and dynamic updates of the local data structures, (ii) determination of the resulting interpartition boundary and (iii) identification of the communication pattern of processors. Several representative applications are included to evaluate the method.

  9. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  10. Calculating C-grids with fine and embedded mesh regions

    NASA Technical Reports Server (NTRS)

    Loyd, B.

    1984-01-01

    A program for calculating a C-type mesh around airfoil like shapes is described. The Jameson/Caughey approach is used: a parabolic transformation coupled with a shearing transformation. The algebraic algorithm is capable of efficiently generating nearly orthogonal grids. A high degree of grid control is possible. The user may specify grid boundaries, number of grid lines, and location of (and spacing in) trailing edge and leading edge fine mesh areas. The capability of embedding fine mesh regions, for use with new adaptive grid techniques, is being developed. Grids generated by the program were used in Euler flow flow calculatons by W. Usab. Results superior to results calculated on previous O-type grids were obtained. Specifically, calculations converged faster using C-grids rather than 0-grids, total pressure loss spikes at the trailing edge of the airfoil were eliminated, and the Ni method converged with zero artificial smoothing for a subcritical case (resulting overall total pressure loss was then nearly zero). These improvements were attributed to higher grid orthogonality, especially at the trailing edge. The program itself is fairly straightforward. Roughly half of the 800 code lines are comment lines.

  11. Diffraction analysis of mesh deployable reflector antennas

    NASA Astrophysics Data System (ADS)

    Rahmat-Samii, Y.

    1985-04-01

    A formulation and many representative numerical results for mesh reflector antennas are presented. The reflection coefficient matrix for the prescribed mesh configuration was determined and the local coordinate system of the mesh cells at each point on the curved reflector surface was accentuated. A novel strip aperture model was used to formulate the transmission coefficient matrix for a variety of mesh cell configurations. Numerical data are tailored to the dimensions of a conceptually designed land mobile satellite system (LMSS) which employs a large mesh deployable offset parabolic antenna. Results are shown for an offset parabolic reflector with mesh surfaces similar to the mesh surface of tracking and data relay satellite system (TDRSS).

  12. Diffraction Analysis of Mesh Deployable Reflector Antennas

    NASA Technical Reports Server (NTRS)

    Rahmat-Samii, Y.

    1985-01-01

    A formulation and many representative numerical results for mesh reflector antennas are presented. The reflection coefficient matrix for the prescribed mesh configuration was determined and the local coordinate system of the mesh cells at each point on the curved reflector surface was accentuated. A novel strip aperture model was used to formulate the transmission coefficient matrix for a variety of mesh cell configurations. Numerical data are tailored to the dimensions of a conceptually designed land mobile satellite system (LMSS) which employs a large mesh deployable offset parabolic antenna. Results are shown for an offset parabolic reflector with mesh surfaces similar to the mesh surface of tracking and data relay satellite system (TDRSS).

  13. Assessment of mesh simplification algorithm quality

    NASA Astrophysics Data System (ADS)

    Roy, Michael; Nicolier, Frederic; Foufou, S.; Truchetet, Frederic; Koschan, Andreas; Abidi, Mongi A.

    2002-03-01

    Traditionally, medical geneticists have employed visual inspection (anthroposcopy) to clinically evaluate dysmorphology. In the last 20 years, there has been an increasing trend towards quantitative assessment to render diagnosis of anomalies more objective and reliable. These methods have focused on direct anthropometry, using a combination of classical physical anthropology tools and new instruments tailor-made to describe craniofacial morphometry. These methods are painstaking and require that the patient remain still for extended periods of time. Most recently, semiautomated techniques (e.g., structured light scanning) have been developed to capture the geometry of the face in a matter of seconds. In this paper, we establish that direct anthropometry and structured light scanning yield reliable measurements, with remarkably high levels of inter-rater and intra-rater reliability, as well as validity (contrasting the two methods).

  14. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  15. Algebra of Majorana doubling.

    PubMed

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  16. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  17. User Manual for the PROTEUS Mesh Tools

    SciTech Connect

    Smith, Micheal A.; Shemon, Emily R.

    2015-06-01

    This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial or .merge) can be used as “mesh” input for any of the mesh tools discussed in this manual.

  18. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  19. Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies

    NASA Astrophysics Data System (ADS)

    Gahalaut, K. P. S.; Tomar, S. K.; Kraus, J. K.

    2013-11-01

    We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size $h$ is given for $p=2,3,4$ and for $C^{0}$- and $C^{p-1}$-continuity. The presented methods show $h$- and (almost) $p$-independent convergence rates. Supporting numerical results for convergence factor and iterations count for AMLI cycles ($V$-, linear $W$-, nonlinear $W$-) are provided. Numerical tests are performed, in two-dimensions on square domain and quarter annulus, and in three-dimensions on quarter thick ring.

  20. Single port laparoscopic mesh rectopexy

    PubMed Central

    2016-01-01

    Introduction Traditionally, laparoscopic mesh rectopexy is performed with four ports, in an attempt to improve cosmetic results. Following laparoscopic mesh rectopexy there is a new operative technique called single-port laparoscopic mesh rectopexy. Aim To evaluate the single-port laparoscopic mesh rectopexy technique in control of rectal prolapse and the cosmesis and body image issues of this technique. Material and methods The study was conducted in El Fayoum University Hospital between July 2013 and November 2014 in elective surgery for symptomatic rectal prolapse with single-port laparoscopic mesh rectopexy on 10 patients. Results The study included 10 patients: 3 (30%) males and 7 (70%) females. Their ages ranged between 19 years and 60 years (mean: 40.3 ±6 years), and they all underwent laparoscopic mesh rectopexy. There were no conversions to open technique, nor injuries to the rectum or bowel, and there were no mortalities. Mean operative time was 120 min (range: 90–150 min), and mean hospital stay was 2 days (range: 1–3 days). Preoperatively, incontinence was seen in 5 (50%) patients and constipation in 4 (40%). Postoperatively, improvement in these symptoms was seen in 3 (60%) patients for incontinence and in 3 (75%) for constipation. Follow-up was done for 6 months and no recurrence was found with better cosmetic appearance for all patients. Conclusions Single-port laparoscopic mesh rectopexy is a safe procedure with good results as regards operative time, improvement in bowel function, morbidity, cost, and recurrence, and with better cosmetic appearance. PMID:27350840

  1. On the cohomology of Leibniz conformal algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Jiao

    2015-04-01

    We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.

  2. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  3. PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

    NASA Technical Reports Server (NTRS)

    Oliker, Leonid

    1998-01-01

    Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at

  4. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075

  5. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  6. Second-Order Algebraic Theories

    NASA Astrophysics Data System (ADS)

    Fiore, Marcelo; Mahmoud, Ola

    Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.

  7. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  8. A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases.

    PubMed

    Bucki, Marek; Lobos, Claudio; Payan, Yohan

    2010-06-01

    Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. In the latter case, both skin and bone surfaces were taken into account by the mesh registration process in order to model the face muscles and fat layers. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software.

  9. Cache-oblivious mesh layouts

    SciTech Connect

    Yoon, Sung-Eui; Lindstrom, Peter; Pascucci, Valerio; Manocha, Dinesh

    2005-07-01

    We present a novel method for computing cache-oblivious layouts of large meshes that improve the performance of interactive visualization and geometric processing algorithms. Given that the mesh is accessed in a reasonably coherent manner, we assume no particular data access patterns or cache parameters of the memory hierarchy involved in the computation. Furthermore, our formulation extends directly to computing layouts of multi-resolution and bounding volume hierarchies of large meshes. We develop a simple and practical cache-oblivious metric for estimating cache misses. Computing a coherent mesh layout is reduced to a combinatorial optimization problem. We designed and implemented an out-of-core multilevel minimization algorithm and tested its performance on unstructured meshes composed of tens to hundreds of millions of triangles. Our layouts can significantly reduce the number of cache misses. We have observed 2-20 times speedups in view-dependent rendering, collision detection, and isocontour extraction without any modification of the algorithms or runtime applications.

  10. Self-Organizing Mesh Generation

    1991-11-01

    A set of five programs which make up a self organizing mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily shaped two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchal input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program,more » RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight node elements (with mid side nodes) may be obtained with RENUM8. QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers, An overall plot showing the position of the selected plot areas is produced.« less

  11. LayTracks3D: A new approach for meshing general solids using medial axis transform

    SciTech Connect

    Quadros, William Roshan

    2015-08-22

    This study presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.

  12. 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Shavkat; Kudaybergenov, Karimbergen

    2016-03-01

    The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.

  13. Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

    NASA Astrophysics Data System (ADS)

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2016-05-01

    A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

  14. Plethystic algebras and vector symmetric functions.

    PubMed Central

    Rota, G C; Stein, J A

    1994-01-01

    An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504

  15. On Linear Spaces of Polyhedral Meshes.

    PubMed

    Poranne, Roi; Chen, Renjie; Gotsman, Craig

    2015-05-01

    Polyhedral meshes (PM)-meshes having planar faces-have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes having that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology.

  16. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  17. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  18. Handheld Computer Algebra Systems in the Pre-Algebra Classroom

    ERIC Educational Resources Information Center

    Gantz, Linda Ann Galofaro

    2010-01-01

    This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…

  19. Deformable mesh registration for the validation of automatic target localization algorithms

    PubMed Central

    Robertson, Scott; Weiss, Elisabeth; Hugo, Geoffrey D.

    2013-01-01

    Purpose: To evaluate deformable mesh registration (DMR) as a tool for validating automatic target registration algorithms used during image-guided radiation therapy. Methods: DMR was implemented in a hierarchical model, with rigid, affine, and B-spline transforms optimized in succession to register a pair of surface meshes. The gross tumor volumes (primary tumor and involved lymph nodes) were contoured by a physician on weekly CT scans in a cohort of lung cancer patients and converted to surface meshes. The meshes from weekly CT images were registered to the mesh from the planning CT, and the resulting registered meshes were compared with the delineated surfaces. Known deformations were also applied to the meshes, followed by mesh registration to recover the known deformation. Mesh registration accuracy was assessed at the mesh surface by computing the symmetric surface distance (SSD) between vertices of each registered mesh pair. Mesh registration quality in regions within 5 mm of the mesh surface was evaluated with respect to a high quality deformable image registration. Results: For 18 patients presenting with a total of 19 primary lung tumors and 24 lymph node targets, the SSD averaged 1.3 ± 0.5 and 0.8 ± 0.2 mm, respectively. Vertex registration errors (VRE) relative to the applied known deformation were 0.8 ± 0.7 and 0.2 ± 0.3 mm for the primary tumor and lymph nodes, respectively. Inside the mesh surface, corresponding average VRE ranged from 0.6 to 0.9 and 0.2 to 0.9 mm, respectively. Outside the mesh surface, average VRE ranged from 0.7 to 1.8 and 0.2 to 1.4 mm. The magnitude of errors generally increased with increasing distance away from the mesh. Conclusions: Provided that delineated surfaces are available, deformable mesh registration is an accurate and reliable method for obtaining a reference registration to validate automatic target registration algorithms for image-guided radiation therapy, specifically in regions on or near the target surfaces

  20. Issues in adaptive mesh refinement

    SciTech Connect

    Dai, William Wenlong

    2009-01-01

    In this paper, we present an approach for a patch-based adaptive mesh refinement (AMR) for multi-physics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, and management of patches. Among the special features of this patch-based AMR are symmetry preserving, efficiency of refinement, special implementation offlux correction, and patch management in parallel computing environments. Here, higher efficiency of refinement means less unnecessarily refined cells for a given set of cells to be refined. To demonstrate the capability of the AMR framework, hydrodynamics simulations with many levels of refinement are shown in both two- and three-dimensions.

  1. Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

    NASA Astrophysics Data System (ADS)

    Slattery, Stuart R.

    2016-02-01

    In this paper we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. These scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

  2. Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

    SciTech Connect

    Slattery, Stuart R.

    2015-12-02

    In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

  3. Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

    DOE PAGES

    Slattery, Stuart R.

    2015-12-02

    In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

  4. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  5. Algebraic Multigrid Benchmark

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less

  6. Mesh-on-lead anodes for copper electrowinning

    NASA Astrophysics Data System (ADS)

    Moats, Michael; Hardee, Kenneth; Brown, Carl

    2003-07-01

    ELTECH System Corporation has developed and patented a Mesh-on-Lead™ (MOL™) (Mesh-on-Lead and MOL are trademarks of ELTECH Systems Corporation) anode for primary copper electrowinning operations. Over the past five years, ELTECH has demonstrated the MOL concept with full-scale anodes at several premier commercial tankhouses. During these demonstrations MOL anodes exhibited numerous performance advantages relative to standard Pb-Ca-Sn anodes, including reduced power consumption due to lower oxygen evolution over-potential, improved cathode quality, minimized lead sludge generation, eliminated cobalt addition as a result of stabilized lead substrate, and improved current efficiency due to reduced short circuiting.

  7. Adaptive mesh refinement techniques for 3-D skin electrode modeling.

    PubMed

    Sawicki, Bartosz; Okoniewski, Michal

    2010-03-01

    In this paper, we develop a 3-D adaptive mesh refinement technique. The algorithm is constructed with an electric impedance tomography forward problem and the finite-element method in mind, but is applicable to a much wider class of problems. We use the method to evaluate the distribution of currents injected into a model of a human body through skin contact electrodes. We demonstrate that the technique leads to a significantly improved solution, particularly near the electrodes. We discuss error estimation, efficiency, and quality of the refinement algorithm and methods that allow for preserving mesh attributes in the refinement process.

  8. Novel biomedical tetrahedral mesh methods: algorithms and applications

    NASA Astrophysics Data System (ADS)

    Yu, Xiao; Jin, Yanfeng; Chen, Weitao; Huang, Pengfei; Gu, Lixu

    2007-12-01

    Tetrahedral mesh generation algorithm, as a prerequisite of many soft tissue simulation methods, becomes very important in the virtual surgery programs because of the real-time requirement. Aiming to speed up the computation in the simulation, we propose a revised Delaunay algorithm which makes a good balance of quality of tetrahedra, boundary preservation and time complexity, with many improved methods. Another mesh algorithm named Space-Disassembling is also presented in this paper, and a comparison of Space-Disassembling, traditional Delaunay algorithm and the revised Delaunay algorithm is processed based on clinical soft-tissue simulation projects, including craniofacial plastic surgery and breast reconstruction plastic surgery.

  9. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  10. Linear algebra and image processing

    NASA Astrophysics Data System (ADS)

    Allali, Mohamed

    2010-09-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.

  11. A Programmed Course in Algebra.

    ERIC Educational Resources Information Center

    Mewborn, Ancel C.; Hively, Wells II

    This programed textbook consists of short sections of text interspersed with questions designed to aid the student in understanding the material. The course is designed to increase the student's understanding of some of the basic ideas of algebra. Some general experience and manipulative skill with respect to high school algebra is assumed.…

  12. Astro Algebra [CD-ROM].

    ERIC Educational Resources Information Center

    1997

    Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

  13. Gamow functionals on operator algebras

    NASA Astrophysics Data System (ADS)

    Castagnino, M.; Gadella, M.; Betán, R. Id; Laura, R.

    2001-11-01

    We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.

  14. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  15. Patterns to Develop Algebraic Reasoning

    ERIC Educational Resources Information Center

    Stump, Sheryl L.

    2011-01-01

    What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

  16. Algebra: Grades 8-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…

  17. Elementary maps on nest algebras

    NASA Astrophysics Data System (ADS)

    Li, Pengtong

    2006-08-01

    Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.

  18. Condensing Algebra for Technical Mathematics.

    ERIC Educational Resources Information Center

    Greenfield, Donald R.

    Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…

  19. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  20. A tuned mesh-generation strategy for image representation based on data-dependent triangulation.

    PubMed

    Li, Ping; Adams, Michael D

    2013-05-01

    A mesh-generation framework for image representation based on data-dependent triangulation is proposed. The proposed framework is a modified version of the frameworks of Rippa and Garland and Heckbert that facilitates the development of more effective mesh-generation methods. As the proposed framework has several free parameters, the effects of different choices of these parameters on mesh quality are studied, leading to the recommendation of a particular set of choices for these parameters. A mesh-generation method is then introduced that employs the proposed framework with these best parameter choices. This method is demonstrated to produce meshes of higher quality (both in terms of squared error and subjectively) than those generated by several competing approaches, at a relatively modest computational and memory cost.

  1. Implementation OSEM mesh-domain SPECT reconstruction with explicit prior information

    NASA Astrophysics Data System (ADS)

    Krol, Andrzej; Vogelsang, Levon; Lu, Yao; Xu, Yuesheng; Hu, Xiaofei; Shen, Lixin; Feiglin, David; Lipson, Edward

    2009-02-01

    In order to improve reconstructed image quality, we investigated performance of OSEM mesh-domain SPECT reconstruction with explicit prior anatomical and physiological information that was used to perform accurate attenuation compensation. It was accomplished in the following steps: (i) Obtain anatomical and physiological atlas of desired region of interest; (ii) Generate mesh that encodes properties of the atlas; (iii) Perform initial pixel-based reconstruction on projection dataset; (iv) Register the expected emission atlas to the initial pixel-based reconstruction and apply resulting transformation to meshed atlas; (v) Perform reconstruction in mesh-domain using deformed mesh of the atlas. This approach was tested on synthetic SPECT noise-free and noisy data. Comparative quantitative analysis demonstrated that this method outperformed pixel-based OSEM with uniform AC and is a promising approach that might lead to improved SPECT reconstruction quality.

  2. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  3. Hybrid Mesh for Nasal Airflow Studies

    PubMed Central

    Zubair, Mohammed; Abdullah, Mohammed Zulkifly; Ahmad, Kamarul Arifin

    2013-01-01

    The accuracy of the numerical result is closely related to mesh density as well as its distribution. Mesh plays a very significant role in the outcome of numerical simulation. Many nasal airflow studies have employed unstructured mesh and more recently hybrid mesh scheme has been utilized considering the complexity of anatomical architecture. The objective of this study is to compare the results of hybrid mesh with unstructured mesh and study its effect on the flow parameters inside the nasal cavity. A three-dimensional nasal cavity model is reconstructed based on computed tomographic images of a healthy Malaysian adult nose. Navier-Stokes equation for steady airflow is solved numerically to examine inspiratory nasal flow. The pressure drop obtained using the unstructured computational grid is about 22.6 Pa for a flow rate of 20 L/min, whereas the hybrid mesh resulted in 17.8 Pa for the same flow rate. The maximum velocity obtained at the nasal valve using unstructured grid is 4.18 m/s and that with hybrid mesh is around 4.76 m/s. Hybrid mesh reported lower grid convergence index (GCI) than the unstructured mesh. Significant differences between unstructured mesh and hybrid mesh are determined highlighting the usefulness of hybrid mesh for nasal airflow studies. PMID:23983811

  4. Hybrid mesh for nasal airflow studies.

    PubMed

    Zubair, Mohammed; Abdullah, Mohammed Zulkifly; Ahmad, Kamarul Arifin

    2013-01-01

    The accuracy of the numerical result is closely related to mesh density as well as its distribution. Mesh plays a very significant role in the outcome of numerical simulation. Many nasal airflow studies have employed unstructured mesh and more recently hybrid mesh scheme has been utilized considering the complexity of anatomical architecture. The objective of this study is to compare the results of hybrid mesh with unstructured mesh and study its effect on the flow parameters inside the nasal cavity. A three-dimensional nasal cavity model is reconstructed based on computed tomographic images of a healthy Malaysian adult nose. Navier-Stokes equation for steady airflow is solved numerically to examine inspiratory nasal flow. The pressure drop obtained using the unstructured computational grid is about 22.6 Pa for a flow rate of 20 L/min, whereas the hybrid mesh resulted in 17.8 Pa for the same flow rate. The maximum velocity obtained at the nasal valve using unstructured grid is 4.18 m/s and that with hybrid mesh is around 4.76 m/s. Hybrid mesh reported lower grid convergence index (GCI) than the unstructured mesh. Significant differences between unstructured mesh and hybrid mesh are determined highlighting the usefulness of hybrid mesh for nasal airflow studies. PMID:23983811

  5. Multigrid for refined triangle meshes

    SciTech Connect

    Shapira, Yair

    1997-02-01

    A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefficients.

  6. Mesh Size Control of Friction

    NASA Astrophysics Data System (ADS)

    Pitenis, Angela; Uruena, Juan Manuel; Schulze, Kyle D.; Cooper, Andrew C.; Angelini, Thomas E.; Sawyer, W. Gregory

    Soft, permeable sliding interfaces in aqueous environments are ubiquitous in nature but their ability to maintain high lubricity in a poor lubricant (water) has not been well understood. Hydrogels are excellent materials for fundamental soft matter and biotribology studies due to their high water content. While mesh size controls the material and transport properties of a hydrogel, its effects on friction were only recently explored. Polyacrylamide hydrogels slid in a Gemini (self-mated) interface produced low friction under low speeds, low pressures, macroscopic contact areas, and room temperature aqueous environments. The friction coefficients at these interfaces are lowest at low speeds and are speed-independent. This behavior is due to thermal fluctuations at the interface separating the surfaces, with water shearing in this region being the main source of dissipation. We found that mesh size had an inverse correlation with friction. We further investigated a transition from this behavior at higher speeds, and found that the transition speed correlated with the mesh size and relaxation time of the polymer network. Very soft and correspondingly large mesh size Gemini hydrogels show superlubricity under specific conditions with friction being less than 0.005.

  7. Optimal imaging with adaptive mesh refinement in electrical impedance tomography.

    PubMed

    Molinari, Marc; Blott, Barry H; Cox, Simon J; Daniell, Geoffrey J

    2002-02-01

    In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical chi2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.

  8. Parallel paving: An algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers

    SciTech Connect

    Lober, R.R.; Tautges, T.J.; Vaughan, C.T.

    1997-03-01

    Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.

  9. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  10. Hybrid mesh generation using advancing reduction technique

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This study presents an extension of the application of the advancing reduction technique to the hybrid mesh generation. The proposed algorithm is based on a pre-generated rectangle mesh (RM) with a certain orientation. The intersection points between the two sets of perpendicular mesh lines in RM an...

  11. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  12. An Automatic 3D Mesh Generation Method for Domains with Multiple Materials.

    PubMed

    Zhang, Yongjie; Hughes, Thomas J R; Bajaj, Chandrajit L

    2010-01-01

    This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided. PMID:20161555

  13. Constraint algebra in bigravity

    SciTech Connect

    Soloviev, V. O.

    2015-07-15

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  14. Constraint algebra in bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    2015-07-01

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  15. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  16. Readiness and Preparation for Beginning Algebra.

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…

  17. Hopf algebras and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Weinzierl, Stefan

    2016-06-01

    In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.

  18. Two-parameter twisted quantum affine algebras

    NASA Astrophysics Data System (ADS)

    Jing, Naihuan; Zhang, Honglian

    2016-09-01

    We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.

  19. A randomised, multi-centre, prospective, double blind pilot-study to evaluate safety and efficacy of the non-absorbable Optilene® Mesh Elastic versus the partly absorbable Ultrapro® Mesh for incisional hernia repair

    PubMed Central

    2010-01-01

    Background Randomised controlled trials with a long term follow-up (3 to 10 years) have demonstrated that mesh repair is superior to suture closure of incisional hernia with lower recurrence rates (5 to 20% versus 20 to 63%). Yet, the ideal size and material of the mesh are not defined. So far, there are few prospective studies that evaluate the influence of the mesh texture on patient's satisfaction, recurrence and complication rate. The aim of this study is to evaluate, if a non-absorbable mesh (Optilene® Mesh Elastic) will result in better health outcomes compared to a partly absorbable mesh (Ultrapro® Mesh). Methods/Design In this prospective, randomised, double blind study, eighty patients with incisional hernia after a midline laparotomy will be included. Primary objective of this study is to investigate differences in the physical functioning score from the SF-36 questionnaire 21 days after mesh insertion. Secondary objectives include the evaluation of the patients' daily activity, pain, wound complication and other surgical complications (hematomas, seromas), and safety within six months after intervention. Discussion This study investigates mainly from the patient perspective differences between meshes for treatment of incisional hernias. Whether partly absorbable meshes improve quality of life better than non-absorbable meshes is unclear and therefore, this trial will generate further evidence for a better treatment of patients. Trial registration NCT00646334 PMID:20624273

  20. Compatible Relaxation and Coarsening in Algebraic Multigrid

    SciTech Connect

    Brannick, J J; Falgout, R D

    2009-09-22

    We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.

  1. Unstructured mesh algorithms for aerodynamic calculations

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.

    1992-01-01

    The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined.

  2. Confined helium on Lagrange meshes.

    PubMed

    Baye, D; Dohet-Eraly, J

    2015-12-21

    The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method. It is applied to the study of a confined helium atom. Two types of confinement are considered. Soft confinements by potentials are studied in perimetric coordinates. Hard confinement in impenetrable spherical cavities is studied in a system of rescaled perimetric coordinates varying in [0,1] intervals. Energies and mean values of the distances between electrons and between an electron and the helium nucleus are calculated. A high accuracy of 11 to 15 significant figures is obtained with small computing times. Pressures acting on the confined atom are also computed. For sphere radii smaller than 1, their relative accuracies are better than 10(-10). For larger radii up to 10, they progressively decrease to 10(-3), still improving the best literature results.

  3. The moving mesh code SHADOWFAX

    NASA Astrophysics Data System (ADS)

    Vandenbroucke, B.; De Rijcke, S.

    2016-07-01

    We introduce the moving mesh code SHADOWFAX, which can be used to evolve a mixture of gas, subject to the laws of hydrodynamics and gravity, and any collisionless fluid only subject to gravity, such as cold dark matter or stars. The code is written in C++ and its source code is made available to the scientific community under the GNU Affero General Public Licence. We outline the algorithm and the design of our implementation, and demonstrate its validity through the results of a set of basic test problems, which are also part of the public version. We also compare SHADOWFAX with a number of other publicly available codes using different hydrodynamical integration schemes, illustrating the advantages and disadvantages of the moving mesh technique.

  4. Implicit solvers for unstructured meshes

    NASA Technical Reports Server (NTRS)

    Venkatakrishnan, V.; Mavriplis, Dimitri J.

    1991-01-01

    Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

  5. Implicit solvers for unstructured meshes

    NASA Technical Reports Server (NTRS)

    Venkatakrishnan, V.; Mavriplis, Dimitri J.

    1991-01-01

    Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

  6. COSMOLOGICAL ADAPTIVE MESH REFINEMENT MAGNETOHYDRODYNAMICS WITH ENZO

    SciTech Connect

    Collins, David C.; Xu Hao; Norman, Michael L.; Li Hui; Li Shengtai

    2010-02-01

    In this work, we present EnzoMHD, the extension of the cosmological code Enzo to include the effects of magnetic fields through the ideal magnetohydrodynamics approximation. We use a higher order Godunov method for the computation of interface fluxes. We use two constrained transport methods to compute the electric field from those interface fluxes, which simultaneously advances the induction equation and maintains the divergence of the magnetic field. A second-order divergence-free reconstruction technique is used to interpolate the magnetic fields in the block-structured adaptive mesh refinement framework already extant in Enzo. This reconstruction also preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non-cosmological test problems to demonstrate the quality of solution resulting from this combination of solvers.

  7. All-quad meshing without cleanup

    DOE PAGES

    Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.; Bajaj, Chandrajit C.; Ebeida, Mohamed S.

    2016-08-22

    Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning wemore » have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.« less

  8. Progressive Compression of Volumetric Subdivision Meshes

    SciTech Connect

    Laney, D; Pascucci, V

    2004-04-16

    We present a progressive compression technique for volumetric subdivision meshes based on the slow growing refinement algorithm. The system is comprised of a wavelet transform followed by a progressive encoding of the resulting wavelet coefficients. We compare the efficiency of two wavelet transforms. The first transform is based on the smoothing rules used in the slow growing subdivision technique. The second transform is a generalization of lifted linear B-spline wavelets to the same multi-tier refinement structure. Direct coupling with a hierarchical coder produces progressive bit streams. Rate distortion metrics are evaluated for both wavelet transforms. We tested the practical performance of the scheme on synthetic data as well as data from laser indirect-drive fusion simulations with multiple fields per vertex. Both wavelet transforms result in high quality trade off curves and produce qualitatively good coarse representations.

  9. Meshing, Visualization, and Computational Environments

    NASA Technical Reports Server (NTRS)

    Chawner, John R.

    2004-01-01

    There was probably no higher profile application of meshing, visualization, and computational software this past year than that performed in support of the space shuttle's Return to Flight activities. After heavy use of simulation during the accident investigation, these same tools are now helping address safety and operational issues. In turn, these applications are raising the bar for computational tools in terms of simulation fidelity and turnaround time.

  10. Adaptive Mesh Refinement in CTH

    SciTech Connect

    Crawford, David

    1999-05-04

    This paper reports progress on implementing a new capability of adaptive mesh refinement into the Eulerian multimaterial shock- physics code CTH. The adaptivity is block-based with refinement and unrefinement occurring in an isotropic 2:1 manner. The code is designed to run on serial, multiprocessor and massive parallel platforms. An approximate factor of three in memory and performance improvements over comparable resolution non-adaptive calculations has-been demonstrated for a number of problems.

  11. Parallelization of irregularly coupled regular meshes

    NASA Technical Reports Server (NTRS)

    Chase, Craig; Crowley, Kay; Saltz, Joel; Reeves, Anthony

    1992-01-01

    Regular meshes are frequently used for modeling physical phenomena on both serial and parallel computers. One advantage of regular meshes is that efficient discretization schemes can be implemented in a straight forward manner. However, geometrically-complex objects, such as aircraft, cannot be easily described using a single regular mesh. Multiple interacting regular meshes are frequently used to describe complex geometries. Each mesh models a subregion of the physical domain. The meshes, or subdomains, can be processed in parallel, with periodic updates carried out to move information between the coupled meshes. In many cases, there are a relatively small number (one to a few dozen) subdomains, so that each subdomain may also be partitioned among several processors. We outline a composite run-time/compile-time approach for supporting these problems efficiently on distributed-memory machines. These methods are described in the context of a multiblock fluid dynamics problem developed at LaRC.

  12. Dynamic mesh for TCAD modeling with ECORCE

    NASA Astrophysics Data System (ADS)

    Michez, A.; Boch, J.; Touboul, A.; Saigné, F.

    2016-08-01

    Mesh generation for TCAD modeling is challenging. Because densities of carriers can change by several orders of magnitude in thin areas, a significant change of the solution can be observed for two very similar meshes. The mesh must be defined at best to minimize this change. To address this issue, a criterion based on polynomial interpolation on adjacent nodes is proposed that adjusts accurately the mesh to the gradients of Degrees of Freedom. Furthermore, a dynamic mesh that follows changes of DF in DC and transient mode is a powerful tool for TCAD users. But, in transient modeling, adding nodes to a mesh induces oscillations in the solution that appears as spikes at the current collected at the contacts. This paper proposes two schemes that solve this problem. Examples show that using these techniques, the dynamic mesh generator of the TCAD tool ECORCE handle semiconductors devices in DC and transient mode.

  13. Automatic Mesh Coarsening for Discrete Ordinates Codes

    SciTech Connect

    Turner, Scott A.

    1999-03-11

    This paper describes the use of a ''mesh potential'' function for automatic coarsening of meshes in discrete ordinates neutral particle transport codes. For many transport calculations, a user may find it helpful to have the code determine a ''good'' neutronics mesh. The complexity of a problem involving millions of mesh cells, dozens of materials, and many energy groups makes it difficult to determine an adequate level of mesh refinement with a minimum number of cells. A method has been implemented in PARTISN (Parallel Time-dependent SN) to calculate a ''mesh potential'' in each original cell of a problem, and use this information to determine the maximum coarseness allowed in the mesh while maintaining accuracy in the solution. Results are presented for a simple x-y-z fuel/control/reflector problem.

  14. SHARP/PRONGHORN Interoperability: Mesh Generation

    SciTech Connect

    Avery Bingham; Javier Ortensi

    2012-09-01

    Progress toward collaboration between the SHARP and MOOSE computational frameworks has been demonstrated through sharing of mesh generation and ensuring mesh compatibility of both tools with MeshKit. MeshKit was used to build a three-dimensional, full-core very high temperature reactor (VHTR) reactor geometry with 120-degree symmetry, which was used to solve a neutron diffusion critical eigenvalue problem in PRONGHORN. PRONGHORN is an application of MOOSE that is capable of solving coupled neutron diffusion, heat conduction, and homogenized flow problems. The results were compared to a solution found on a 120-degree, reflected, three-dimensional VHTR mesh geometry generated by PRONGHORN. The ability to exchange compatible mesh geometries between the two codes is instrumental for future collaboration and interoperability. The results were found to be in good agreement between the two meshes, thus demonstrating the compatibility of the SHARP and MOOSE frameworks. This outcome makes future collaboration possible.

  15. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  16. Ada Linear-Algebra Program

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  17. GCD, LCM, and Boolean Algebra?

    ERIC Educational Resources Information Center

    Cohen, Martin P.; Juraschek, William A.

    1976-01-01

    This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

  18. The Rationality of Four Metrics of Network Robustness: A Viewpoint of Robust Growth of Generalized Meshes

    PubMed Central

    Yang, Xiaofan; Zhu, Yuanrui; Hong, Jing; Yang, Lu-Xing; Wu, Yingbo; Tang, Yuan Yan

    2016-01-01

    There are quite a number of different metrics of network robustness. This paper addresses the rationality of four metrics of network robustness (the algebraic connectivity, the effective resistance, the average edge betweenness, and the efficiency) by investigating the robust growth of generalized meshes (GMs). First, a heuristic growth algorithm (the Proximity-Growth algorithm) is proposed. The resulting proximity-optimal GMs are intuitively robust and hence are adopted as the benchmark. Then, a generalized mesh (GM) is grown up by stepwise optimizing a given measure of network robustness. The following findings are presented: (1) The algebraic connectivity-optimal GMs deviate quickly from the proximity-optimal GMs, yielding a number of less robust GMs. This hints that the rationality of the algebraic connectivity as a measure of network robustness is still in doubt. (2) The effective resistace-optimal GMs and the average edge betweenness-optimal GMs are in line with the proximity-optimal GMs. This partly justifies the two quantities as metrics of network robustness. (3) The efficiency-optimal GMs deviate gradually from the proximity-optimal GMs, yielding some less robust GMs. This suggests the limited utility of the efficiency as a measure of network robustness. PMID:27518448

  19. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  20. ALGEBRA v.1.27

    SciTech Connect

    Sjaardema, G.; Gilkey, A.; Smith, M.; Forsythe, C.

    2005-04-11

    The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.

  1. A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.

    1999-01-01

    The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

  2. h-Refinement for simple corner balance scheme of SN transport equation on distorted meshes

    NASA Astrophysics Data System (ADS)

    Yang, Rong; Yuan, Guangwei

    2016-11-01

    The transport sweep algorithm is a common method for solving discrete ordinate transport equation, but it breaks down once a concave cell appears in spatial meshes. To deal with this issue a local h-refinement for simple corner balance (SCB) scheme of SN transport equation on arbitrary quadrilateral meshes is presented in this paper by using a new subcell partition. It follows that a hybrid mesh with both triangle and quadrilateral cells is generated, and the geometric quality of these cells improves, especially it is ensured that all cells become convex. Combining with the original SCB scheme, an adaptive transfer algorithm based on the hybrid mesh is constructed. Numerical experiments are presented to verify the utility and accuracy of the new algorithm, especially for some application problems such as radiation transport coupled with Lagrangian hydrodynamic flow. The results show that it performs well on extremely distorted meshes with concave cells, on which the original SCB scheme does not work.

  3. Algebraic Systems and Pushdown Automata

    NASA Astrophysics Data System (ADS)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  4. Automatic generation of endocardial surface meshes with 1-to-1 correspondence from cine-MR images

    NASA Astrophysics Data System (ADS)

    Su, Yi; Teo, S.-K.; Lim, C. W.; Zhong, L.; Tan, R. S.

    2015-03-01

    In this work, we develop an automatic method to generate a set of 4D 1-to-1 corresponding surface meshes of the left ventricle (LV) endocardial surface which are motion registered over the whole cardiac cycle. These 4D meshes have 1- to-1 point correspondence over the entire set, and is suitable for advanced computational processing, such as shape analysis, motion analysis and finite element modelling. The inputs to the method are the set of 3D LV endocardial surface meshes of the different frames/phases of the cardiac cycle. Each of these meshes is reconstructed independently from border-delineated MR images and they have no correspondence in terms of number of vertices/points and mesh connectivity. To generate point correspondence, the first frame of the LV mesh model is used as a template to be matched to the shape of the meshes in the subsequent phases. There are two stages in the mesh correspondence process: (1) a coarse matching phase, and (2) a fine matching phase. In the coarse matching phase, an initial rough matching between the template and the target is achieved using a radial basis function (RBF) morphing process. The feature points on the template and target meshes are automatically identified using a 16-segment nomenclature of the LV. In the fine matching phase, a progressive mesh projection process is used to conform the rough estimate to fit the exact shape of the target. In addition, an optimization-based smoothing process is used to achieve superior mesh quality and continuous point motion.

  5. Practical implementation of tetrahedral mesh reconstruction in emission tomography.

    PubMed

    Boutchko, R; Sitek, A; Gullberg, G T

    2013-05-01

    projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise.

  6. An arbitrary boundary triangle mesh generation method for multi-modality imaging

    NASA Astrophysics Data System (ADS)

    Zhang, Xuanxuan; Deng, Yong; Gong, Hui; Meng, Yuanzheng; Yang, Xiaoquan; Luo, Qingming

    2011-11-01

    Low-resolution and ill-posedness are the major challenges in diffuse optical tomography(DOT)/fluorescence molecular tomography(FMT). Recently, the multi-modality imaging technology that combines micro-computed tomography (micro-CT) with DOT/FMT is developed to improve resolution and ill-posedness. To take advantage of the fine priori anatomical maps obtained from micro-CT, we present an arbitrary boundary triangle mesh generation method for FMT/DOT/micro-CT multi-modality imaging. A planar straight line graph (PSLG) based on the image of micro-CT is obtained by an adaptive boundary sampling algorithm. The subregions of mesh are accurately matched with anatomical structures by a two-step solution, firstly, the triangles and nodes during mesh refinement are labeled respectively, and then a revising algorithm is used to modifying meshes of each subregion. The triangle meshes based on a regular model and a micro-CT image are generated respectively. The results show that the subregions of triangle meshes can match with anatomical structures accurately and triangle meshes have good quality. This provides an arbitrary boundaries triangle mesh generation method with the ability to incorporate the fine priori anatomical information into DOT/FMT reconstructions.

  7. An arbitrary boundary triangle mesh generation method for multi-modality imaging

    NASA Astrophysics Data System (ADS)

    Zhang, Xuanxuan; Deng, Yong; Gong, Hui; Meng, Yuanzheng; Yang, Xiaoquan; Luo, Qingming

    2012-03-01

    Low-resolution and ill-posedness are the major challenges in diffuse optical tomography(DOT)/fluorescence molecular tomography(FMT). Recently, the multi-modality imaging technology that combines micro-computed tomography (micro-CT) with DOT/FMT is developed to improve resolution and ill-posedness. To take advantage of the fine priori anatomical maps obtained from micro-CT, we present an arbitrary boundary triangle mesh generation method for FMT/DOT/micro-CT multi-modality imaging. A planar straight line graph (PSLG) based on the image of micro-CT is obtained by an adaptive boundary sampling algorithm. The subregions of mesh are accurately matched with anatomical structures by a two-step solution, firstly, the triangles and nodes during mesh refinement are labeled respectively, and then a revising algorithm is used to modifying meshes of each subregion. The triangle meshes based on a regular model and a micro-CT image are generated respectively. The results show that the subregions of triangle meshes can match with anatomical structures accurately and triangle meshes have good quality. This provides an arbitrary boundaries triangle mesh generation method with the ability to incorporate the fine priori anatomical information into DOT/FMT reconstructions.

  8. Mesh-based enhancement schemes in diffuse optical tomography.

    PubMed

    Gu, Xuejun; Xu, Yong; Jiang, Huabei

    2003-05-01

    Two mesh-based methods including dual meshing and adaptive meshing are developed to improve the finite element-based reconstruction of both absorption and scattering images of heterogeneous turbid media. The idea of dual meshing scheme is to use a fine mesh for the solution of photon propagation and a coarse mesh for the inversion of optical property distributions. The adaptive meshing method is accomplished by the automatic mesh refinement in the region of heterogeneity during reconstruction. These schemes are validated using tissue-like phantom measurements. Our results demonstrate the capabilities of the dual meshing and adaptive meshing in both qualitative and quantitative improvement of optical image reconstruction.

  9. Smooth Rotation Enhanced As-Rigid-As-Possible Mesh Animation.

    PubMed

    Levi, Zohar; Gotsman, Craig

    2015-02-01

    In recent years, the As-Rigid-As-Possible (ARAP) shape deformation and shape interpolation techniques gained popularity, and the ARAP energy was successfully used in other applications as well. We improve the ARAP animation technique in two aspects. First, we introduce a new ARAP-type energy, named SR-ARAP, which has a consistent discretization for surfaces (triangle meshes). The quality of our new surface deformation scheme competes with the quality of the volumetric ARAP deformation (for tetrahedral meshes). Second, we propose a new ARAP shape interpolation method that is superior to prior art also based on the ARAP energy. This method is compatible with our new SR-ARAP energy, as well as with the ARAP volume energy.

  10. Invertible linear transformations and the Lie algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yufeng; Tam, Honwah; Guo, Fukui

    2008-07-01

    With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.

  11. Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes.

    PubMed

    Misztal, Marek K; Erleben, Kenny; Bargteil, Adam; Fursund, Jens; Christensen, Brian Bunch; Bærentzen, J Andreas; Bridson, Robert

    2013-07-01

    In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization. PMID:23836703

  12. Multiphase flow of immiscible fluids on unstructured moving meshes.

    PubMed

    Misztal, Marek Krzysztof; Erleben, Kenny; Bargteil, Adam; Fursund, Jens; Christensen, Brian Bunch; Bærentzen, Jakob Andreas; Bridson, Robert

    2014-01-01

    In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization. PMID:24201322

  13. A Novel Coarsening Method for Scalable and Efficient Mesh Generation

    SciTech Connect

    Yoo, A; Hysom, D; Gunney, B

    2010-12-02

    In this paper, we propose a novel mesh coarsening method called brick coarsening method. The proposed method can be used in conjunction with any graph partitioners and scales to very large meshes. This method reduces problem space by decomposing the original mesh into fixed-size blocks of nodes called bricks, layered in a similar way to conventional brick laying, and then assigning each node of the original mesh to appropriate brick. Our experiments indicate that the proposed method scales to very large meshes while allowing simple RCB partitioner to produce higher-quality partitions with significantly less edge cuts. Our results further indicate that the proposed brick-coarsening method allows more complicated partitioners like PT-Scotch to scale to very large problem size while still maintaining good partitioning performance with relatively good edge-cut metric. Graph partitioning is an important problem that has many scientific and engineering applications in such areas as VLSI design, scientific computing, and resource management. Given a graph G = (V,E), where V is the set of vertices and E is the set of edges, (k-way) graph partitioning problem is to partition the vertices of the graph (V) into k disjoint groups such that each group contains roughly equal number of vertices and the number of edges connecting vertices in different groups is minimized. Graph partitioning plays a key role in large scientific computing, especially in mesh-based computations, as it is used as a tool to minimize the volume of communication and to ensure well-balanced load across computing nodes. The impact of graph partitioning on the reduction of communication can be easily seen, for example, in different iterative methods to solve a sparse system of linear equation. Here, a graph partitioning technique is applied to the matrix, which is basically a graph in which each edge is a non-zero entry in the matrix, to allocate groups of vertices to processors in such a way that many of

  14. Resource optimization scheme for multimedia-enabled wireless mesh networks.

    PubMed

    Ali, Amjad; Ahmed, Muhammad Ejaz; Piran, Md Jalil; Suh, Doug Young

    2014-08-08

    Wireless mesh networking is a promising technology that can support numerous multimedia applications. Multimedia applications have stringent quality of service (QoS) requirements, i.e., bandwidth, delay, jitter, and packet loss ratio. Enabling such QoS-demanding applications over wireless mesh networks (WMNs) require QoS provisioning routing protocols that lead to the network resource underutilization problem. Moreover, random topology deployment leads to have some unused network resources. Therefore, resource optimization is one of the most critical design issues in multi-hop, multi-radio WMNs enabled with multimedia applications. Resource optimization has been studied extensively in the literature for wireless Ad Hoc and sensor networks, but existing studies have not considered resource underutilization issues caused by QoS provisioning routing and random topology deployment. Finding a QoS-provisioned path in wireless mesh networks is an NP complete problem. In this paper, we propose a novel Integer Linear Programming (ILP) optimization model to reconstruct the optimal connected mesh backbone topology with a minimum number of links and relay nodes which satisfies the given end-to-end QoS demands for multimedia traffic and identification of extra resources, while maintaining redundancy. We further propose a polynomial time heuristic algorithm called Link and Node Removal Considering Residual Capacity and Traffic Demands (LNR-RCTD). Simulation studies prove that our heuristic algorithm provides near-optimal results and saves about 20% of resources from being wasted by QoS provisioning routing and random topology deployment.

  15. Resource Optimization Scheme for Multimedia-Enabled Wireless Mesh Networks

    PubMed Central

    Ali, Amjad; Ahmed, Muhammad Ejaz; Piran, Md. Jalil; Suh, Doug Young

    2014-01-01

    Wireless mesh networking is a promising technology that can support numerous multimedia applications. Multimedia applications have stringent quality of service (QoS) requirements, i.e., bandwidth, delay, jitter, and packet loss ratio. Enabling such QoS-demanding applications over wireless mesh networks (WMNs) require QoS provisioning routing protocols that lead to the network resource underutilization problem. Moreover, random topology deployment leads to have some unused network resources. Therefore, resource optimization is one of the most critical design issues in multi-hop, multi-radio WMNs enabled with multimedia applications. Resource optimization has been studied extensively in the literature for wireless Ad Hoc and sensor networks, but existing studies have not considered resource underutilization issues caused by QoS provisioning routing and random topology deployment. Finding a QoS-provisioned path in wireless mesh networks is an NP complete problem. In this paper, we propose a novel Integer Linear Programming (ILP) optimization model to reconstruct the optimal connected mesh backbone topology with a minimum number of links and relay nodes which satisfies the given end-to-end QoS demands for multimedia traffic and identification of extra resources, while maintaining redundancy. We further propose a polynomial time heuristic algorithm called Link and Node Removal Considering Residual Capacity and Traffic Demands (LNR-RCTD). Simulation studies prove that our heuristic algorithm provides near-optimal results and saves about 20% of resources from being wasted by QoS provisioning routing and random topology deployment. PMID:25111241

  16. BRST charges for finite nonlinear algebras

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.

    2010-07-01

    Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.

  17. Some Remarks on Kite Pseudo Effect Algebras

    NASA Astrophysics Data System (ADS)

    Dvurečenskij, Anatolij; Holland, W. Charles

    2014-05-01

    Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ, ρ: I→ I. Using a clever construction on the ordinal sum of ( G +) I and ( G -) I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.

  18. High Performance Woven Mesh Heat Exchangers

    NASA Astrophysics Data System (ADS)

    Wirtz, Richard A.; Li, Chen; Park, Ji-Wook; Xu, Jun

    2002-07-01

    Simple-to-fabricate woven mesh structures, consisting of bonded laminates of two-dimensional plain-weave conductive screens, or three-dimensional orthogonal weaves are described. Geometric equations show that these porous matrices can be fabricated to have a wide range of porosity and a highly anisotropic thermal conductivity vector. A mathematical model of the thermal performance of such a mesh, deployed as a heat exchange surface, is developed. Measurements of pressure drop and overall heat transfer rate are reported and used with the performance model to develop correlation equations of mesh friction factor and Colburn j-factor as a function of coolant properties, mesh characteristics and flow rate through the mesh. A heat exchanger performance analysis delineates conditions where the two mesh technologies offer superior performance.

  19. Algebraic coarsening methods for linear and nonlinear PDE and systems

    SciTech Connect

    McWilliams, J C

    2000-11-06

    In [l] Brandt describes a general approach for algebraic coarsening. Given fine-grid equations and a prescribed relaxation method, an approach is presented for defining both the coarse-grid variables and the coarse-grid equations corresponding to these variables. Although, these two tasks are not necessarily related (and, indeed, are often performed independently and with distinct techniques) in the approaches of [1] both revolve around the same underlying observation. To determine whether a given set of coarse-grid variables is appropriate it is suggested that one should employ compatible relaxation. This is a generalization of so-called F-relaxation (e.g., [2]). Suppose that the coarse-grid variables are defined as a subset of the fine-grid variables. Then, F-relaxation simply means relaxing only the F-variables (i.e., fine-grid variables that do not correspond to coarse-grid variables), while leaving the remaining fine-grid variables (C-variables) unchanged. The generalization of compatible relaxation is in allowing the coarse-grid variables to be defined differently, say as linear combinations of fine-grid variables, or even nondeterministically (see examples in [1]). For the present summary it suffices to consider the simple case. The central observation regarding the set of coarse-grid variables is the following [1]: Observation 1--A general measure for the quality of the set of coarse-grid variables is the convergence rate of compatible relaxation. The conclusion is that a necessary condition for efficient multigrid solution (e.g., with convergence rates independent of problem size) is that the compatible-relaxation convergence be bounded away from 1, independently of the number of variables. This is often a sufficient condition, provided that the coarse-grid equations are sufficiently accurate. Therefore, it is suggested in [1] that the convergence rate of compatible relaxation should be used as a criterion for choosing and evaluating the set of coarse

  20. Operator product expansion algebra

    SciTech Connect

    Holland, Jan; Hollands, Stefan

    2013-07-15

    We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE, =Σ{sub C}C{sub A{sub 1A{sub 2A{sub 3}{sup C}}}}, usually interpreted only as an asymptotic short distance expansion, actually converges at finite, and even large, distances. We further show that the factorization identity C{sub A{sub 1A{sub 2A{sub 3}{sup B}}}}=Σ{sub C}C{sub A{sub 1A{sub 2}{sup C}}}C{sub CA{sub 3}{sup B}} is satisfied for suitable configurations of the spacetime arguments. Again, the infinite sum is shown to be convergent. Our proofs rely on explicit bounds on the remainders of these expansions, obtained using refined versions, mostly due to Kopper et al., of the renormalization group flow equation method. These bounds also establish that each OPE coefficient is a real analytic function in the spacetime arguments for non-coinciding points. Our results hold for arbitrary but finite loop orders. They lend support to proposals for a general axiomatic framework of quantum field theory, based on such “consistency conditions” and akin to vertex operator algebras, wherein the OPE is promoted to the defining structure of the theory.

  1. Unstructured Polyhedral Mesh Thermal Radiation Diffusion

    SciTech Connect

    Palmer, T.S.; Zika, M.R.; Madsen, N.K.

    2000-07-27

    Unstructured mesh particle transport and diffusion methods are gaining wider acceptance as mesh generation, scientific visualization and linear solvers improve. This paper describes an algorithm that is currently being used in the KULL code at Lawrence Livermore National Laboratory to solve the radiative transfer equations. The algorithm employs a point-centered diffusion discretization on arbitrary polyhedral meshes in 3D. We present the results of a few test problems to illustrate the capabilities of the radiation diffusion module.

  2. Delaunay triangulation and computational fluid dynamics meshes

    NASA Technical Reports Server (NTRS)

    Posenau, Mary-Anne K.; Mount, David M.

    1992-01-01

    In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements.

  3. Auto-adaptive finite element meshes

    NASA Technical Reports Server (NTRS)

    Richter, Roland; Leyland, Penelope

    1995-01-01

    Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

  4. Constructing a parasupersymmetric Virasoro algebra

    NASA Astrophysics Data System (ADS)

    Kuwata, S.

    2011-03-01

    We construct a para SUSY Virasoro algebra by generalizing the ordinary fermion in SUSY Virasoro algebra (Ramond or Neveu-Schwarz algebra) to the parafermion. First, we obtain a polynomial relation (PR) between different-mode parafermion fi's by generalizing the corresponding single-mode PR to such that is invariant under the unitary transformation of fi (Green's condition). Differently from a usual context, where the Green's condition is imposed only on the defining relation of fi (degree three with respect to fi and fi†), we impose it on any degree of PR. For the case of order-two parafermion (the simplest case of para SUSY), we calculate a PR between the parasupercharge G0, the bosonic hamiltonian LB0 and parafermionic one LF0, although it is difficult to obtain a PR between G0 and the total hamiltonian L0 (= LB0 + LF0). Finally, we construct a para SUSY Virasoro algebra by generalizing L0 to the Ln's such that form a Virasoro algebra.

  5. Mesh infrastructure for coupled multiprocess geophysical simulations

    SciTech Connect

    Garimella, Rao V.; Perkins, William A.; Buksas, Mike W.; Berndt, Markus; Lipnikov, Konstantin; Coon, Ethan; Moulton, John D.; Painter, Scott L.

    2014-01-01

    We have developed a sophisticated mesh infrastructure capability to support large scale multiphysics simulations such as subsurface flow and reactive contaminant transport at storage sites as well as the analysis of the effects of a warming climate on the terrestrial arctic. These simulations involve a wide range of coupled processes including overland flow, subsurface flow, freezing and thawing of ice rich soil, accumulation, redistribution and melting of snow, biogeochemical processes involving plant matter and finally, microtopography evolution due to melting and degradation of ice wedges below the surface. In addition to supporting the usual topological and geometric queries about the mesh, the mesh infrastructure adds capabilities such as identifying columnar structures in the mesh, enabling deforming of the mesh subject to constraints and enabling the simultaneous use of meshes of different dimensionality for subsurface and surface processes. The generic mesh interface is capable of using three different open source mesh frameworks (MSTK, MOAB and STKmesh) under the hood allowing the developers to directly compare them and choose one that is best suited for the application's needs. We demonstrate the results of some simulations using these capabilities as well as present a comparison of the performance of the different mesh frameworks.

  6. Mesh infrastructure for coupled multiprocess geophysical simulations

    DOE PAGES

    Garimella, Rao V.; Perkins, William A.; Buksas, Mike W.; Berndt, Markus; Lipnikov, Konstantin; Coon, Ethan; Moulton, John D.; Painter, Scott L.

    2014-01-01

    We have developed a sophisticated mesh infrastructure capability to support large scale multiphysics simulations such as subsurface flow and reactive contaminant transport at storage sites as well as the analysis of the effects of a warming climate on the terrestrial arctic. These simulations involve a wide range of coupled processes including overland flow, subsurface flow, freezing and thawing of ice rich soil, accumulation, redistribution and melting of snow, biogeochemical processes involving plant matter and finally, microtopography evolution due to melting and degradation of ice wedges below the surface. In addition to supporting the usual topological and geometric queries about themore » mesh, the mesh infrastructure adds capabilities such as identifying columnar structures in the mesh, enabling deforming of the mesh subject to constraints and enabling the simultaneous use of meshes of different dimensionality for subsurface and surface processes. The generic mesh interface is capable of using three different open source mesh frameworks (MSTK, MOAB and STKmesh) under the hood allowing the developers to directly compare them and choose one that is best suited for the application's needs. We demonstrate the results of some simulations using these capabilities as well as present a comparison of the performance of the different mesh frameworks.« less

  7. Method of generating a surface mesh

    DOEpatents

    Shepherd, Jason F.; Benzley, Steven; Grover, Benjamin T.

    2008-03-04

    A method and machine-readable medium provide a technique to generate and modify a quadrilateral finite element surface mesh using dual creation and modification. After generating a dual of a surface (mesh), a predetermined algorithm may be followed to generate and modify a surface mesh of quadrilateral elements. The predetermined algorithm may include the steps of generating two-dimensional cell regions in dual space, determining existing nodes in primal space, generating new nodes in the dual space, and connecting nodes to form the quadrilateral elements (faces) for the generated and modifiable surface mesh.

  8. Design of electrospinning mesh devices

    NASA Astrophysics Data System (ADS)

    Russo, Giuseppina; Peters, Gerrit W. M.; Solberg, Ramon H. M.; Vittoria, Vittoria

    2012-07-01

    This paper describes the features of new membranes that can act as local biomedical devices owing to their peculiar shape in the form of mesh structure. These materials are designed to provide significant effects to reduce local inflammations and improve the tissue regeneration. Lamellar Hydrotalcite loaded with Diclofenac Sodium (HTLc-DIK) was homogenously dispersed inside a polymeric matrix of Poly-caprolactone (PCL) to manufacture membranes by electrospinning technique. The experimental procedure and the criteria employed have shown to be extremely effective at increasing potentiality and related applications. The employed technique has proved to be very useful to manufacture polymeric fibers with diameters in the range of nano-micro scale. In this work a dedicated collector based on a proprietary technology of IME Technologies and Eindhoven University of Technology (TU/e) was used. It allowed to obtain devices with a macro shape of a 3D-mesh. Atomic Force Microscopy (AFM) highlights a very interesting texture of the electrospun fibers. They show a lamellar morphology that is only slightly modified by the inclusion of the interclay embedded in the devices to control the drug release phenomena.

  9. MOAB : a mesh-oriented database.

    SciTech Connect

    Tautges, Timothy James; Ernst, Corey; Stimpson, Clint; Meyers, Ray J.; Merkley, Karl

    2004-04-01

    A finite element mesh is used to decompose a continuous domain into a discretized representation. The finite element method solves PDEs on this mesh by modeling complex functions as a set of simple basis functions with coefficients at mesh vertices and prescribed continuity between elements. The mesh is one of the fundamental types of data linking the various tools in the FEA process (mesh generation, analysis, visualization, etc.). Thus, the representation of mesh data and operations on those data play a very important role in FEA-based simulations. MOAB is a component for representing and evaluating mesh data. MOAB can store structured and unstructured mesh, consisting of elements in the finite element 'zoo'. The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh. MOAB is optimized for efficiency in space and time, based on access to mesh in chunks rather than through individual entities, while also versatile enough to support individual entity access. The MOAB data model consists of a mesh interface instance, mesh entities (vertices and elements), sets, and tags. Entities are addressed through handles rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms is a powerful yet simple interface for representing metadata or application

  10. Unstructured Mesh Methods for the Simulation of Hypersonic Flows

    NASA Technical Reports Server (NTRS)

    Peraire, Jaime; Bibb, K. L. (Technical Monitor)

    2001-01-01

    This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite

  11. PREFACE: Algebra, Geometry, and Mathematical Physics 2010

    NASA Astrophysics Data System (ADS)

    Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.

    2012-02-01

    This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants

  12. A Metric Conceptual Space Algebra

    NASA Astrophysics Data System (ADS)

    Adams, Benjamin; Raubal, Martin

    The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.

  13. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  14. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  15. Performance of High Strength Rock Fall Meshes: Effect of Block Size and Mesh Geometry

    NASA Astrophysics Data System (ADS)

    Buzzi, Olivier; Leonarduzzi, E.; Krummenacher, B.; Volkwein, A.; Giacomini, A.

    2015-05-01

    In rockfall science, the bullet effect refers to the perforation of a rockfall mesh by a small block traveling at high speed. To date, there is still no comprehensive experimental data set investigating the underlying mechanisms of such effect. The bullet effect illustrates the fact that the capacity of a rockfall mesh depends on the size and speed of the impacting block. This paper presents the results of an experimental study on the effect of block size and mesh geometry (aperture and wire diameter) on the mesh performance. The results clearly show that the amount of energy required to perforate the mesh drops as the blocks get smaller. They also suggest that the mesh performance reaches a maximum and reduces to zero when the mesh cannot sustain the static load imposed by very large blocks. The outcome of the first series validates an analytical model for mesh perforation, making it the first simple model capturing the bullet effect. A second series of tests focused on the effect of mesh geometry and it was found that decreasing the mesh aperture by 19 % improves the performance by 50 % while only an extra 30 % could be gained by increasing the wire diameter by 33 %. The outcomes of the second series were used to discuss and redefine a dimensionless geometrical parameter G* and to validate a simple power type equation relating the mesh characteristics and the mesh performance.

  16. Colored Quantum Algebra and Its Bethe State

    NASA Astrophysics Data System (ADS)

    Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun

    2014-12-01

    We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

  17. Generalized Galilean algebras and Newtonian gravity

    NASA Astrophysics Data System (ADS)

    González, N.; Rubio, G.; Salgado, P.; Salgado, S.

    2016-04-01

    The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

  18. Motivating Activities that Lead to Algebra

    ERIC Educational Resources Information Center

    Menon, Ramakrishnan

    2004-01-01

    Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.

  19. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    Bank, R; Lu, S; Tong, C; Vassilevski, P

    2005-03-23

    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  20. Discrimination in a General Algebraic Setting.

    PubMed

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.

  1. Discrimination in a General Algebraic Setting

    PubMed Central

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421

  2. Characteristic Numbers of Matrix Lie Algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Fan, En-Gui

    2008-04-01

    A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.

  3. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  4. Twining characters and orbit Lie algebras

    SciTech Connect

    Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph

    1996-12-05

    We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.

  5. New family of Maxwell like algebras

    NASA Astrophysics Data System (ADS)

    Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.

    2016-08-01

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  6. Unifying the Algebra for All Movement

    ERIC Educational Resources Information Center

    Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

    2015-01-01

    There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

  7. Build an Early Foundation for Algebra Success

    ERIC Educational Resources Information Center

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  8. Difficulties in Initial Algebra Learning in Indonesia

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-01-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

  9. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  10. Algebra? A Gate! A Barrier! A Mystery!

    ERIC Educational Resources Information Center

    Mathematics Educatio Dialogues, 2000

    2000-01-01

    This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

  11. Computer Algebra Systems, Pedagogy, and Epistemology

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2004-01-01

    The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…

  12. Teaching Strategies to Improve Algebra Learning

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  13. Adaptive mesh refinement in titanium

    SciTech Connect

    Colella, Phillip; Wen, Tong

    2005-01-21

    In this paper, we evaluate Titanium's usability as a high-level parallel programming language through a case study, where we implement a subset of Chombo's functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for high-performance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson's equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.

  14. Parallel mesh management using interoperable tools.

    SciTech Connect

    Tautges, Timothy James; Devine, Karen Dragon

    2010-10-01

    This presentation included a discussion of challenges arising in parallel mesh management, as well as demonstrated solutions. They also described the broad range of software for mesh management and modification developed by the Interoperable Technologies for Advanced Petascale Simulations (ITAPS) team, and highlighted applications successfully using the ITAPS tool suite.

  15. Scalable L-infinite coding of meshes.

    PubMed

    Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

    2010-01-01

    The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec. PMID:20224144

  16. 7th International Meshing Roundtable '98

    SciTech Connect

    Eldred, T.J.

    1998-10-01

    The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries.

  17. Mesh Sutured Repairs of Abdominal Wall Defects

    PubMed Central

    Lanier, Steven T.; Jordan, Sumanas W.; Miller, Kyle R.; Ali, Nada A.; Stock, Stuart R.

    2016-01-01

    Background: A new closure technique is introduced, which uses strips of macroporous polypropylene mesh as a suture for closure of abdominal wall defects due to failures of standard sutures and difficulties with planar meshes. Methods: Strips of macroporous polypropylene mesh of 2 cm width were passed through the abdominal wall and tied as simple interrupted sutures. The surgical technique and surgical outcomes are presented. Results: One hundred and seven patients underwent a mesh sutured abdominal wall closure. Seventy-six patients had preoperative hernias, and the mean hernia width by CT scan for those with scans was 9.1 cm. Forty-nine surgical fields were clean-contaminated, contaminated, or dirty. Five patients had infections within the first 30 days. Only one knot was removed as an office procedure. Mean follow-up at 234 days revealed 4 recurrent hernias. Conclusions: Mesh sutured repairs reliably appose tissue under tension using concepts of force distribution and resistance to suture pull-through. The technique reduces the amount of foreign material required in comparison to sheet meshes, and avoids the shortcomings of monofilament sutures. Mesh sutured closures seem to be tolerant of bacterial contamination with low hernia recurrence rates and have replaced our routine use of mesh sheets and bioprosthetic grafts. PMID:27757361

  18. [Management of mesh-related infections].

    PubMed

    Dietz, U A; Spor, L; Germer, C-T

    2011-03-01

    Infections of an implanted hernia mesh are a major challenge. The incidence of mesh infections after incisional hernia repair is about 1% for endoscopic techniques and can be more than 15% in open techniques. Intraoperative mesh contamination is considered to be the primary cause. All woven or knitted hernia meshes have recesses where bacteria may adhere and establish colonies. The bacterial spectrum for mesh infection includes skin pathogens, such as Staphylococcus aureus (including MRSA), Streptococcus spp., as well as E. coli, Enterococcus and Mycobacteria. The therapy approach needs to be tailored to the morphological findings and the treatment for uncomplicated phlegmon is broad spectrum antibiotic therapy. If there is encapsulated fluid accumulation, CT-controlled drainage and daily infusion of antiseptics via the drain is a good option. For dermal necrosis, mesh fistula, exposed mesh or enterocutaneous fistula, a precise CT evaluation is necessary to tailor the operation. Vacuum systems are gaining increased acceptance in conditioning the local findings. For most patients the therapeutic concept will be based on individual decisions. If parts of a formerly infected mesh remain in the patient, a lifelong follow-up is necessary.

  19. An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data.

    PubMed

    Kuprat, Andrew P; Einstein, Daniel R

    2009-02-20

    We present a boundary-fitted, scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local feature size. Given an input triangulated surface mesh, a feature size field is determined by casting rays normal to the surface and into the geometry and then performing gradient-limiting operations to enforce continuity of the resulting field. Surface mesh density is adjusted to be proportional to the feature size field and then a layered anisotropic volume mesh is generated. This mesh is "scale-invariant" in that roughly the same number of layers of mesh exist in mesh cross-sections, between a minimum scale size L(min) and a maximum scale size L(max). We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex biological surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[14]. Research funded by the National Heart and Blood Institute Award 1RO1HL073598-01A1. PMID:19784397

  20. Feature recognition applications in mesh generation

    SciTech Connect

    Tautges, T.J.; Liu, S.S.; Lu, Y.; Kraftcheck, J.; Gadh, R.

    1997-06-01

    The use of feature recognition as part of an overall decomposition-based hexahedral meshing approach is described in this paper. The meshing approach consists of feature recognition, using a c-loop or hybrid c-loop method, and the use of cutting surfaces to decompose the solid model. These steps are part of an iterative process, which proceeds either until no more features can be recognized or until the model has been completely decomposed into meshable sub-volumes. This method can greatly reduce the time required to generate an all-hexahedral mesh, either through the use of more efficient meshing algorithms on more of the geometry or by reducing the amount of manual decomposition required to mesh a volume.

  1. Modified mesh-connected parallel computers

    SciTech Connect

    Carlson, D.A. )

    1988-10-01

    The mesh-connected parallel computer is an important parallel processing organization that has been used in the past for the design of supercomputing systems. In this paper, the authors explore modifications of a mesh-connected parallel computer for the purpose of increasing the efficiency of executing important application programs. These modifications are made by adding one or more global mesh structures to the processing array. They show how our modifications allow asymptotic improvements in the efficiency of executing computations having low to medium interprocessor communication requirements (e.g., tree computations, prefix computations, finding the connected components of a graph). For computations with high interprocessor communication requirements such as sorting, they show that they offer no speedup. They also compare the modified mesh-connected parallel computer to other similar organizations including the pyramid, the X-tree, and the mesh-of-trees.

  2. Attenuation compensation in mesh-domain OSEM SPECT reconstruction

    NASA Astrophysics Data System (ADS)

    Vogelsang, Levon; Lu, Yao; Yu, Bo; Krol, Andrzej; Xu, Yuesheng; Hu, Xiaofei; Feiglin, David; Lipson, Edward

    2009-02-01

    A new method for attenuation compensation (AC) in mesh-domain SPECT OSEM reconstruction using strip-area approximation (SAAC) is introduced and compared to single-ray AC (SRAC). SAAC uses the polygonal area of the intersection of a mesh element (ME) and a tube-of-response (TOR) for defining an effective length of photon transit and an effective attenuation coefficient. This approach to AC is compared to SRAC, which defines the effective length of photon transit as the intersection of a single ray and a ME and the effective attenuation coefficient as the mean along the ray path. Comparative quantitative and qualitative analysis demonstrated that SAAC outperformed SRAC in terms of reconstruction image accuracy and quality.

  3. Entropy algebras and Birkhoff factorization

    NASA Astrophysics Data System (ADS)

    Marcolli, Matilde; Tedeschi, Nicolas

    2015-11-01

    We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.

  4. Algebraic Activities Aid Discovery Lessons

    ERIC Educational Resources Information Center

    Wallace-Gomez, Patricia

    2013-01-01

    After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

  5. Putting the Modern in Algebra

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Ries, Heather; Chandler, Kayla

    2012-01-01

    Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…

  6. Dimension independence in exterior algebra.

    PubMed Central

    Hawrylycz, M

    1995-01-01

    The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520

  7. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  8. A New Age for Algebra

    ERIC Educational Resources Information Center

    Oishi, Lindsay

    2011-01-01

    "Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…

  9. Weaving Geometry and Algebra Together

    ERIC Educational Resources Information Center

    Cetner, Michelle

    2015-01-01

    When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

  10. Algebraic methods in system theory

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Willems, J. C.; Willsky, A. S.

    1975-01-01

    Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

  11. Algebra from Chips and Chopsticks

    ERIC Educational Resources Information Center

    Yun, Jeong Oak; Flores, Alfinio

    2012-01-01

    Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

  12. Celestial mechanics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

  13. Algebra for All. Research Brief

    ERIC Educational Resources Information Center

    Bleyaert, Barbara

    2009-01-01

    The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless national…

  14. Kinds of Knowledge in Algebra.

    ERIC Educational Resources Information Center

    Lewis, Clayton

    Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

  15. Adventures in Flipping College Algebra

    ERIC Educational Resources Information Center

    Van Sickle, Jenna

    2015-01-01

    This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

  16. An Algebraic Route to Pi

    ERIC Educational Resources Information Center

    Deakin, Michael A. B.

    1974-01-01

    Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

  17. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  18. Math for All Learners: Algebra.

    ERIC Educational Resources Information Center

    Meader, Pam; Storer, Judy

    This book consists of a series of activities aimed at providing a problem solving, hands-on approach so that students can experience concepts in algebra. Topics include ratio and proportion, patterns and formulas, integers, polynomials, linear equations, graphs, and probability. The activities come in the form of reproducible blackline masters…

  19. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…

  20. Algebra, Home Mortgages, and Recessions

    ERIC Educational Resources Information Center

    Mariner, Jean A. Miller; Miller, Richard A.

    2009-01-01

    The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

  1. Math Sense: Algebra and Geometry.

    ERIC Educational Resources Information Center

    Howett, Jerry

    This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

  2. Polynomial Algebra in Form 4

    NASA Astrophysics Data System (ADS)

    Kuipers, J.

    2012-06-01

    New features of the symbolic algebra package Form 4 are discussed. Most importantly, these features include polynomial factorization and polynomial gcd computation. Examples of their use are shown. One of them is an exact version of Mincer which gives answers in terms of rational polynomials and 5 master integrals.

  3. Advanced Geologic Modeling Using CAD and Unstructured Meshes

    NASA Astrophysics Data System (ADS)

    Melnikova, Y.; Jacquemyn, C.; Osman, H.; Gorman, G.; Hampson, G.; Jackson, M.

    2015-12-01

    Capturing complex, multiscale geologic heterogeneity in subsurface flow models is challenging. Surface-based modeling (SBM) offers an alternative approach to conventional grid-based methods. In SBM, all geologic features that impact the distribution of material properties, such as porosity and permeability, are modeled as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. A typical model contains numerous such domains. The surfaces have parametric, grid-free representation which, in principle, allows for unlimited complexity, since no resolution is implied at the stage of modeling and features of any scale can be included. We demonstrate a method to create stochastic, surface-based models using computer aided design (CAD) and efficiently discretise them for flow simulation. The surfaces are represented using non-uniform, rational B-splines (NURBS), and processed in a CAD environment employing Boolean operations. We show examples of fluvial channels, fracture networks and scour events. Cartesian-like grids are not able to capture the complex geometries in these models without using excessively large numbers of grid blocks. Unstructured meshes can more efficiently approximate the geometries. However, high aspect ratio features and varying curvatures present challenges for algorithms to produce quality, unstructured meshes without excessive user interaction. We contribute an automated integrated workflow that processes the input geometry created in the CAD environment, creates the final model, and discretises it with a quality tetrahedral mesh. For computational efficiency, we use a geometry-adaptive mesh that distributes the element density and size in accordance with the geometrical complexity of the model. We show examples of finite-element flow simulations of the resulting geologic models. The new approach has broad application in modeling subsurface flow.

  4. Automatic Mesh Generation of Hybrid Mesh on Valves in Multiple Positions in Feedline Systems

    NASA Technical Reports Server (NTRS)

    Ross, Douglass H.; Ito, Yasushi; Dorothy, Fredric W.; Shih, Alan M.; Peugeot, John

    2010-01-01

    Fluid flow simulations through a valve often require evaluation of the valve in multiple opening positions. A mesh has to be generated for the valve for each position and compounding. The problem is the fact that the valve is typically part of a larger feedline system. In this paper, we propose to develop a system to create meshes for feedline systems with parametrically controlled valve openings. Herein we outline two approaches to generate the meshes for a valve in a feedline system at multiple positions. There are two issues that must be addressed. The first is the creation of the mesh on the valve for multiple positions. The second is the generation of the mesh for the total feedline system including the valve. For generation of the mesh on the valve, we will describe the use of topology matching and mesh generation parameter transfer. For generation of the total feedline system, we will describe two solutions that we have implemented. In both cases the valve is treated as a component in the feedline system. In the first method the geometry of the valve in the feedline system is replaced with a valve at a different opening position. Geometry is created to connect the valve to the feedline system. Then topology for the valve is created and the portion of the topology for the valve is topology matched to the standard valve in a different position. The mesh generation parameters are transferred and then the volume mesh for the whole feedline system is generated. The second method enables the user to generate the volume mesh on the valve in multiple open positions external to the feedline system, to insert it into the volume mesh of the feedline system, and to reduce the amount of computer time required for mesh generation because only two small volume meshes connecting the valve to the feedline mesh need to be updated.

  5. Array algebra estimation in signal processing

    NASA Astrophysics Data System (ADS)

    Rauhala, U. A.

    A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.

  6. Formal scattering theory by an algebraic approach

    NASA Astrophysics Data System (ADS)

    Alhassid, Y.; Levine, R. D.

    1985-02-01

    Formal scattering theory is recast in a Lie-algebraic form. The central result is an algebraic Lippmann-Schwinger equation for the wave operator from which an algebraic form of the Born series (containing only linked terms) is obtained. When a finite Lie algebra is sufficient, The Mo/ller wave operator, on the energy shell, can be solved for explicitly as an element of the corresponding group. The method is illustrated for the separable potential whose relevant algebra is found to be U(1,1).

  7. Method of modifying a volume mesh using sheet extraction

    DOEpatents

    Borden, Michael J.; Shepherd, Jason F.

    2007-02-20

    A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet extraction. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of determining a sheet of hexahedral mesh elements, generating nodes for merging, and merging the nodes to delete the sheet of hexahedral mesh elements and modify the volume mesh.

  8. A comparison of gradient estimation methods for volume rendering on unstructured meshes.

    PubMed

    Correa, Carlos D; Hero, Robert; Ma, Kwan-Liu

    2011-03-01

    This paper presents a study of gradient estimation methods for rendering unstructured-mesh volume data. Gradient estimation is necessary for rendering shaded isosurfaces and specular highlights, which provide important cues for shape and depth. Gradient estimation has been widely studied and deployed for regular-grid volume data to achieve local illumination effects, but has been, otherwise, for unstructured-mesh data. As a result, most of the unstructured-mesh volume visualizations made so far were unlit. In this paper, we present a comprehensive study of gradient estimation methods for unstructured meshes with respect to their cost and performance. Through a number of benchmarks, we discuss the effects of mesh quality and scalar function complexity in the accuracy of the reconstruction, and their impact in lighting-enabled volume rendering. Based on our study, we also propose two heuristic improvements to the gradient reconstruction process. The first heuristic improves the rendering quality with a hybrid algorithm that combines the results of the multiple reconstruction methods, based on the properties of a given mesh. The second heuristic improves the efficiency of its GPU implementation, by restricting the computation of the gradient on a fixed-size local neighborhood. PMID:21233515

  9. Filiform Lie algebras of order 3

    SciTech Connect

    Navarro, R. M.

    2014-04-15

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

  10. Atomic effect algebras with compression bases

    SciTech Connect

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-15

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  11. Pillowing doublets: Refining a mesh to ensure that faces share at most one edge

    SciTech Connect

    Mitchell, S.A.; Tautges, T.J.

    1995-11-01

    Occasionally one may be confronted by a hexahedral or quadrilateral mesh containing doublets, two faces sharing two edges. In this case, no amount of smoothing will produce a mesh with agreeable element quality: in the planar case, one of these two faces will always have an angle of at least 180 degrees between the two edges. The authors describe a robust scheme for refining a hexahedral or quadrilateral mesh to separate such faces, so that any two faces share at most one edge. Note that this also ensures that two hexahedra share at most one face in the three dimensional case. The authors have implemented this algorithm and incorporated it into the CUBIT mesh generation environment developed at Sandia National Laboratories.

  12. Mesh optimization for microbial fuel cell cathodes constructed around stainless steel mesh current collectors

    NASA Astrophysics Data System (ADS)

    Zhang, Fang; Merrill, Matthew D.; Tokash, Justin C.; Saito, Tomonori; Cheng, Shaoan; Hickner, Michael A.; Logan, Bruce E.

    Mesh current collectors made of stainless steel (SS) can be integrated into microbial fuel cell (MFC) cathodes constructed of a reactive carbon black and Pt catalyst mixture and a poly(dimethylsiloxane) (PDMS) diffusion layer. It is shown here that the mesh properties of these cathodes can significantly affect performance. Cathodes made from the coarsest mesh (30-mesh) achieved the highest maximum power of 1616 ± 25 mW m -2 (normalized to cathode projected surface area; 47.1 ± 0.7 W m -3 based on liquid volume), while the finest mesh (120-mesh) had the lowest power density (599 ± 57 mW m -2). Electrochemical impedance spectroscopy showed that charge transfer and diffusion resistances decreased with increasing mesh opening size. In MFC tests, the cathode performance was primarily limited by reaction kinetics, and not mass transfer. Oxygen permeability increased with mesh opening size, accounting for the decreased diffusion resistance. At higher current densities, diffusion became a limiting factor, especially for fine mesh with low oxygen transfer coefficients. These results demonstrate the critical nature of the mesh size used for constructing MFC cathodes.

  13. Engagement of Metal Debris into Gear Mesh

    NASA Technical Reports Server (NTRS)

    handschuh, Robert F.; Krantz, Timothy L.

    2010-01-01

    A series of bench-top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material, shim stock and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the "chip" through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined.

  14. H(curl) Auxiliary Mesh Preconditioning

    SciTech Connect

    Kolev, T V; Pasciak, J E; Vassilevski, P S

    2006-08-31

    This paper analyzes a two-level preconditioning scheme for H(curl) bilinear forms. The scheme utilizes an auxiliary problem on a related mesh that is more amenable for constructing optimal order multigrid methods. More specifically, we analyze the case when the auxiliary mesh only approximately covers the original domain. The latter assumption is important since it allows for easy construction of nested multilevel spaces on regular auxiliary meshes. Numerical experiments in both two and three space dimensions illustrate the optimal performance of the method.

  15. Adaptive radial basis function mesh deformation using data reduction

    NASA Astrophysics Data System (ADS)

    Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.

    2016-09-01

    Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBF's), but the parallel efficiency reduces due to the limited

  16. Linear algebra algorithms for divisors on an algebraic curve

    NASA Astrophysics Data System (ADS)

    Khuri-Makdisi, Kamal

    We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and matrices of size $O(g^2)\\times O(g)$. When the base field $k$ is finite, or if $C$ has a rational point over $k$, these give algorithms for working on the Jacobian of $C$ that require $O(g^4)$ field operations, arising from the Gaussian elimination. Our point of view is strongly geometric, and our representation of points on the Jacobian is fairly simple to work with; in particular, none of our algorithms involves arithmetic with polynomials. We note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in Hess' 1999 Ph.D. thesis, which works with function fields as extensions of $k[x]$. However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and Smart), and $C_{ab}$ curves (Harasawa and Suzuki); in all those cases, one can attain a complexity of $O(g^2)$.

  17. Numerical simulation of H2/air detonation using unstructured mesh

    NASA Astrophysics Data System (ADS)

    Togashi, Fumiya; Löhner, Rainald; Tsuboi, Nobuyuki

    2009-06-01

    To explore the capability of unstructured mesh to simulate detonation wave propagation phenomena, numerical simulation of H2/air detonation using unstructured mesh was conducted. The unstructured mesh has several adv- antages such as easy mesh adaptation and flexibility to the complicated configurations. To examine the resolution dependency of the unstructured mesh, several simulations varying the mesh size were conducted and compared with a computed result using a structured mesh. The results show that the unstructured mesh solution captures the detailed structure of detonation wave, as well as the structured mesh solution. To capture the detailed detonation cell structure, the unstructured mesh simulations required at least twice, ideally 5times the resolution of structured mesh solution.

  18. Effects on Diagnostic Parameters After Removing Additional Synchronous Gear Meshes

    NASA Technical Reports Server (NTRS)

    Decker, Harry J.

    2003-01-01

    Gear cracks are typically difficult to diagnose with sufficient time before catastrophic damage occurs. Significant damage must be present before algorithms appear to be able to detect the damage. Frequently there are multiple gear meshes on a single shaft. Since they are all synchronous with the shaft frequency, the commonly used synchronous averaging technique is ineffective in removing other gear mesh effects. Carefully applying a filter to these extraneous gear mesh frequencies can reduce the overall vibration signal and increase the accuracy of commonly used vibration metrics. The vibration signals from three seeded fault tests were analyzed using this filtering procedure. Both the filtered and unfiltered vibration signals were then analyzed using commonly used fault detection metrics and compared. The tests were conducted on aerospace quality spur gears in a test rig. The tests were conducted at speeds ranging from 2500 to 5000 revolutions per minute and torques from 184 to 228 percent of design load. The inability to detect these cracks with high confidence results from the high loading which is causing fast fracture as opposed to stable crack growth. The results indicate that these techniques do not currently produce an indication of damage that significantly exceeds experimental scatter.

  19. Alternative algebraic approaches in quantum chemistry

    SciTech Connect

    Mezey, Paul G.

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  20. The algebras of large N matrix mechanics

    SciTech Connect

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  1. ALGEBRA IIVer 1.22

    SciTech Connect

    2003-06-03

    The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran code is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.

  2. ALGEBRA IIVer 1.22

    2003-06-03

    The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less

  3. Anisotropic norm-oriented mesh adaptation for a Poisson problem

    NASA Astrophysics Data System (ADS)

    Brèthes, Gautier; Dervieux, Alain

    2016-10-01

    We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.

  4. LR: Compact connectivity representation for triangle meshes

    SciTech Connect

    Gurung, T; Luffel, M; Lindstrom, P; Rossignac, J

    2011-01-28

    We propose LR (Laced Ring) - a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.

  5. Optimal fully adaptive wormhole routing for meshes

    SciTech Connect

    Schwiebert, L.; Jayasimha, D.N.

    1993-12-31

    A deadlock-free fully adaptive routing algorithm for 2D meshes which is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. The routing algorithm imposes less than half as many routing restrictions as any previous fully adaptive routing algorithm. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm that achieves both of these goals. The implementation of the routing algorithm requires relatively simple router control logic. The new algorithm is extended, in a straightforward manner to arbitrary dimension meshes. It needs only 4n-2 virtual channels, the minimum number for an n-dimensional mesh. All previous algorithms require an exponential number of virtual channels in the dimension of the mesh.

  6. Grid adaptation using chimera composite overlapping meshes

    NASA Technical Reports Server (NTRS)

    Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

    1994-01-01

    The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.

  7. Grid adaptation using Chimera composite overlapping meshes

    NASA Technical Reports Server (NTRS)

    Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

    1993-01-01

    The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

  8. Grid adaption using Chimera composite overlapping meshes

    NASA Technical Reports Server (NTRS)

    Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

    1993-01-01

    The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

  9. A mesh gradient technique for numerical optimization

    NASA Technical Reports Server (NTRS)

    Willis, E. A., Jr.

    1973-01-01

    A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

  10. Surface Generation and Cartesian Mesh Support

    NASA Technical Reports Server (NTRS)

    Haimes, Robert

    2004-01-01

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

  11. Efficiently Sorting Zoo-Mesh Data Sets

    SciTech Connect

    Cook, R; Max, N; Silva, C; Williams, P

    2001-03-26

    The authors describe the SXMPVO algorithm for performing a visibility ordering zoo-meshed polyhedra. The algorithm runs in practice in linear time and the visibility ordering which it produces is exact.

  12. BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1994-01-01

    The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

  13. Computer algebra and transport theory.

    SciTech Connect

    Warsa, J. S.

    2004-01-01

    Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.

  14. Introduction to Image Algebra Ada

    NASA Astrophysics Data System (ADS)

    Wilson, Joseph N.

    1991-07-01

    Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.

  15. MHD simulations on an unstructured mesh

    SciTech Connect

    Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Longcope, D.W.; Sugiyama, L.E.

    1998-12-31

    Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D.

  16. Adaptive Mesh Refinement for Microelectronic Device Design

    NASA Technical Reports Server (NTRS)

    Cwik, Tom; Lou, John; Norton, Charles

    1999-01-01

    Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of

  17. Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement

    SciTech Connect

    Koniges, A.; Eder, D.; Masters, N.; Fisher, A.; Anderson, R.; Gunney, B.; Wang, P.; Benson, D.; Dixit, P.

    2009-09-29

    This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being applied to slurry flow (landslides).

  18. Quadrilateral/hexahedral finite element mesh coarsening

    DOEpatents

    Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E

    2012-10-16

    A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.

  19. Early- Versus Late-Onset Prosthetic Mesh Infection: More than Time Alone.

    PubMed

    Kong, Wencheng; Wang, Jian; Mao, Qi; Ren, Lele; Zhang, Shaoyi; Yao, Danhua; Guo, Mingxiao; Li, Yousheng

    2015-12-01

    Prosthetic mesh used for ventral incisional hernia makes hernia repair surgery simple, effective, and safe. The mesh infection is a formidable complication and bimodal distribution. The differences between early- and late-onset are unknown. This is a cohort study of patients undergoing ventral incisional hernia (VIH) repair from January 2003 to September 2013. Data of specific risk variables were collected from electronic medical record systems in Jinling Hospital. And, the quality of lives was evaluated by WHO Quality of Life-BREF. A total of 102 VIH repair patients were analyzed and followed including the noninfection group and early- and late-onset group. There were significant differences between the early- and late-onset group in clinical manifestation, descriptive analysis of the study population, and postoperative quality of lives. These differences might imply the different pathophysiologic process of early- and late-onset mesh infection. Permanent prosthetic mesh should be used with caution, and the study of intraperitoneal onlay mesh is still needed in long-term follow-up. PMID:27011528

  20. Mesh geometry impact on Micromegas performance with an Exchangeable Mesh prototype

    NASA Astrophysics Data System (ADS)

    Kuger, F.; Bianco, M.; Iengo, P.; Sekhniaidze, G.; Veenhof, R.; Wotschack, J.

    2016-07-01

    The reconstruction precision of gaseous detectors is limited by losses of primary electrons during signal formation. In addition to common gas related losses, like attachment, Micromegas suffer from electron absorption during its transition through the micro mesh. This study aims for a deepened understanding of electron losses and their dependency on the mesh geometry. It combines experimental results obtained with a novel designed Exchangeable Mesh Micromegas (ExMe) and advanced microscopic-tracking simulations (ANSYS and Garfield++) of electron drift and mesh transition.

  1. TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

    NASA Astrophysics Data System (ADS)

    Denner, Fabian; van Wachem, Berend G. M.

    2015-10-01

    Total variation diminishing (TVD) schemes are a widely applied group of monotonicity-preserving advection differencing schemes for partial differential equations in numerical heat transfer and computational fluid dynamics. These schemes are typically designed for one-dimensional problems or multidimensional problems on structured equidistant quadrilateral meshes. Practical applications, however, often involve complex geometries that cannot be represented by Cartesian meshes and, therefore, necessitate the application of unstructured meshes, which require a more sophisticated discretisation to account for their additional topological complexity. In principle, TVD schemes are applicable to unstructured meshes, however, not all the data required for TVD differencing is readily available on unstructured meshes, and the solution suffers from considerable numerical diffusion as a result of mesh skewness. In this article we analyse TVD differencing on unstructured three-dimensional meshes, focusing on the non-linearity of TVD differencing and the extrapolation of the virtual upwind node. Furthermore, we propose a novel monotonicity-preserving correction method for TVD schemes that significantly reduces numerical diffusion caused by mesh skewness. The presented numerical experiments demonstrate the importance of accounting for the non-linearity introduced by TVD differencing and of imposing carefully chosen limits on the extrapolated virtual upwind node, as well as the efficacy of the proposed method to correct mesh skewness.

  2. How to model wireless mesh networks topology

    NASA Astrophysics Data System (ADS)

    Sanni, M. L.; Hashim, A. A.; Anwar, F.; Ahmed, G. S. M.; Ali, S.

    2013-12-01

    The specification of network connectivity model or topology is the beginning of design and analysis in Computer Network researches. Wireless Mesh Networks is an autonomic network that is dynamically self-organised, self-configured while the mesh nodes establish automatic connectivity with the adjacent nodes in the relay network of wireless backbone routers. Researches in Wireless Mesh Networks range from node deployment to internetworking issues with sensor, Internet and cellular networks. These researches require modelling of relationships and interactions among nodes including technical characteristics of the links while satisfying the architectural requirements of the physical network. However, the existing topology generators model geographic topologies which constitute different architectures, thus may not be suitable in Wireless Mesh Networks scenarios. The existing methods of topology generation are explored, analysed and parameters for their characterisation are identified. Furthermore, an algorithm for the design of Wireless Mesh Networks topology based on square grid model is proposed in this paper. The performance of the topology generated is also evaluated. This research is particularly important in the generation of a close-to-real topology for ensuring relevance of design to the intended network and validity of results obtained in Wireless Mesh Networks researches.

  3. Hybrid Surface Mesh Adaptation for Climate Modeling

    SciTech Connect

    Ahmed Khamayseh; Valmor de Almeida; Glen Hansen

    2008-10-01

    Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called “mesh motion” (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.

  4. Hybrid Surface Mesh Adaptation for Climate Modeling

    SciTech Connect

    Khamayseh, Ahmed K; de Almeida, Valmor F; Hansen, Glen

    2008-01-01

    Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called "mesh motion" (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.

  5. Discrete differential geometry: the nonplanar quadrilateral mesh.

    PubMed

    Twining, Carole J; Marsland, Stephen

    2012-06-01

    We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

  6. JTpack90: A parallel, object-based, Fortran 90 linear algebra package

    SciTech Connect

    Turner, J.A.; Kothe, D.B.; Ferrell, R.C.

    1997-03-01

    The authors have developed an object-based linear algebra package, currently with emphasis on sparse Krylov methods, driven primarily by needs of the Los Alamos National Laboratory parallel unstructured-mesh casting simulation tool Telluride. Support for a number of sparse storage formats, methods, and preconditioners have been implemented, driven primarily by application needs. They describe the object-based Fortran 90 approach, which enhances maintainability, performance, and extensibility, the parallelization approach using a new portable gather/scatter library (PGSLib), current capabilities and future plans, and present preliminary performance results on a variety of platforms.

  7. Algebra: A Challenge at the Crossroads of Policy and Practice

    ERIC Educational Resources Information Center

    Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

    2011-01-01

    The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

  8. View-dependent progressive mesh coding for graphic streaming

    NASA Astrophysics Data System (ADS)

    Yang, Sheng; Kim, Chang-Su; Kuo, C.-C. Jay

    2001-11-01

    A view-dependent progressive mesh (VDPM) coding algorithm is proposed in this research to facilitate interactive 3D graphics streaming and browsing. The proposed algorithm splits a 3D graphics model into several partitions, progressively compresses each partition, and reorganizes topological and geometrical data to enable the transmission of visible parts with a higher priority. With the real-time streaming protocol (RTSP), the server is informed of the viewing parameters before transmission. Then, the server can adaptively transmit visible parts in detail, while cutting off invisible parts. Experimental results demonstrate that the proposed algorithm reduces the required transmission bandwidth, and exhibits acceptable visual quality even at low bit rates.

  9. (Fuzzy) Ideals of BN-Algebras

    PubMed Central

    Walendziak, Andrzej

    2015-01-01

    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

  10. Kumjian-Pask algebras of desourcification

    NASA Astrophysics Data System (ADS)

    Rosjanuardi, Rizky; Yusnitha, Isnie

    2016-02-01

    Kumjian-Pask algebra which was introduced by Pino, Clark, an Huef and Raeburn [1] in 2013, gives a purely algebraic version of a k-graph algebra. Rosjanuardi [2] gave necessary and sufficient condition of finitely dimensional complex Kumjian-Pask algebra of row-finite k-graph without sources. We will improve the previous results which allows us to deal with sources. We will consider Kumjian-Pask algebra for locally convex row-finite k-graph which was introduced by Clark, Flynn and an Huef [3], and use the desourcification of the graph to get conditions which characterise when the complex Kumjian-Pask algebra of locally convex row-finite k-graph is finite dimensional.

  11. Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Tianjie; Gao, Xing; Guo, Li

    2016-10-01

    The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

  12. The design and application of upwind schemes on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Jespersen, Dennis C.

    1989-01-01

    Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.

  13. Positive Contrast MRI Techniques for Visualization of Iron-Loaded Hernia Mesh Implants in Patients

    PubMed Central

    Ciritsis, Alexander; Truhn, Daniel; Hansen, Nienke L.; Otto, Jens; Kuhl, Christiane K.; Kraemer, Nils A.

    2016-01-01

    Object In MRI, implants and devices can be delineated via susceptibility artefacts. To discriminate susceptibility voids from proton-free structures, different positive contrast techniques were implemented. The purpose of this study was to evaluate a pulse sequence-based positive contrast technique (PCSI) and a post-processing susceptibility gradient mapping algorithm (SGM) for visualization of iron loaded mesh implants in patients. Material and Methods Five patients with iron-loaded MR-visible inguinal hernia mesh implants were examined at 1.5 Tesla. A gradient echo sequence (GRE; parameters: TR: 8.3ms; TE: 4.3ms; NSA:2; FA:20°; FOV:350mm²) and a PCSI sequence (parameters: TR: 25ms; TE: 4.6ms; NSA:4; FA:20°; FOV:350mm²) with on-resonant proton suppression were performed. SGM maps were calculated using two algorithms. Image quality and mesh delineation were independently evaluated by three radiologists. Results On GRE, the iron-loaded meshes generated distinct susceptibility-induced signal voids. PCSI exhibited susceptibility differences including the meshes as hyperintense signals. SGM exhibited susceptibility differences with positive contrast. Visually, the different algorithms presented no significant differences. Overall, the diagnostic value was rated best in GRE whereas PCSI and SGM were barely “sufficient”. Conclusion Both “positive contrast” techniques depicted implanted meshes with hyperintense signal. SGM comes without additional acquisition time and can therefore be utilized in every patient. PMID:27192201

  14. LayTracks3D: A new approach for meshing general solids using medial axis transform

    DOE PAGES

    Quadros, William Roshan

    2015-08-22

    This study presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to themore » MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.« less

  15. Coverings of topological semi-abelian algebras

    NASA Astrophysics Data System (ADS)

    Mucuk, Osman; Demir, Serap

    2016-08-01

    In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.

  16. Method of modifying a volume mesh using sheet insertion

    DOEpatents

    Borden, Michael J.; Shepherd, Jason F.

    2006-08-29

    A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet insertion. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify (refine) the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of locating a sheet of hexahedral mesh elements, determining a plurality of hexahedral elements within the sheet to refine, shrinking the plurality of elements, and inserting a new sheet of hexahedral elements adjacently to modify the volume mesh. Additionally, another predetermined algorithm using mesh cutting may be followed to modify a volume mesh.

  17. Effect of a concave grid mesh in a carbon nanotube-based field emission X-ray source

    SciTech Connect

    Kim, Hyun Suk; Castro, Edward Joseph D.; Lee, Choong Hun

    2014-10-15

    Highlights: • Successful design using a concave grid mesh for the focusing electron. • Much better X-ray image due to the concave grid mesh. • Higher anode current efficiency using the concave grid mesh versus a flat grid mesh. - Abstract: This study introduces a simple approach to improve the X-ray image quality produced by the carbon nanotube (CNT) field emitter X-ray source by altering the geometrical shape of the grid mesh from the conventional flat shape to a concave one in a typical triode structure. The concave shape of the grid electrode increases the effective number of the grid cells in the mesh, which exerted an electric field in the direction of the emitted electrons, thereby increasing the emission current reaching the anode. Furthermore, the curved mesh (concave grid mesh), which was responsible for the extraction of electrons from the field emitter, exhibited a focusing effect on the electron beam trajectory thereby, reducing the focal spot size impinging on the anode and resulted in a better spatial resolution of the X-ray images produced.

  18. Multicloning and Multibroadcasting in Operator Algebras

    NASA Astrophysics Data System (ADS)

    Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej

    2015-12-01

    We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.

  19. On Realization of Generalized Effect Algebras

    NASA Astrophysics Data System (ADS)

    Paseka, Jan

    2012-12-01

    A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G(H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G(H) possesses an order determining set of generalized states.

  20. A Structure of BCI-Algebras

    NASA Astrophysics Data System (ADS)

    Chajda, Ivan

    2014-10-01

    Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11-21, 2007) showing that they can be considered as structures essentially weaker than semilattices but still with certain involutions in sections. The aim of this paper is to involve a similar approach for BCI-algebras.

  1. Difficulties in initial algebra learning in Indonesia

    NASA Astrophysics Data System (ADS)

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-12-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

  2. Literal algebra for satellite dynamics. [perturbation analysis

    NASA Technical Reports Server (NTRS)

    Gaposchkin, E. M.

    1975-01-01

    A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.

  3. Entanglement and algebraic independence in fermion systems

    NASA Astrophysics Data System (ADS)

    Benatti, Fabio; Floreanini, Roberto

    2014-04-01

    In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence.

  4. Facial expression reconstruction on the basis of selected vertices of triangle mesh

    NASA Astrophysics Data System (ADS)

    Peszor, Damian; Wojciechowska, Marzena

    2016-06-01

    Facial expression reconstruction is an important issue in the field of computer graphics. While it is relatively easy to create an animation based on meshes constructed through video recordings, this kind of high-quality data is often not transferred to another model because of lack of intermediary, anthropometry-based way to do so. However, if a high-quality mesh is sampled with sufficient density, it is possible to use obtained feature points to encode the shape of surrounding vertices in a way that can be easily transferred to another mesh with corresponding feature points. In this paper we present a method used for obtaining information for the purpose of reconstructing changes in facial surface on the basis of selected feature points.

  5. Some C∗-algebras which are coronas of non-C∗-Banach algebras

    NASA Astrophysics Data System (ADS)

    Voiculescu, Dan-Virgil

    2016-07-01

    We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.

  6. An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

    ERIC Educational Resources Information Center

    Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

    2016-01-01

    This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

  7. Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra

    NASA Astrophysics Data System (ADS)

    Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.

    2016-03-01

    In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.

  8. Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

    ERIC Educational Resources Information Center

    Ozgun-Koca, S. Ash

    2010-01-01

    Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

  9. An Approach for Patient-Specific Multi-domain Vascular Mesh Generation Featuring Spatially Varying Wall Thickness Modeling

    PubMed Central

    Raut, Samarth S.; Liu, Peng; Finol, Ender A.

    2015-01-01

    In this work, we present a computationally efficient image-derived volume mesh generation approach for vasculatures that implements spatially varying patient-specific wall thickness with a novel inward extrusion of the wall surface mesh. Multi-domain vascular meshes with arbitrary numbers, locations, and patterns of both iliac bifurcations and thrombi can be obtained without the need to specify features or landmark points as input. In addition, the mesh output is coordinate-frame independent and independent of the image grid resolution with high dimensional accuracy and mesh quality, devoid of errors typically found in off-the-shelf image-based model generation workflows. The absence of deformable template models or Cartesian grid-based methods enables the present approach to be robust by handling aneurysmatic geometries with highly irregular shapes, arterial branches nearly parallel to the image plane, and variable wall thickness. The assessment of the methodology was based on i) estimation of the surface reconstruction accuracy, ii) validation of the output mesh using an aneurysm phantom, and iii) benchmarking the volume mesh quality against other frameworks. For the phantom image dataset (pixel size 0.105 mm; slice spacing 0.7 mm; mean wall thickness 1.401 ± 0.120 mm), the average wall thickness in the mesh was 1.459 ± 0.123 mm. The absolute error in average wall thickness was 0.060 ± 0.036 mm, or about 8.6% of the largest image grid spacing (0.7 mm) and 4.36% of the actual mean wall thickness. Mesh quality metrics and the ability to reproduce regional variations of wall thickness were found superior to similar alternative frameworks. PMID:25976018

  10. Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes.

    PubMed

    Bijar, Ahmad; Rohan, Pierre-Yves; Perrier, Pascal; Payan, Yohan

    2016-01-01

    Generation of subject-specific 3D finite element (FE) models requires the processing of numerous medical images in order to precisely extract geometrical information about subject-specific anatomy. This processing remains extremely challenging. To overcome this difficulty, we present an automatic atlas-based method that generates subject-specific FE meshes via a 3D registration guided by Magnetic Resonance images. The method extracts a 3D transformation by registering the atlas' volume image to the subject's one, and establishes a one-to-one correspondence between the two volumes. The 3D transformation field deforms the atlas' mesh to generate the subject-specific FE mesh. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline free-form deformations is used, which guarantees a non-folding and one-to-one transformation. Two evaluations of the method are provided. First, a publicly available CT-database is used to assess the capability to accurately capture the complexity of each subject-specific Lung's geometry. Second, FE tongue meshes are generated for two healthy volunteers and two patients suffering from tongue cancer using MR images. It is shown that the method generates an appropriate representation of the subject-specific geometry while preserving the quality of the FE meshes for subsequent FE analysis. To demonstrate the importance of our method in a clinical context, a subject-specific mesh is used to simulate tongue's biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.

  11. Cluster automorphism groups of cluster algebras with coefficients

    NASA Astrophysics Data System (ADS)

    Chang, Wen; Zhu, Bin

    2016-10-01

    We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e. the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.

  12. The Structure of Parafermion Vertex Operator Algebras: General Case

    NASA Astrophysics Data System (ADS)

    Dong, Chongying; Wang, Qing

    2010-11-01

    The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.

  13. A nanobursa mesh: a graded electrospun nanofiber mesh with metal nanoparticles on carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Senturk-Ozer, Semra; Chen, Tao; Degirmenbasi, Nebahat; Gevgilili, Halil; Podkolzin, Simon G.; Kalyon, Dilhan M.

    2014-07-01

    A new type of material, a ``nanobursa'' mesh (from ``bursa'' meaning ``sac or pouch''), is introduced. This material consists of sequential layers of porous polymeric nanofibers encapsulating carbon nanotubes, which are functionalized with different metal nanoparticles in each layer. The nanobursa mesh is fabricated via a novel combination of twin-screw extrusion and electrospinning. Use of this hybrid process at industrially-relevant rates is demonstrated by producing a nanobursa mesh with graded layers of Pd, Co, Ag, and Pt nanoparticles. The potential use of the fabricated nanobursa mesh is illustrated by modeling of catalytic hydrocarbon oxidation.A new type of material, a ``nanobursa'' mesh (from ``bursa'' meaning ``sac or pouch''), is introduced. This material consists of sequential layers of porous polymeric nanofibers encapsulating carbon nanotubes, which are functionalized with different metal nanoparticles in each layer. The nanobursa mesh is fabricated via a novel combination of twin-screw extrusion and electrospinning. Use of this hybrid process at industrially-relevant rates is demonstrated by producing a nanobursa mesh with graded layers of Pd, Co, Ag, and Pt nanoparticles. The potential use of the fabricated nanobursa mesh is illustrated by modeling of catalytic hydrocarbon oxidation. Electronic supplementary information (ESI) available: Experimental methods and computational details. See DOI: 10.1039/c4nr01145g

  14. Mixed-element Octree: a meshing technique toward fast and real-time simulations in biomedical applications.

    PubMed

    Lobos, Claudio; González, Eugenio

    2015-12-01

    This article introduces a meshing technique focused on fast and real-time simulation in a biomedical context. We describe in details our algorithm, which starts from a basic Octree regarding the constraints imposed by the simulation, and then, mixed-element patterns are applied over transitions between coarse and fine regions. The use of surface patterns, also composed by mixed elements, allows us to better represent curved domains decreasing the odds of creating invalid elements by adding as few nodes as possible. In contrast with other meshing techniques, we let the user define regions of greater refinement, and as a consequence of that refinement, we add as few nodes as possible to produce a mesh that is topologically correct. Therefore, our meshing technique gives more control on the number of nodes of the final mesh. We show several examples where the quality of the final mesh is acceptable, even without using quality filters. We believe that this new meshing technique is in the correct direction toward real-time simulation in the biomedical field.

  15. MeSH indexing based on automatically generated summaries

    PubMed Central

    2013-01-01

    Background MEDLINE citations are manually indexed at the U.S. National Library of Medicine (NLM) using as reference the Medical Subject Headings (MeSH) controlled vocabulary. For this task, the human indexers read the full text of the article. Due to the growth of MEDLINE, the NLM Indexing Initiative explores indexing methodologies that can support the task of the indexers. Medical Text Indexer (MTI) is a tool developed by the NLM Indexing Initiative to provide MeSH indexing recommendations to indexers. Currently, the input to MTI is MEDLINE citations, title and abstract only. Previous work has shown that using full text as input to MTI increases recall, but decreases precision sharply. We propose using summaries generated automatically from the full text for the input to MTI to use in the task of suggesting MeSH headings to indexers. Summaries distill the most salient information from the full text, which might increase the coverage of automatic indexing approaches based on MEDLINE. We hypothesize that if the results were good enough, manual indexers could possibly use automatic summaries instead of the full texts, along with the recommendations of MTI, to speed up the process while maintaining high quality of indexing results. Results We have generated summaries of different lengths using two different summarizers, and evaluated the MTI indexing on the summaries using different algorithms: MTI, individual MTI components, and machine learning. The results are compared to those of full text articles and MEDLINE citations. Our results show that automatically generated summaries achieve similar recall but higher precision compared to full text articles. Compared to MEDLINE citations, summaries achieve higher recall but lower precision. Conclusions Our results show that automatic summaries produce better indexing than full text articles. Summaries produce similar recall to full text but much better precision, which seems to indicate that automatic summaries can

  16. MESH Pakistan: Prospects and Challenges

    ERIC Educational Resources Information Center

    Leask, Marilyn; Jumani, Nabi Bux

    2015-01-01

    The Organisation for Economic Co-operation and Development periodically surveys teaching and learning issues (the TALIS surveys) in the most developed countries. In their 2009 report, they commented that although teacher quality is the fundamental component in high performing systems, the education sector has been slow to develop systemic…

  17. Gene algebra from a genetic code algebraic structure.

    PubMed

    Sanchez, R; Morgado, E; Grau, R

    2005-10-01

    By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z(64), +) of the integer module 64. On the Z(64)-algebra of the set of 64(N) codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z(64))(N)-->(Z(64))(N). Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z(64)-algebra will help us explain the quantitative relationships between genes.

  18. Hyperparameter selection for OSEM SPECT reconstruction in mesh domain with total variation regularization

    NASA Astrophysics Data System (ADS)

    Krol, A.; Lu, Y.; Vogelsang, L.; Yu, B.; Xu, Y.; Feiglin, D.

    2010-04-01

    The purpose of this study was investigation of the L-curve method performance for the optimized hyperparameter selection in maximum a posteriori (MAP) Ordered Subsets Expectation Maximization (OSEM) Single Photon Computed Emission Tomography (SPECT) reconstruction in mesh domain with Total Variation (TV) regularization for different noise levels and three different mesh resolutions. Reconstruction with TV prior requires tuning of only one Bayesian hyperparameter β. This was accomplished by application of the L-curve method. We analyzed the reconstructed image quality for various values of β and investigated the relationship between the optimized β, the mesh structure and the noise level in the projection data. We have found that each obtained L-curve exhibited one well-defined minimum and the optimal trade-off between noise and spatial resolution in the reconstructed images occurred for the value of β defined by that minimum. The L-curves minima shifted towards lower values with increasing mesh resolution and towards higher values with increasing noise in the SPECT data. The shape of the L-curve depended on the mesh resolution and the noise level. By analyzing the reconstructed image quality, we have verified that the L-curve method is a suitable tool for estimation of the optimized value for the hyperparameter.

  19. Dirac matrices as elements of a superalgebraic matrix algebra

    NASA Astrophysics Data System (ADS)

    Monakhov, V. V.

    2016-08-01

    The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix algebra exists in this algebra, the Clifford exten-sion of the Grassmann algebra is a generalization of the matrix algebra and contains superalgebraic operators expanding matrix algebra and produces supersymmetric transformations.

  20. Automated Angular Momentum Recoupling Algebra

    NASA Astrophysics Data System (ADS)

    Williams, H. T.; Silbar, Richard R.

    1992-04-01

    We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.

  1. Anisotropic mesh adaptation on Lagrangian Coherent Structures

    NASA Astrophysics Data System (ADS)

    Miron, Philippe; Vétel, Jérôme; Garon, André; Delfour, Michel; Hassan, Mouhammad El

    2012-08-01

    The finite-time Lyapunov exponent (FTLE) is extensively used as a criterion to reveal fluid flow structures, including unsteady separation/attachment surfaces and vortices, in laminar and turbulent flows. However, for large and complex problems, flow structure identification demands computational methodologies that are more accurate and effective. With this objective in mind, we propose a new set of ordinary differential equations to compute the flow map, along with its first (gradient) and second order (Hessian) spatial derivatives. We show empirically that the gradient of the flow map computed in this way improves the pointwise accuracy of the FTLE field. Furthermore, the Hessian allows for simple interpolation error estimation of the flow map, and the construction of a continuous optimal and multiscale Lp metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. Typically, the L1 norm provides meshes best suited to capturing small scale structures, while the L∞ norm provides meshes optimized to capture large scale structures. This means that the mesh density near large scale structures will be greater with the L∞ norm than with the L1 norm for the same mesh complexity, which is why we chose this technique for this paper. We use it to optimize the mesh in the vicinity of LCS. It is found that Lagrangian Coherent Structures are best revealed with the minimum number of vertices with the L∞ metric.

  2. Variational Mesh Adaptation: Isotropy and Equidistribution

    NASA Astrophysics Data System (ADS)

    Huang, Weizhang

    2001-12-01

    We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error behavior for linear interpolation. The criterion is then decomposed into two aspects, the isotropy (or conformity) and uniformity (or equidistribution) requirements, each of which can be easier to deal with. The functionals that satisfy these conditions approximately are constructed using discrete and continuous inequalities. A new functional is finally formulated by combining the functionals corresponding to the isotropy and uniformity requirements. The features of the functional are analyzed and demonstrated by numerical results. In particular, unlike the existing mesh adaptation functionals, the new functional has clear geometric meanings of minimization. A mesh that has the desired properties of isotropy and equidistribution can be obtained by properly choosing the values of two parameters. The analysis presented in this article also provides a better understanding of the increasingly popular method of harmonic mapping in two dimensions.

  3. Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras

    NASA Astrophysics Data System (ADS)

    Ondrus, Matthew; Wiesner, Emilie

    2016-07-01

    This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.

  4. Mesh Surgery for Anterior Vaginal Wall Prolapse: A Meta-analysis.

    PubMed

    Juliato, Cássia Raquel Teatin; Santos Júnior, Luiz Carlos do; Haddad, Jorge Milhem; Castro, Rodrigo Aquino; Lima, Marcelo; Castro, Edilson Benedito de

    2016-07-01

    Purpose Pelvic organ prolapse (POP) is a major health issue worldwide, affecting 6-8% of women. The most affected site is the anterior vaginal wall. Multiple procedures and surgical techniques have been used, with or without the use of vaginal meshes, due to common treatment failure, reoperations, and complication rates in some studies. Methods Systematic review of the literature and meta-analysis regarding the use of vaginal mesh in anterior vaginal wall prolapse was performed. A total of 115 papers were retrieved after using the medical subject headings (MESH) terms: 'anterior pelvic organ prolapse OR cystocele AND surgery AND (mesh or colporrhaphy)' in the PubMed database. Exclusion criteria were: follow-up shorter than 1 year, use of biological or absorbable meshes, and inclusion of other vaginal wall prolapses. Studies were put in a data chart by two independent editors; results found in at least two studies were grouped for analysis. Results After the review of the titles by two independent editors, 70 studies were discarded, and after abstract assessment, 18 trials were eligible for full text screening. For final screening and meta-analysis, after applying the Jadad score (> 2), 12 studies were included. Objective cure was greater in the mesh surgery group (odds ratio [OR] = 1,28 [1,07-1,53]), which also had greater blood loss (mean deviation [MD] = 45,98 [9,72-82,25]), longer surgery time (MD = 15,08 [0,48-29,67]), but less prolapse recurrence (OR = 0,22 [01,3-0,38]). Dyspareunia, symptom resolution and reoperation rates were not statistically different between groups. Quality of life (QOL) assessment through the pelvic organ prolapse/urinary incontinence sexual questionnaire (PISQ-12), the pelvic floor distress inventory (PFDI-20), the pelvic floor impact questionnaire (PFIQ-7), and the perceived quality of life scale (PQOL) was not significantly different. Conclusions Anterior vaginal prolapse mesh surgery has greater anatomic

  5. Algebraic Thinking through Koch Snowflake Constructions

    ERIC Educational Resources Information Center

    Ghosh, Jonaki B.

    2016-01-01

    Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

  6. Investigating Algebraic Procedures Using Discussion and Writing

    ERIC Educational Resources Information Center

    Harper, Jonathan; Ford, Jeffrey

    2012-01-01

    This study reports on the implementation of an intermediate algebra curriculum centered on a framework of student-centered questions designed to investigate algebraic procedures. Instructional activities were designed to build discourse in the small-group discussion meetings of the course. Students were assigned writing prompts to emphasize the…

  7. Practicing Algebraic Skills: A Conceptual Approach

    ERIC Educational Resources Information Center

    Friedlander, Alex; Arcavi, Abraham

    2012-01-01

    Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…

  8. Using Students' Interests as Algebraic Models

    ERIC Educational Resources Information Center

    Whaley, Kenneth A.

    2012-01-01

    Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

  9. THE RADICAL OF A JORDAN ALGEBRA

    PubMed Central

    McCrimmon, Kevin

    1969-01-01

    In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736

  10. The operator algebra approach to quantum groups

    PubMed Central

    Kustermans, Johan; Vaes, Stefaan

    2000-01-01

    A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116

  11. Situated Learning in an Abstract Algebra Classroom

    ERIC Educational Resources Information Center

    Ticknor, Cindy S.

    2012-01-01

    Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content…

  12. Solving Absolute Value Equations Algebraically and Geometrically

    ERIC Educational Resources Information Center

    Shiyuan, Wei

    2005-01-01

    The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

  13. Predicting Turkish Ninth Grade Students' Algebra Performance

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kursat

    2005-01-01

    The prediction of students' achievement in algebra in eighth and ninth grades has become a research interest for practical issues of placement. A group of simple, easily accessible variables was used to predict student performance in algebra after completion of eighth grade. The three variables of school type, grade level, and previous year…

  14. Success in Algebra among Community College Students

    ERIC Educational Resources Information Center

    Reyes, Czarina

    2010-01-01

    College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…

  15. Calif. Laws Shift Gears on Algebra, Textbooks

    ERIC Educational Resources Information Center

    Robelen, Erik W.

    2012-01-01

    New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…

  16. How To Prepare Students for Algebra.

    ERIC Educational Resources Information Center

    Wu, H.

    2001-01-01

    Suggests that no matter how much algebraic thinking is introduced in the early grades, and no matter how worthwhile this might be, the failure rate in algebra will continue unless the teaching of fractions and decimals is radically revamped. The proper study of fractions provides a ramp that leads students gently from whole number arithmetic up to…

  17. Using the Internet To Investigate Algebra.

    ERIC Educational Resources Information Center

    Sherwood, Walter

    The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

  18. New directions in algebraic dynamical systems

    NASA Astrophysics Data System (ADS)

    Schmidt, Klaus; Verbitskiy, Evgeny

    2011-02-01

    The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.

  19. Classical and quantum Kummer shape algebras

    NASA Astrophysics Data System (ADS)

    Odzijewicz, A.; Wawreniuk, E.

    2016-07-01

    We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.

  20. Fourier theory and C∗-algebras

    NASA Astrophysics Data System (ADS)

    Bédos, Erik; Conti, Roberto

    2016-07-01

    We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.

  1. Teaching Algebra to Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Impecoven-Lind, Linda S.; Foegen, Anne

    2010-01-01

    Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

  2. Arithmetic and Cognitive Contributions to Algebra

    ERIC Educational Resources Information Center

    Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.

    2013-01-01

    Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

  3. Just Say Yes to Early Algebra!

    ERIC Educational Resources Information Center

    Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy

    2015-01-01

    Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…

  4. An Inquiry-Based Linear Algebra Class

    ERIC Educational Resources Information Center

    Wang, Haohao; Posey, Lisa

    2011-01-01

    Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…

  5. Parabolas: Connection between Algebraic and Geometrical Representations

    ERIC Educational Resources Information Center

    Shriki, Atara

    2011-01-01

    A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…

  6. Algebraic Geodesics on Three-Dimensional Quadrics

    NASA Astrophysics Data System (ADS)

    Kai, Yue

    2015-12-01

    By Hamilton-Jacobi method, we study the problem of algebraic geodesics on the third-order surface. By the implicit function theorem, we proved the existences of the real geodesics which are the intersections of two algebraic surfaces, and we also give some numerical examples.

  7. Algebra: How Is It for You?

    ERIC Educational Resources Information Center

    Rickard, Caroline

    2008-01-01

    Shortly after starting work for the University of Chichester in the School of Teacher Education, the author was planning a session relating to algebra and found herself inspired by an article in MT182: "Algebraic Infants" by Andrews and Sayers (2003). Based on the making of families of "Multilink" animals, Andrews and Sayers (2003) claim that…

  8. Focus on Fractions to Scaffold Algebra

    ERIC Educational Resources Information Center

    Ooten, Cheryl Thomas

    2013-01-01

    Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

  9. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…

  10. A Technology-Intensive Approach to Algebra.

    ERIC Educational Resources Information Center

    Heid, M. Kathleen; Zbiek, Rose Mary

    1995-01-01

    Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)

  11. Modern Algebra, Mathematics: 5293.36.

    ERIC Educational Resources Information Center

    Edwards, Raymond J.

    This guidebook covers Boolean algebra, matrices, linear transformations of the plane, characteristic values, vectors, and algebraic structures. Overall course goals and performance objectives for each unit are specified; sequencing of units and various time schedules are suggested. A sample pretest and posttest are given, and an annotated list of…

  12. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  13. NASA Lewis Meshed VSAT Workshop meeting summary

    NASA Technical Reports Server (NTRS)

    Ivancic, William

    1993-01-01

    NASA Lewis Research Center's Space Electronics Division (SED) hosted a workshop to address specific topics related to future meshed very small-aperture terminal (VSAT) satellite communications networks. The ideas generated by this workshop will help to identify potential markets and focus technology development within the commercial satellite communications industry and NASA. The workshop resulted in recommendations concerning these principal points of interest: the window of opportunity for a meshed VSAT system; system availability; ground terminal antenna sizes; recommended multifrequency for time division multiple access (TDMA) uplink; a packet switch design concept for narrowband; and fault tolerance design concepts. This report presents a summary of group presentations and discussion associated with the technological, economic, and operational issues of meshed VSAT architectures that utilize processing satellites.

  14. NASA Lewis Meshed VSAT Workshop meeting summary

    NASA Astrophysics Data System (ADS)

    Ivancic, William

    1993-11-01

    NASA Lewis Research Center's Space Electronics Division (SED) hosted a workshop to address specific topics related to future meshed very small-aperture terminal (VSAT) satellite communications networks. The ideas generated by this workshop will help to identify potential markets and focus technology development within the commercial satellite communications industry and NASA. The workshop resulted in recommendations concerning these principal points of interest: the window of opportunity for a meshed VSAT system; system availability; ground terminal antenna sizes; recommended multifrequency for time division multiple access (TDMA) uplink; a packet switch design concept for narrowband; and fault tolerance design concepts. This report presents a summary of group presentations and discussion associated with the technological, economic, and operational issues of meshed VSAT architectures that utilize processing satellites.

  15. GRChombo: Numerical relativity with adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran

    2015-12-01

    In this work, we introduce {\\mathtt{GRChombo}}: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial ‘many-boxes-in-many-boxes’ mesh hierarchies and massive parallelism through the message passing interface. {\\mathtt{GRChombo}} evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, while also significantly simplifying the process of setting up the mesh for these problems. We show that {\\mathtt{GRChombo}} can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.

  16. Mesh convergence differences based on failure mechanisms

    SciTech Connect

    Pilat, K.R.; Revelli, V.D.

    1994-04-01

    Material properties affect the deformation and failure modes in structural parts. When performing finite element analyses to compare response for different materials, different levels of mesh discretization may be necessary for each analyses because the failure mode changes, even through the part geometry and loading remain the same. Take, for example, strain localization, a material dependent phenomenon. When localization occurs, the mesh needs to be much finer to capture the steep strain gradients in the region of localization than in a case where localization does not occur. Although this requirement is almost intuitive once stated, it is often not used in practice because the effects are less pronounced when failure is not present, and also because failure modes are difficult to anticipate. The lack of availability of constitutive models for failure prediction is also a contributing factor. This paper describes a recent study regarding the effect of mesh refinement on failure prediction in a part modeled with two different materials.

  17. MODEL IDENTIFICATION AND COMPUTER ALGEBRA

    PubMed Central

    Bollen, Kenneth A.; Bauldry, Shawn

    2011-01-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  18. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.

  19. Spatial watermarking of 3D triangle meshes

    NASA Astrophysics Data System (ADS)

    Cayre, Francois; Macq, Benoit M. M.

    2001-12-01

    Although it is obvious that watermarking has become of great interest in protecting audio, videos, and still pictures, few work has been done considering 3D meshes. We propose a new method for watermarking 3D triangle meshes. This method embeds the watermark as triangles deformations. The list of watermarked triangles is obtained through a similar way to the one used in the TSPS (Triangle Strip Peeling Sequence) method. Unlike TSPS, our method is automatic and more secure. We also show that it is reversible.

  20. Adaptive mesh refinement for storm surge

    NASA Astrophysics Data System (ADS)

    Mandli, Kyle T.; Dawson, Clint N.

    2014-03-01

    An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble forecasting framework without significant computing resources. The application of adaptive mesh refinement algorithms substantially lowers the computational cost of a storm surge model run while retaining much of the desired coastal resolution. The approach presented is implemented in the GEOCLAW framework and compared to ADCIRC for Hurricane Ike along with observed tide gauge data and the computational cost of each model run.

  1. Laparoscopic rectocele repair using polyglactin mesh.

    PubMed

    Lyons, T L; Winer, W K

    1997-05-01

    We assessed the efficacy of laparoscopic treatment of rectocele defect using a polyglactin mesh graft. From May 1, 1995, through September 30, 1995, we prospectively evaluated 20 women (age 38-74 yrs) undergoing pelvic floor reconstruction for symptomatic pelvic floor prolapse, with or without hysterectomy. Morbidity of the procedure was extremely low compared with standard transvaginal and transrectal approaches. Patients were followed at 3-month intervals for 1 year. Sixteen had resolution of symptoms. Laparoscopic application of polyglactin mesh for the repair of the rectocele defect is a viable option, although long-term follow-up is necessary. PMID:9154790

  2. Development of modular cable mesh deployable antenna

    NASA Astrophysics Data System (ADS)

    Meguro, Akira; Mitsugi, Jin; Andou, Kazuhide

    1993-03-01

    This report describes a concept and key technologies for the modular mesh deployable antenna. The antenna reflector composed of independently manufactured and tested modules is presented. Each module consists of a mesh surface, a cable network, and a deployable truss structure. The cable network comprises three kinds of cables, surface, tie, and back cables. Adjustment of tie cable lengths improves the surface accuracy. Synchronous deployment truss structures are considered as a supporting structure. Their design method, BBM's (Bread Board Model) and deployment analysis are also explained.

  3. Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement

    2009-09-29

    This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being appliedmore » to slurry flow (landslides).« less

  4. Multigrid solution strategies for adaptive meshing problems

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1995-01-01

    This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.

  5. Generalization of n-ary Nambu algebras and beyond

    SciTech Connect

    Ataguema, H.; Makhlouf, A.; Silvestrov, S.

    2009-08-15

    The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

  6. Studies in computational geometry motivated by mesh generation

    SciTech Connect

    Smith, W.D.

    1989-01-01

    This thesis sprawls over most of discrete and computational geometry. There are four loose bodies of theory developed. (1) A quantitative and algorithmic theory of crossing number and crossing-free line segment graphs in the plane. As five applications of this theory: the author disproves two long - standing conjectures on the crossing number of the complete and complete bipartite graphs, he presents the first exponential algorithm for planar minimum Steiner tree, and the first subexponential algorithms for planar traveling salesman tour and optimum triangulation, and he presents an algorithm for generating all non-isomorphic V-vertex planar graphs, in O(V{sup 3)}time per graph, using O(V) total workspace. (2) Mesh generation, and the triangulation of polytopes: He has the strongest bounds on the number of d-simplices required to triangulate the d-cube, and new triangulation methods in the plane. A quantitative and qualitative - and practical - theory of finite element mesh quality suggest a new, simple strategy for generating good meshes. (3) The theory of geometrical graphs on N point sites in d-space. This subsumes many new results in: geometrical probability, sphere packing, and extremal configurations. An array of new multidimensional search date structures are used to devise fast algorithms for construction many geometrical graphs. (4) Useful new results concerning the mensuration and structure of d-polytopes. In particular he extensively generalizes the famous formula of Heron and Alexandria (75 AD), for the area of a triangle, and he presents the first linear time congruence algorithm for 3 -dimensional polyhedra. He closes with the largest bibliography of the field, containing over 3000 references.

  7. Highly Symmetric and Congruently Tiled Meshes for Shells and Domes

    PubMed Central

    Rasheed, Muhibur; Bajaj, Chandrajit

    2016-01-01

    We describe the generation of all possible shell and dome shapes that can be uniquely meshed (tiled) using a single type of mesh face (tile), and following a single meshing (tiling) rule that governs the mesh (tile) arrangement with maximal vertex, edge and face symmetries. Such tiling arrangements or congruently tiled meshed shapes, are frequently found in chemical forms (fullerenes or Bucky balls, crystals, quasi-crystals, virus nano shells or capsids), and synthetic shapes (cages, sports domes, modern architectural facades). Congruently tiled meshes are both aesthetic and complete, as they support maximal mesh symmetries with minimal complexity and possess simple generation rules. Here, we generate congruent tilings and meshed shape layouts that satisfy these optimality conditions. Further, the congruent meshes are uniquely mappable to an almost regular 3D polyhedron (or its dual polyhedron) and which exhibits face-transitive (and edge-transitive) congruency with at most two types of vertices (each type transitive to the other). The family of all such congruently meshed polyhedra create a new class of meshed shapes, beyond the well-studied regular, semi-regular and quasi-regular classes, and their duals (platonic, Catalan and Johnson). While our new mesh class is infinite, we prove that there exists a unique mesh parametrization, where each member of the class can be represented by two integer lattice variables, and moreover efficiently constructable. PMID:27563368

  8. Feasibility of an electromagnetic compatibility method for MRgFUS using a wire mesh screen.

    PubMed

    Wu, Hao; Shen, Guofeng; Chen, Yazhu

    2016-12-01

    This study evaluated an electromagnetic compatibility method for high-intensity focused ultrasound (HIFU) and magnetic resonance (MR) imaging in an MR-guided focused ultrasound surgery using a conductive wire mesh screen. This screen has a good ultrasound transmission and shielding effectiveness. A hybrid acoustic simulation method was developed to analyze the effects of mesh parameters and the HIFU working frequency on the acoustic field. Experiments were performed to measure both acoustic pressure profile and radiated electromagnetic noise. With the proposed mesh screen, the electromagnetic radiation emission was reduced by 14dB at 128MHz while the acoustic focal intensity was reduced by less than 11% using one screen. This shielding method is easy to implement and requires no additional phase correction method. This method also improves the quality of MR images. PMID:27448456

  9. Functionalized Nanofiber Meshes Enhance Immunosorbent Assays.

    PubMed

    Hersey, Joseph S; Meller, Amit; Grinstaff, Mark W

    2015-12-01

    Three-dimensional substrates with high surface-to-volume ratios and subsequently large protein binding capacities are of interest for advanced immunosorbent assays utilizing integrated microfluidics and nanosensing elements. A library of bioactive and antifouling electrospun nanofiber substrates, which are composed of high-molecular-weight poly(oxanorbornene) derivatives, is described. Specifically, a set of copolymers are synthesized from three 7-oxanorbornene monomers to create a set of water insoluble copolymers with both biotin (bioactive) and triethylene glycol (TEG) (antifouling) functionality. Porous three-dimensional nanofiber meshes are electrospun from these copolymers with the ability to specifically bind streptavidin while minimizing the nonspecific binding of other proteins. Fluorescently labeled streptavidin is used to quantify the streptavidin binding capacity of each mesh type through confocal microscopy. A simplified enzyme-linked immunosorbent assay (ELISA) is presented to assess the protein binding capabilities and detection limits of these nanofiber meshes under both static conditions (26 h) and flow conditions (1 h) for a model target protein (i.e., mouse IgG) using a horseradish peroxidase (HRP) colorimetric assay. Bioactive and antifouling nanofiber meshes outperform traditional streptavidin-coated polystyrene plates under flow, validating their use in future advanced immunosorbent assays and their compatibility with microfluidic-based biosensors.

  10. Broadcasting on linear arrays and meshes

    SciTech Connect

    Seidel, S.R. . Dept. of Computer Science)

    1993-03-01

    The well known spanning binomial tree broadcast algorithm is generalized to obtain several new broadcast algorithms for linear arrays and meshes. These generalizations take advantage of bidirectional communication, the connectivity of two-dimensional meshes, and the difference between node-to-network and network-to-network bandwidth. It is shown how these algorithms can be further generalized so that any node can be the source of the broadcast message. A partitioning scheme is given that allows these algorithms to be used on linear arrays and meshes of any size. One of these algorithms, the bidirectional spanning tree broadcast, always has lower cost than the recursive halving broadcast for linear arrays. All of these algorithms offer significant performance improvements over the basic spanning tree broadcast. These algorithms do not rely on a knowledge of machine dependent constants for network bandwidth and latency, so their performance is not as sensitive to changes in machine characteristics as that of hybrid and pipelined algorithms. Performance measurements are given for some of these broadcast algorithms on the Intel Delta mesh.

  11. A unified approach for a posteriori high-order curved mesh generation using solid mechanics

    NASA Astrophysics Data System (ADS)

    Poya, Roman; Sevilla, Ruben; Gil, Antonio J.

    2016-09-01

    The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.

  12. Working memory, worry, and algebraic ability.

    PubMed

    Trezise, Kelly; Reeve, Robert A

    2014-05-01

    Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra). Moreover, researchers have tended to examine MA/worry separate from math problem solving activities and have used general WM tasks rather than domain-relevant WM measures. Furthermore, it seems to have been assumed that MA affects all areas of math. It is possible, however, that MA is restricted to particular math domains. To examine these issues, the current research assessed claims about the impact on algebraic problem solving of differences in WM and algebraic worry. A sample of 80 14-year-old female students completed algebraic worry, algebraic WM, algebraic problem solving, nonverbal IQ, and general math ability tasks. Latent profile analysis of worry and WM measures identified four performance profiles (subgroups) that differed in worry level and WM capacity. Consistent with expectations, subgroup membership was associated with algebraic problem solving performance: high WM/low worry>moderate WM/low worry=moderate WM/high worry>low WM/high worry. Findings are discussed in terms of the conceptual relationship between emotion and cognition in mathematics and implications for the MA-WM-performance relationship.

  13. Weak homological dimensions and biflat Koethe algebras

    SciTech Connect

    Pirkovskii, A Yu

    2008-06-30

    The homological properties of metrizable Koethe algebras {lambda}(P) are studied. A criterion for an algebra A={lambda}(P) to be biflat in terms of the Koethe set P is obtained, which implies, in particular, that for such algebras the properties of being biprojective, biflat, and flat on the left are equivalent to the surjectivity of the multiplication operator A otimes-hat A{yields}A. The weak homological dimensions (the weak global dimension w.dg and the weak bidimension w.db) of biflat Koethe algebras are calculated. Namely, it is shown that the conditions w.db {lambda}(P)<=1 and w.dg {lambda}(P)<=1 are equivalent to the nuclearity of {lambda}(P); and if {lambda}(P) is non-nuclear, then w.dg {lambda}(P)=w.db {lambda}(P)=2. It is established that the nuclearity of a biflat Koethe algebra {lambda}(P), under certain additional conditions on the Koethe set P, implies the stronger estimate db {lambda}(P), where db is the (projective) bidimension. On the other hand, an example is constructed of a nuclear biflat Koethe algebra {lambda}(P) such that db {lambda}(P)=2 (while w.db {lambda}(P)=1). Finally, it is shown that many biflat Koethe algebras, while not being amenable, have trivial Hochschild homology groups in positive degrees (with arbitrary coefficients). Bibliography: 37 titles.

  14. Algebraic curves of maximal cyclicity

    NASA Astrophysics Data System (ADS)

    Caubergh, Magdalena; Dumortier, Freddy

    2006-01-01

    The paper deals with analytic families of planar vector fields, studying methods to detect the cyclicity of a non-isolated closed orbit, i.e. the maximum number of limit cycles that can locally bifurcate from it. It is known that this multi-parameter problem can be reduced to a single-parameter one, in the sense that there exist analytic curves in parameter space along which the maximal cyclicity can be attained. In that case one speaks about a maximal cyclicity curve (mcc) in case only the number is considered and of a maximal multiplicity curve (mmc) in case the multiplicity is also taken into account. In view of obtaining efficient algorithms for detecting the cyclicity, we investigate whether such mcc or mmc can be algebraic or even linear depending on certain general properties of the families or of their associated Bautin ideal. In any case by well chosen examples we show that prudence is appropriate.

  15. Inequalities, assessment and computer algebra

    NASA Astrophysics Data System (ADS)

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.

  16. Local Algebras of Differential Operators

    NASA Astrophysics Data System (ADS)

    Church, P. T.; Timourian, J. G.

    2002-05-01

    There is an increasing literature devoted to the study of boundary value problems using singularity theory. The resulting differential operators are typically Fredholm with index 0, defined on infinite-dimensional spaces, and they have often led to folds, cusps, and even higher-order Morin singularities. In this paper we develop some of the local algebras of germs of such differential Fredholm operators, extending the theory of the finite-dimensional case. We apply this work to nonlinear elliptic boundary value problems: in particular, we make further progress on a question proposed and initially studied by Ruf [1999, J. Differential Equations 151, 111-133]. We also make comments on several problems raised by others.

  17. PC Basic Linear Algebra Subroutines

    1992-03-09

    PC-BLAS is a highly optimized version of the Basic Linear Algebra Subprograms (BLAS), a standardized set of thirty-eight routines that perform low-level operations on vectors of numbers in single and double-precision real and complex arithmetic. Routines are included to find the index of the largest component of a vector, apply a Givens or modified Givens rotation, multiply a vector by a constant, determine the Euclidean length, perform a dot product, swap and copy vectors, andmore » find the norm of a vector. The BLAS have been carefully written to minimize numerical problems such as loss of precision and underflow and are designed so that the computation is independent of the interface with the calling program. This independence is achieved through judicious use of Assembly language macros. Interfaces are provided for Lahey Fortran 77, Microsoft Fortran 77, and Ryan-McFarland IBM Professional Fortran.« less

  18. Evaluation of mesh morphing and mapping techniques in patient specific modelling of the human pelvis.

    PubMed

    Salo, Zoryana; Beek, Maarten; Whyne, Cari Marisa

    2012-08-01

    Robust generation of pelvic finite element models is necessary to understand variation in mechanical behaviour resulting from differences in gender, aging, disease and injury. The objective of this study was to apply and evaluate mesh morphing and mapping techniques to facilitate the creation and structural analysis of specimen-specific finite element (FE) models of the pelvis. A specimen-specific pelvic FE model (source mesh) was generated following a traditional user-intensive meshing scheme. The source mesh was morphed onto a computed tomography scan generated target surface of a second pelvis using a landmarked-based approach, in which exterior source nodes were shifted to target surface vertices, while constrained along a normal. A second copy of the morphed model was further refined through mesh mapping, in which surface nodes of the initial morphed model were selected in patches and remapped onto the surfaces of the target model. Computed tomography intensity-based material properties were assigned to each model. The source, target, morphed and mapped models were analyzed under axial compression using linear static FE analysis, and their strain distributions were evaluated. Morphing and mapping techniques were effectively applied to generate good quality and geometrically complex specimen-specific pelvic FE models. Mapping significantly improved strain concurrence with the target pelvis FE model.

  19. Evaluation of mesh morphing and mapping techniques in patient specific modeling of the human pelvis.

    PubMed

    Salo, Zoryana; Beek, Maarten; Whyne, Cari Marisa

    2013-01-01

    Robust generation of pelvic finite element models is necessary to understand the variation in mechanical behaviour resulting from differences in gender, aging, disease and injury. The objective of this study was to apply and evaluate mesh morphing and mapping techniques to facilitate the creation and structural analysis of specimen-specific finite element (FE) models of the pelvis. A specimen-specific pelvic FE model (source mesh) was generated following a traditional user-intensive meshing scheme. The source mesh was morphed onto a computed tomography scan generated target surface of a second pelvis using a landmarked-based approach, in which exterior source nodes were shifted to target surface vertices, while constrained along a normal. A second copy of the morphed model was further refined through mesh mapping, in which surface nodes of the initial morphed model were selected in patches and remapped onto the surfaces of the target model. Computed tomography intensity based material properties were assigned to each model. The source, target, morphed and mapped models were analyzed under axial compression using linear static FE analysis and their strain distributions evaluated. Morphing and mapping techniques were effectively applied to generate good quality geometrically complex specimen-specific pelvic FE models. Mapping significantly improved strain concurrence with the target pelvis FE model.

  20. System matrix for OSEM SPECT with attenuation compensation in mesh domain

    NASA Astrophysics Data System (ADS)

    Vogelsang, Levon; Krol, Andrzej; Feiglin, David H.; Lipson, Edward

    2010-04-01

    The purpose of this study was to develop and implement an accurate and computationally efficient method for determination of the mesh-domain ssssssystem matrix including attenuation compensation for Ordered Subsets Expectation Maximization (OSEM) Single Photon Emission Computed Tomography (SPECT). The mesh-domain system matrix elements were estimated by first partitioning the object domain into strips parallel to detector face and with width not exceeding the size of a detector unit. This was followed by approximating the integration over the strip/mesh-element union. This approximation is product of: (i) strip width, (ii) intersection length of a ray central to strip with a mesh element, and (iii) the response and expansion function evaluated at midpoint of the intersection length. Reconstruction was performed using OSEM without regularization and with exact knowledge of the attenuation map. The method was evaluated using synthetic SPECT data generated using SIMIND Monte Carlo simulation software. Comparative quantitative and qualitative analysis included: bias, variance, standard deviation and line-profiles within three different regions of interest. We found that no more than two divisions per detector bin were needed for good quality reconstructed images when using a high resolution mesh.