Science.gov

Sample records for algebraic mesh quality

  1. Algebraic mesh quality metrics

    SciTech Connect

    KNUPP,PATRICK

    2000-04-24

    Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.

  2. 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.

  3. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

    SciTech Connect

    Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; Salinger, Andrew G.; Price, Stephen

    2016-10-06

    A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.

  4. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

    DOE PAGES

    Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...

    2016-10-06

    A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less

  5. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

    SciTech Connect

    Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; Salinger, Andrew G.; Price, Stephen

    2016-10-06

    A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.

  6. Mesh quality control for multiply-refined tetrahedral grids

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Strawn, Roger

    1994-01-01

    A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.

  7. 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)

  8. 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)

  9. Quality Multi-domain Meshing for Volumetric Data

    PubMed Central

    Zhang, Qin; Subramanian, Bharadwaj; Xu, Guoliang; Bajaj, Chandrajit L.

    2011-01-01

    Multi-domain meshing from volumetric data is of great importance in many fields like medicine, biology and geology. This paper proposes a new approach to produce a high quality mesh with separated multiple domains. A point cloud is generated from a preliminary mesh representing the boundary between different domains from the discrete volumetric representation used as input. A higher-order level-set method is employed to produce a quality sub-mesh from this point cloud and geometric flow is used as smoothing mechanism. A new approach to detect and curate intersections within an assembly of these 2-manifold sub-meshes by utilizing the intermediate volumetric representation is developed. The separation between sub-meshes can be controlled by the user using a gap threshold parameter. The resulting high quality multi-domain mesh is free from self- and inter-domain intersections and can be further utilized in finite element and boundary element computations. The proposed pipeline has been efficiently implemented and sample meshes have been provided for visualization. PMID:21544233

  10. Unstructured mesh quality assessment and upwind Euler solution algorithm validation

    NASA Astrophysics Data System (ADS)

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

    1994-05-01

    Quality assessment procedures are described for two 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 the Euler equations for these meshes are obtained at low angle of attack, transonic conditions. Results for these cases, obtained as part of a validation study, investigate accuracy of an implicit upwind Euler solution algorithm.

  11. 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.

  12. 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.

  13. Teacher Quality and Teaching Quality of 7th-Grade Algebra I Honors Teachers

    ERIC Educational Resources Information Center

    Perez, Barbara

    2013-01-01

    With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to…

  14. A computational study of the effect of unstructured mesh quality on solution efficiency

    SciTech Connect

    Batdorf, M.; Freitag, L.A.; Ollivier-Gooch, C.

    1997-09-01

    It is well known that mesh quality affects both efficiency and accuracy of CFD solutions. Meshes with distorted elements make solutions both more difficult to compute and less accurate. We review a recently proposed technique for improving mesh quality as measured by element angle (dihedral angle in three dimensions) using a combination of optimization-based smoothing techniques and local reconnection schemes. Typical results that quantify mesh improvement for a number of application meshes are presented. We then examine effects of mesh quality as measured by the maximum angle in the mesh on the convergence rates of two commonly used CFD solution techniques. Numerical experiments are performed that quantify the cost and benefit of using mesh optimization schemes for incompressible flow over a cylinder and weakly compressible flow over a cylinder.

  15. 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

  16. Quality Partitioned Meshing of Multi-Material Objects.

    PubMed

    Zhang, Qin; Cha, Deukhyun; Bajaj, Chandrajit

    We present a simple but effective algorithm for generating topologically and geometrically consistent quality triangular surface meshing of compactly packed multiple heterogeneous domains in [Formula: see text]. 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 [Formula: see text] 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.

  17. 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.

  18. 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.

  19. A priori mesh quality metric error analysis applied to a high-order finite element method

    NASA Astrophysics Data System (ADS)

    Lowrie, W.; Lukin, V. S.; Shumlak, U.

    2011-06-01

    Characterization of computational mesh's quality prior to performing a numerical simulation is an important step in insuring that the result is valid. A highly distorted mesh can result in significant errors. It is therefore desirable to predict solution accuracy on a given mesh. The HiFi/SEL high-order finite element code is used to study the effects of various mesh distortions on solution quality of known analytic problems for spatial discretizations with different order of finite elements. The measured global error norms are compared to several mesh quality metrics by independently varying both the degree of the distortions and the order of the finite elements. It is found that the spatial spectral convergence rates are preserved for all considered distortion types, while the total error increases with the degree of distortion. For each distortion type, correlations between the measured solution error and the different mesh metrics are quantified, identifying the most appropriate overall mesh metric. The results show promise for future a priori computational mesh quality determination and improvement.

  20. 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.

  1. 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.

  2. Maintaining tetrahedral mesh quality in response to time-dependent topological and geometrical deformation

    SciTech Connect

    Kuprat, A.; George, D.

    1998-12-01

    When modeling deformation of geometrically complex regions, unstructured tetrahedral meshes provide the flexibility necessary to track interfaces as they change geometrically and topologically. In the class of time-dependent simulations considered in this paper, multimaterial interfaces are represented by sets of triangular facets, and motion of the interfaces is controlled by physical considerations. The motion of interior points in the conforming tetrahedral mesh (i.e., points not on interfaces) is arbitrary and may be chosen to produce good element shapes. In the context of specified boundary motion driven by physical considerations, they have found that a rather large glossary of mesh changes is required to allow the simulation to survive all the transitions of interface geometry and topology that occur during time evolution. This paper will describe mesh changes required to maintain good element quality as the geometry evolves, as well as mesh changes required to capture changes i n topology that occur when material regions collapse or pinch off. This paper will present a detailed description of mesh changes necessary for capturing the aforementioned geometrical and topological changes, as implemented in the code GRAIN3D, and will provide examples from a metallic grain growth simulation in which the normal velocity of the grain boundary is proportional to mean curvature.

  3. 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.

  4. Shape reconstruction from medical images and quality mesh generation via implicit surfaces

    NASA Astrophysics Data System (ADS)

    Peiró, J.; Formaggia, L.; Gazzola, M.; Radaelli, A.; Rigamonti, V.

    2007-03-01

    The ability of automatically reconstructing physiological shapes, of generating computational meshes, and of calculating flow solutions from medical images is enabling the introduction of computational fluid dynamics (CFD) techniques as an additional tool to aid clinical practice.This article presents a set of procedures for the shape reconstruction and triangulation of geometries derived from a set of medical images representing planar cross sections of the object. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is an iso-surface of the implicit function that is approximated by a triangulation extracted by the method of marching cubes. The quality of this triangulation is often neither suitable for mesh generation nor for flow solution. We discuss the use of mesh enhancement techniques to maximize the quality of the triangulation together with curvature adaption to optimize mesh resolution.The proposed methodology is applied to the reconstruction and discretization of two physiological geometries: a femoral by-pass graft and a nasal cavity.

  5. 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

  6. Quality of pharmacy-specific Medical Subject Headings (MeSH) assignment in pharmacy journals indexed in MEDLINE.

    PubMed

    Minguet, Fernando; Salgado, Teresa M; van den Boogerd, Lucienne; Fernandez-Llimos, Fernando

    2015-01-01

    The Medical Subject Headings (MeSH) is the National Library of Medicine (NLM) controlled vocabulary for indexing articles. Inaccuracies in the MeSH thesaurus have been reported for several areas including pharmacy. To assess the quality of pharmacy-specific MeSH assignment to articles indexed in pharmacy journals. The 10 journals containing the highest number of articles published in 2012 indexed under the MeSH 'Pharmacists' were identified. All articles published over a 5-year period (2008-2012) in the 10 previously selected journals were retrieved from PubMed. MeSH terms used to index these articles were extracted and pharmacy-specific MeSH terms were identified. The frequency of use of pharmacy-specific MeSH terms was calculated across journals. A total of 6989 articles were retrieved from the 10 pharmacy journals, of which 328 (4.7%) were articles not fully indexed and therefore did not contain any MeSH terms assigned. Among the 6661 articles fully indexed, the mean number of MeSH terms was 10.1 (SD = 4.0), being 1.0 (SD = 1.3) considered as Major MeSH. Both values significantly varied across journals. The mean number of pharmacy-specific MeSH terms per article was 0.9 (SD = 1.2). A total of 3490 (52.4%) of the 6661 articles were indexed in pharmacy journals without a single pharmacy-specific MeSH. Of the total 67193 MeSH terms assigned to articles, on average 10.5% (SD = 13.9) were pharmacy-specific MeSH. A statistically significant different pattern of pharmacy-specific MeSH assignment was identified across journals (Kruskal-Wallis P < 0.001). The quality of assignment of the existing pharmacy-specific MeSH terms to articles indexed in pharmacy journals can be improved to further enhance evidence gathering in pharmacy. Over half of the articles published in the top-10 journals publishing pharmacy literature were indexed without a single pharmacy-specific MeSH. Copyright © 2015 Elsevier Inc. All rights reserved.

  7. 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.

  8. 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.

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

    PubMed

    Loderer, Christian; Wörle, Anna; Fuchs, Werner

    2012-04-03

    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

  10. 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.

  11. 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.

  12. 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.

  13. 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.; Batina, John T.; Yang, Henry T. Y.

    1992-01-01

    Quality assessment procedures are described for two-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 accuracy of an implicit upwind Euler solution algorithm.

  14. 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.

  15. Long-term quality of life and functionality after ventral hernia mesh repair.

    PubMed

    Langbach, Odd; Bukholm, Ida; Benth, Jūratė Šaltytė; Røkke, Ola

    2016-11-01

    The absence of recurrence and pain are important for good quality of life (QoL) after ventral hernia mesh repair. We wanted to study long-term outcome after laparoscopic (LVHR) and open ventral hernia mesh repair (OVHR) using validated scales to measure QoL and functional outcome. We conducted a single-center follow-up study of 194 consecutive patients after LVHR and OVHR between March 2000 and June 2010. Of these, 27 patients (13.9 %) died and 14 (7.2 %) failed to attend their follow-up appointment. Of 153 (78.9 %) patients who attended, 81 (52.9 %) patients had LVHR and 72 (47.1 %) patients had OVHR, including 11 conversions (surgery group). One hundred and twelve patients with non-recurrent ventral hernia were also enrolled consecutively as controls (non-surgery group). Quality of life was measured by the SF-36 short form questionnaire and functional outcome by the Activities Assessment Scale (AAS) with the revised Life Orientation Test to measure the influence of dispositional optimism on pain and functionality. Assessment of pain was done using a 100-mm visual analogue scale ruler anchored by word descriptors. Median time from hernia mesh repair to follow-up was 48 and 52 months after LVHR and OVHR, respectively. There were no long-term differences between LVHR and OVHR measured by SF-36 and AAS. Physical dimensions in SF-36: physical function, restrictions in physical function and bodily pain, were significantly better in the surgery group compared to the non-surgery group, but only for incisional hernia. Recurrence was associated with a significant reduction in QoL in all dimensions of SF-36 in both hernia repair cohorts. Chronic pain and impairment were closely related. Optimistic patients had less impairment than pessimistic patients. LVHR and OVHR reduce chronic pain and physical impairment and improve long-term QoL. Hernia recurrence and persistent pain reduce the beneficial effect of hernia surgery. Dispositional optimism can modulate Qo

  16. Survivable Lightpath Provisioning in WDM Mesh Networks Under Shared Path Protection and Signal Quality Constraints

    NASA Astrophysics Data System (ADS)

    Yang, Xi; Shen, Lu; Ramamurthy, Byrav

    2005-04-01

    This paper addresses the problem of survivable lightpath provisioning in wavelength-division-multiplexing (WDM) mesh networks, taking into consideration optical-layer protection and some realistic optical signal quality constraints. The investigated networks use sparsely placed optical-electrical-optical (O/E/O) modules for regeneration and wavelength conversion. Given a fixed network topology with a number of sparsely placed O/E/O modules and a set of connection requests, a pair of link-disjoint lightpaths is established for each connection. Due to physical impairments and wavelength continuity,both the working and protection lightpaths need to be regenerated at some intermediate nodes to overcome signal quality degradation and wavelength contention. In the present paper, resource-efficient provisioning solutions are achieved with the objective of maximizing resource sharing. The authors propose a resource-sharing scheme that supports three kinds of resource-sharing scenarios, including a conventional wavelength-link sharing scenario, which shares wavelength links between protection lightpaths, and two new scenarios, which share O/E/O modules between protection lightpaths and between working and protection lightpaths. An integer linear programming (ILP)-based solution approach is used to find optimal solutions. The authors also propose a local optimization heuristic approach and a tabu search heuristic approach to solve this problem for real-world,large mesh networks. Numerical results show that our solution approaches work well under a variety of network settings and achieves a high level of resource-sharing rates (over 60% for O/E/O modules and over 30% for wavelength links), which translate into great savings in network costs.

  17. 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.

  18. 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.

  19. LES of Triangular-stabilized Lean Premixed Turbulent Flames with an algebraic reaction closure: Quality and Error Assessment

    NASA Astrophysics Data System (ADS)

    Manickam, B.; Franke, J.; Muppala, S. P. R.; Dinkelacker, F.

    In this LES study, an algebraic flame surface wrinkling model based on the progress variable gradient approach is validated for lean premixed turbulent propane/air flames measured on VOLVO test rig. These combustion results are analyzed for uncertainty in the solution using two quality assessment techniques.

  20. Onlay with Adhesive Use Compared with Sublay Mesh Placement in Ventral Hernia Repair: Was Chevrel Right? An Americas Hernia Society Quality Collaborative Analysis.

    PubMed

    Haskins, Ivy N; Voeller, Guy R; Stoikes, Nathaniel F; Webb, David L; Chandler, Robert G; Phillips, Sharon; Poulose, Benjamin K; Rosen, Michael J

    2017-05-01

    The use of mesh during ventral hernia repair (VHR) is a well-accepted concept. However, the ideal location of mesh placement remains strongly debated. Although VHR with onlay mesh placement has historically been associated with a high rate of wound events, this surgical approach is technically less challenging than VHR with sublay mesh placement. The purpose of this study was to compare 30-day wound events after onlay mesh placement with adhesive fixation vs those after sublay mesh placement using the Americas Hernia Society Quality Collaborative database. All patients undergoing elective, open VHR with synthetic mesh placement from January 2013 through January 2016 were identified within the Americas Hernia Society Quality Collaborative. Only patients with clean wounds were included. Patients were divided into 2 groups: onlay mesh placement with the use of adhesive and sublay mesh placement. The association of mesh location with 30-day wound events was investigated using a matched analysis. A total of 1,854 patients met inclusion criteria; 1,761 (95.0%) underwent sublay mesh placement and 93 (5.0%) underwent onlay mesh placement with the use of adhesive. A 2:1 sublay to onlay matched analysis was performed based on factors previously shown to influence wound events after VHR. After matching, both groups had a lower mean Ventral Hernia Working Group grade and fewer associated comorbidities. There was no statistically significant difference between the sublay and onlay groups with respect to 30-day surgical site infections (2.9% vs 5.5%; p = 0.30), surgical site occurrences (15.2% vs 7.7%; p = 0.08), or surgical site occurrences requiring procedural intervention (8.2% vs 5.5%; p = 0.42). Ventral hernia repair with onlay mesh placement is a safe alternative to VHR with sublay mesh placement in low-risk patients. Additional studies are needed to determine the long-term mesh outcomes and recurrence rates in both of these groups. Copyright © 2017 American College of

  1. 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.

  2. Pain and quality of life after inguinal hernia surgery: a multicenter randomized controlled trial comparing lightweight vs heavyweight mesh (Supermesh Study).

    PubMed

    Bona, Stefano; Rosati, Riccardo; Opocher, Enrico; Fiore, Barbara; Montorsi, Marco

    2017-08-08

    Mesh repair has significantly reduced recurrence rate after groin hernia surgery. Recently, attention has shifted to issues such as chronic pain and discomfort, leading to development of lightweight and partially re-absorbable meshes. The aim of the study was to evaluate the effect of lightweight mesh vs heavyweight mesh on post-operative pain, discomfort and quality of life in short and medium term after inguinal hernia surgery. Eight hundred and eight patients with primary inguinal hernia were allocated to anterior repair (Lichtenstein technique) using a lightweight mesh (Ultrapro(®)) or a heavyweight mesh (Prolene(®)). Primary outcomes were incidence of chronic pain and discomfort at 6-month follow-up. Secondary endpoints were quality of life (QoL), pain and complication at 1 week, 1 and 6 months. At 6 months, 25% of patients reported pain of some intensity; severe pain was reported by 1% of patients in both groups. A statistically significant difference in favour of lightweight mesh was found at multivariable analysis for pain (1 week and 6 months after surgery: p = 0.02 and p = 0.04, respectively) and QoL at 1 month and 6 months (p = 0.05 and p = 0.02, respectively). There was no difference in complication rate and no hernia recurrences were detected. The use of lightweight mesh in anterior Lichtenstein inguinal hernia repair significantly reduced the incidence of pain and favourably affected the perceived quality of life at 6 months after surgery compared to heavyweight mesh.

  3. DNS of inertial flows in porous media: Assessment of mesh quality and resolution

    NASA Astrophysics Data System (ADS)

    Finn, Justin; Apte, Sourabh; Wood, Brian

    2010-11-01

    At modest flow rates (10 <=Re <=300) through porous media and packed beds, fluid inertia can result in complex steady and unsteady recirculation regions, dependent on the local pore geometry. We present methods to parameterize and simplify mesh generation for packed beds, with an eye toward obtaining efficient mesh independence for Reynolds numbers in the inertial and unsteady regimes. To handle the geometric singularity at the sphere-sphere and sphere-wall contact points, we use a fillet bridge model, in which every pair of contacting entities are bridged by a fillet, eliminating a small fluid region near the contact point. A second order accurate, parallel, incompressible flow solver [Moin and Apte, AIAA J. 2006] is used to simulate flow through three different sphere packings: a periodic simple cubic packing, a wall bounded hexagonal close packing, and a randomly packed tube. Mesh independence is assessed using several measures including Ergun pressure drop coefficients, viscous and pressure components of drag force, kinetic energy, kinetic energy dissipation and interstitial velocity profiles. Progress toward large scale simulations of flow through randomly packed 10^3 pores will be discussed.

  4. 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.

  5. 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…

  6. 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

  7. 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…

  8. 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.

  9. 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.

  10. 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

  11. W algebras are L∞ algebras

    NASA Astrophysics Data System (ADS)

    Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias

    2017-07-01

    It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W_3 algebra.

  12. 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.

  13. Gradient scaling for nonuniform meshes

    SciTech Connect

    Margolin, L.G.; Ruppel, H.M.; Demuth, R.B.

    1985-01-01

    This paper is concerned with the effect of nonuniform meshes on the accuracy of finite-difference calculations of fluid flow. In particular, when a simple shock propagates through a nonuniform mesh, one may fail to model the jump conditions across the shock even when the equations are differenced in manifestly conservative fashion. We develop an approximate dispersion analysis of the numerical equations and identify the source of the mesh dependency with the form of the artificial viscosity. We then derive an algebraic correction to the numerical equations - a scaling factor for the pressure gradient - to essentially eliminate the mesh dependency. We present several calculations to illustrate our theory. We conclude with an alternate interpretation of our results. 14 refs., 5 figs.

  14. Multicenter, Prospective, Longitudinal Study of the Recurrence, Surgical Site Infection, and Quality of Life After Contaminated Ventral Hernia Repair Using Biosynthetic Absorbable Mesh: The COBRA Study.

    PubMed

    Rosen, Michael J; Bauer, Joel J; Harmaty, Marco; Carbonell, Alfredo M; Cobb, William S; Matthews, Brent; Goldblatt, Matthew I; Selzer, Don J; Poulose, Benjamin K; Hansson, Bibi M E; Rosman, Camiel; Chao, James J; Jacobsen, Garth R

    2017-01-01

    The aim of the study was to evaluate biosynthetic absorbable mesh in single-staged contaminated (Centers for Disease Control class II and III) ventral hernia (CVH) repair over 24 months. CVH has an increased risk of postoperative infection. CVH repair with synthetic or biologic meshes has reported chronic biomaterial infections and high hernia recurrence rates. Patients with a contaminated or clean-contaminated operative field and a hernia defect at least 9 cm had a biosynthetic mesh (open, sublay, retrorectus, or intraperitoneal) repair with fascial closure (n = 104). Endpoints included overall Kaplan-Meier estimates for hernia recurrence and postoperative wound infection rates at 24 months, and the EQ-5D and Short Form 12 Health Survey (SF-12). Analyses were conducted on the intent-to-treat population, and health outcome measures evaluated using paired t tests. Patients had a mean age of 58 years, body mass index of 28 kg/m, 77% had contaminated wounds, and 84% completed 24-months follow-up. Concomitant procedures included fistula takedown (n = 24) or removal of infected previously placed mesh (n = 29). Hernia recurrence rate was 17% (n = 16). At the time of CVH repair, intraperitoneal placement of the biosynthetic mesh significantly increased the risk of recurrences (P ≤ 0.04). Surgical site infections (19/104) led to higher risk of recurrence (P < 0.01). Mean 24-month EQ-5D (index and visual analogue) and SF-12 physical component and mental scores improved from baseline (P < 0.05). In this prospective longitudinal study, biosynthetic absorbable mesh showed efficacy in terms of long-term recurrence and quality of life for CVH repair patients and offers an alternative to biologic and permanent synthetic meshes in these complex situations.

  15. Multicenter, Prospective, Longitudinal Study of the Recurrence, Surgical Site Infection, and Quality of Life After Contaminated Ventral Hernia Repair Using Biosynthetic Absorbable Mesh

    PubMed Central

    Rosen, Michael J.; Bauer, Joel J.; Harmaty, Marco; Carbonell, Alfredo M.; Cobb, William S.; Matthews, Brent; Goldblatt, Matthew I.; Selzer, Don J.; Poulose, Benjamin K.; Hansson, Bibi M. E.; Rosman, Camiel; Chao, James J.; Jacobsen, Garth R.

    2017-01-01

    Objective: The aim of the study was to evaluate biosynthetic absorbable mesh in single-staged contaminated (Centers for Disease Control class II and III) ventral hernia (CVH) repair over 24 months. Background: CVH has an increased risk of postoperative infection. CVH repair with synthetic or biologic meshes has reported chronic biomaterial infections and high hernia recurrence rates. Methods: Patients with a contaminated or clean-contaminated operative field and a hernia defect at least 9 cm2 had a biosynthetic mesh (open, sublay, retrorectus, or intraperitoneal) repair with fascial closure (n = 104). Endpoints included overall Kaplan-Meier estimates for hernia recurrence and postoperative wound infection rates at 24 months, and the EQ-5D and Short Form 12 Health Survey (SF-12). Analyses were conducted on the intent-to-treat population, and health outcome measures evaluated using paired t tests. Results: Patients had a mean age of 58 years, body mass index of 28 kg/m2, 77% had contaminated wounds, and 84% completed 24-months follow-up. Concomitant procedures included fistula takedown (n = 24) or removal of infected previously placed mesh (n = 29). Hernia recurrence rate was 17% (n = 16). At the time of CVH repair, intraperitoneal placement of the biosynthetic mesh significantly increased the risk of recurrences (P ≤ 0.04). Surgical site infections (19/104) led to higher risk of recurrence (P < 0.01). Mean 24-month EQ-5D (index and visual analogue) and SF-12 physical component and mental scores improved from baseline (P < 0.05). Conclusions: In this prospective longitudinal study, biosynthetic absorbable mesh showed efficacy in terms of long-term recurrence and quality of life for CVH repair patients and offers an alternative to biologic and permanent synthetic meshes in these complex situations. PMID:28009747

  16. Generating quality word sense disambiguation test sets based on MeSH indexing.

    PubMed

    Fan, Jung-Wei; Friedman, Carol

    2009-11-14

    Word sense disambiguation (WSD) determines the correct meaning of a word that has more than one meaning, and is a critical step in biomedical natural language processing, as interpretation of information in text can be correct only if the meanings of their component terms are correctly identified first. Quality evaluation sets are important to WSD because they can be used as representative samples for developing automatic programs and as referees for comparing different WSD programs. To help create quality test sets for WSD, we developed a MeSH-based automatic sense-tagging method that preferentially annotates terms being topical of the text. Preliminary results were promising and revealed important issues to be addressed in biomedical WSD research. We also suggest that, by cross-validating with 2 or 3 annotators, the method should be able to efficiently generate quality WSD test sets. Online supplement is available at: http://www.dbmi.columbia.edu/~juf7002/AMIA09.

  17. 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.

  18. Matrix Algebra.

    DTIC Science & Technology

    1998-06-01

    on courses being taught at NPS. LIST OF REFERENCES [1] Anton , Howard , Elementary Linear Algebra , John Wiley and Sons, New York, New York, 1994...and computational techniques for solving systems of linear equations. The goal is to enhance current matrix algebra textbooks and help the beginning... algebra is the study of algebraic operations on matrices and of their applications, primarily for solving systems of linear equations. Systems of

  19. 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.

  20. Streaming simplification of tetrahedral meshes.

    PubMed

    Vo, Huy T; Callahan, Steven P; Lindstrom, Peter; Pascucci, Valerio; Silva, Cláudio T

    2007-01-01

    Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

  1. Adaptive algebraic reconstruction technique

    SciTech Connect

    Lu Wenkai; Yin Fangfang

    2004-12-01

    Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency.

  2. Mesh Optimization

    DTIC Science & Technology

    1994-01-01

    AD-A277 644 ARAI !: ’ Mesh Optimization Technical Report # 93-01-01 Hughes Hoppe, Tony DeRose, Tom Duchamp , John McDonald and Werner Stuetzle DTIC...SrECT3D I 94 i 31 108 Mesh Optimization Technical Report # 93-01-01 Hughes Hoppe, Tony DeRose, Tom Duchamp , John McDonald and Werner Stuetzle Department...1:1. Januairy 1991. [2] T. DeRose. 11. Hoppe, T. Duchamp . .1. McDonald. and NV. Stuetzle. Fitting of surfaces to scattered data. ,PIE, 1830:212-220

  3. 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.

  4. DRACO-STEM: An Automatic Tool to Generate High-Quality 3D Meshes of Shoot Apical Meristem Tissue at Cell Resolution.

    PubMed

    Cerutti, Guillaume; Ali, Olivier; Godin, Christophe

    2017-01-01

    Context: The shoot apical meristem (SAM), origin of all aerial organs of the plant, is a restricted niche of stem cells whose growth is regulated by a complex network of genetic, hormonal and mechanical interactions. Studying the development of this area at cell level using 3D microscopy time-lapse imaging is a newly emerging key to understand the processes controlling plant morphogenesis. Computational models have been proposed to simulate those mechanisms, however their validation on real-life data is an essential step that requires an adequate representation of the growing tissue to be carried out. Achievements: The tool we introduce is a two-stage computational pipeline that generates a complete 3D triangular mesh of the tissue volume based on a segmented tissue image stack. DRACO (Dual Reconstruction by Adjacency Complex Optimization) is designed to retrieve the underlying 3D topological structure of the tissue and compute its dual geometry, while STEM (SAM Tissue Enhanced Mesh) returns a faithful triangular mesh optimized along several quality criteria (intrinsic quality, tissue reconstruction, visual adequacy). Quantitative evaluation tools measuring the performance of the method along those different dimensions are also provided. The resulting meshes can be used as input and validation for biomechanical simulations. Availability: DRACO-STEM is supplied as a package of the open-source multi-platform plant modeling library OpenAlea (http://openalea.github.io/) implemented in Python, and is freely distributed on GitHub (https://github.com/VirtualPlants/draco-stem) along with guidelines for installation and use.

  5. DRACO-STEM: An Automatic Tool to Generate High-Quality 3D Meshes of Shoot Apical Meristem Tissue at Cell Resolution

    PubMed Central

    Cerutti, Guillaume; Ali, Olivier; Godin, Christophe

    2017-01-01

    Context: The shoot apical meristem (SAM), origin of all aerial organs of the plant, is a restricted niche of stem cells whose growth is regulated by a complex network of genetic, hormonal and mechanical interactions. Studying the development of this area at cell level using 3D microscopy time-lapse imaging is a newly emerging key to understand the processes controlling plant morphogenesis. Computational models have been proposed to simulate those mechanisms, however their validation on real-life data is an essential step that requires an adequate representation of the growing tissue to be carried out. Achievements: The tool we introduce is a two-stage computational pipeline that generates a complete 3D triangular mesh of the tissue volume based on a segmented tissue image stack. DRACO (Dual Reconstruction by Adjacency Complex Optimization) is designed to retrieve the underlying 3D topological structure of the tissue and compute its dual geometry, while STEM (SAM Tissue Enhanced Mesh) returns a faithful triangular mesh optimized along several quality criteria (intrinsic quality, tissue reconstruction, visual adequacy). Quantitative evaluation tools measuring the performance of the method along those different dimensions are also provided. The resulting meshes can be used as input and validation for biomechanical simulations. Availability: DRACO-STEM is supplied as a package of the open-source multi-platform plant modeling library OpenAlea (http://openalea.github.io/) implemented in Python, and is freely distributed on GitHub (https://github.com/VirtualPlants/draco-stem) along with guidelines for installation and use. PMID:28424704

  6. 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.…

  7. 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.…

  8. Algebra Unplugged.

    ERIC Educational Resources Information Center

    Amdahl, Kenn; Loats, Jim

    This book discusses algebra in a non-threatening, fun way. It explains concepts, vocabulary, and strategies of algebra in understandable terms. Chapter titles include: "Numbers with Interesting Properties"; "Important Concepts"; "Fraction Refresher"; "Terms, Factors, and Polynomials"; "Rearranging Expressions"; "Handy Tricks and Magic Words";…

  9. 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.

  10. Color Algebras

    NASA Technical Reports Server (NTRS)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

  11. Steinberg conformal algebras

    NASA Astrophysics Data System (ADS)

    Mikhalev, A. V.; Pinchuk, I. A.

    2005-06-01

    The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.

  12. An evaluation of the quality of orthodontic attachment offered by single- and double-mesh bracket bases using the finite element method of stress analysis.

    PubMed

    Knox, J; Kralj, B; Hubsch, P; Middleton, J; Jones, M L

    2001-04-01

    The objective of this study was to evaluate the influence of bracket base mesh geometry on the stresses generated in the bracket-cement-tooth continuum by a shear/peel load case. A validated three-dimensional finite element model of the bracket-cement-tooth system was constructed consisting of 15,324 nodes and 2971 finite elements. Cement geometric and physical properties were held constant and bracket base geometry was varied, representing a variety of single-mesh configurations and 1 double-mesh design. For the single-mesh designs, increasing wire diameter (100-400 microm) resulted in a decrease in enamel and cement stresses. Increases in wire mesh spacing (200-750 microm) increased the major principal stress recorded in the enamel and adhesive at all wire diameters. Within the bracket, the major principal stress increased significantly at wire spacing above 400-500 microm. However, within the impregnated wire mesh (IWM), the major principal stress decreased as wire space increased. When the double-mesh bracket base was considered, the combined mesh layers resulted in a decrease in the stresses recorded in the most superficial (coarse) mesh layer and an increase in the stresses recorded in the deepest (fine mesh) layer when compared with the single-layer designs in isolation. Modification of single-mesh spacing and wire diameter influences the magnitude and distribution of stresses within the bracket-cement-tooth continuum. The use of a double-mesh design results in a reduction in the stresses recorded in the most superficial mesh. Mesh design influenced stress distribution in this study, primarily by determining the flexibility of the bracket base.

  13. Compact Mesh Generator

    SciTech Connect

    Grover, Benjamin T.; Nissen, III, Walter I.

    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 mesh tags.

  14. 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.

  15. 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.

  16. Web Algebra.

    ERIC Educational Resources Information Center

    Capani, Antonio; De Dominicis, Gabriel

    This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…

  17. A comparison of tetrahedral mesh improvement techniques

    SciTech Connect

    Freitag, L.A.; Ollivier-Gooch, C.

    1996-12-01

    Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face-swapping techniques that change local connectivity and optimization-based mesh smoothing methods that adjust grid point location. The authors consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. The highest quality meshes are obtained by using a combination of swapping and smoothing techniques.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Γ-conformal algebras

    NASA Astrophysics Data System (ADS)

    Golenishcheva-Kutuzova, Maria I.; Kac, Victor G.

    1998-04-01

    Γ-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group Γ. To every Γ-conformal algebra and a character of Γ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac-Moody algebras, the sin algebra (which is a "Γ-conformal" analogue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.

  3. The generation of hexahedral meshes for assembly geometries: A survey

    SciTech Connect

    TAUTGES,TIMOTHY J.

    2000-02-14

    The finite element method is being used today to model component assemblies in a wide variety of application areas, including structural mechanics, fluid simulations, and others. Generating hexahedral meshes for these assemblies usually requires the use of geometry decomposition, with different meshing algorithms applied to different regions. While the primary motivation for this approach remains the lack of an automatic, reliable all-hexahedral meshing algorithm, requirements in mesh quality and mesh configuration for typical analyses are also factors. For these reasons, this approach is also sometimes required when producing other types of unstructured meshes. This paper will review progress to date in automating many parts of the hex meshing process, which has halved the time to produce all-hex meshes for large assemblies. Particular issues which have been exposed due to this progress will also be discussed, along with their applicability to the general unstructured meshing problem.

  4. 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.

  5. 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)

  6. 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.

  7. 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.

  8. 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…

  9. 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…

  10. 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.

  11. Implicit meshes for surface reconstruction.

    PubMed

    Ilic, Slobodan; Fua, Pascal

    2006-02-01

    Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.

  12. 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

  13. 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.

  14. An interface-fitted mesh generator and virtual element methods for elliptic interface problems

    NASA Astrophysics Data System (ADS)

    Chen, Long; Wei, Huayi; Wen, Min

    2017-04-01

    A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface-fitted mesh in two and three dimensions quickly is developed in this paper. Elements in such interface-fitted meshes are not restricted to simplices but can be polygons or polyhedra. Especially in 3D, the polyhedra instead of tetrahedra can avoid slivers. Virtual element methods are applied to solve elliptic interface problems with solutions and flux jump conditions. Algebraic multigrid solvers are used to solve the resulting linear algebraic system. Numerical results are presented to illustrate the effectiveness of our method.

  15. Ternary algebraic approach to extended superconformal algebras

    NASA Astrophysics Data System (ADS)

    Günaydin, Murat; Hyun, Seungjoon

    1992-04-01

    The construction of extended ( N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4

  16. A prospective, multicenter, observational study on quality of life after laparoscopic inguinal hernia repair with ProGrip laparoscopic, self-fixating mesh according to the European Registry for Abdominal Wall Hernias Quality of Life Instrument.

    PubMed

    Muysoms, Filip E; Vanlander, Aude; Ceulemans, Robrecht; Kyle-Leinhase, Iris; Michiels, Maarten; Jacobs, Ivo; Pletinckx, Pieter; Berrevoet, Frederik

    2016-11-01

    There is an increasing interest in patient-reported outcome measurement to evaluate hernia operations. Several hernia-specific quality of life (QoL) scales have been proposed, but none are constructed for preoperative assessment. The European Registry for Abdominal Wall Hernias (EuraHS) proposed the short, 9-question EuraHS-QoL instrument for assessment pre- and postoperatively. The EuraHS-QoL was evaluated in a prospective, multicenter validation study alongside the Visual Analogue Scale, Verbal Rating Scale, and Carolina Comfort Scale (https://clinicaltrials.gov; NCT01936584). We included 101 patients undergoing unilateral laparoscopic inguinal hernia repair with ProGrip laparoscopic, self-fixating mesh. Clinical follow-up at 12 months was 87% complete. The EuraHS-QoL score shows good internal consistency (Cronbach's α ≥ .90), good test-retest reliability (Spearman correlation coefficient r ≥ 0.72), and high correlation for pain with the Visual Analogue Scale, the Verbal Rating Scale, the Carolina Comfort Scale pain scale (r between 0.64 and 0.86), and for restriction of activity with the Carolina Comfort Scale movement scale (r between 0.65 and 0.79). Our results show significant improvement in quality of life at 3 weeks compared with preoperative and further significant improvement at 12 months (P < .05). No late complications or recurrences were recorded. An operation was performed in day surgery (>75%) or with a <24-hour admission (>95%) in the majority of the patients. The EuraHS-QoL instrument is a short and valid patient-reported outcome measurement following groin hernia repair. Laparoscopic inguinal hernia repair with ProGrip laparoscopic, self-fixating mesh results in a favorable outcome and significant improvement of quality of life compared with the preoperative assessment. Copyright © 2016 Elsevier Inc. All rights reserved.

  17. Mesh deformation based on artificial neural networks

    NASA Astrophysics Data System (ADS)

    Stadler, Domen; Kosel, Franc; Čelič, Damjan; Lipej, Andrej

    2011-09-01

    In the article a new mesh deformation algorithm based on artificial neural networks is introduced. This method is a point-to-point method, meaning that it does not use connectivity information for calculation of the mesh deformation. Two already known point-to-point methods, based on interpolation techniques, are also presented. In contrast to the two known interpolation methods, the new method does not require a summation over all boundary nodes for one displacement calculation. The consequence of this fact is a shorter computational time of mesh deformation, which is proven by different deformation tests. The quality of the deformed meshes with all three deformation methods was also compared. Finally, the generated and the deformed three-dimensional meshes were used in the computational fluid dynamics numerical analysis of a Francis water turbine. A comparison of the analysis results was made to prove the applicability of the new method in every day computation.

  18. 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.

  19. Derive Workshop Matrix Algebra and Linear Algebra.

    ERIC Educational Resources Information Center

    Townsley Kulich, Lisa; Victor, Barbara

    This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…

  20. Exploring the basic science of prolapse meshes

    PubMed Central

    Liang, Rui; Knight, Katrina; Abramowitch, Steve; Moalli, Pamela A.

    2016-01-01

    Purpose of review Polypropylene mesh has been widely used in the surgical repair of pelvic organ prolapse. However, low but persistent rates of complications related to mesh, most commonly mesh exposure and pain, have hampered its use. Complications are higher following transvaginal implantation prompting the Food and Drug Administration to release two public health notifications warning of complications associated with transvaginal mesh use (PHN 2008 and 2011) and to upclassify transvaginal prolapse meshes from Class II to Class III devices. Although there have been numerous studies to determine the incidence and management of mesh complications as well as impact on quality of life, few studies have focused on mechanisms. Recent findings In this review, we summarize the current understanding of how mesh textile properties and mechanical behavior impact vaginal structure and function, as well as the local immune response. We also discuss how mesh properties change in response to loading. Summary We highlight a few areas of current and future research to emphasize collaborative strategies that incorporate basic science research to improve patient outcomes. PMID:27517341

  1. Exploring the basic science of prolapse meshes.

    PubMed

    Liang, Rui; Knight, Katrina; Abramowitch, Steve; Moalli, Pamela A

    2016-10-01

    Polypropylene mesh has been widely used in the surgical repair of pelvic organ prolapse. However, low but persistent rates of complications related to mesh, most commonly mesh exposure and pain, have hampered its use. Complications are higher following transvaginal implantation prompting the Food and Drug Administration to release two public health notifications warning of complications associated with transvaginal mesh use (PHN 2008 and 2011) and to upclassify transvaginal prolapse meshes from Class II to Class III devices. Although there have been numerous studies to determine the incidence and management of mesh complications as well as impact on quality of life, few studies have focused on mechanisms. In this review, we summarize the current understanding of how mesh textile properties and mechanical behavior impact vaginal structure and function, as well as the local immune response. We also discuss how mesh properties change in response to loading. We highlight a few areas of current and future research to emphasize collaborative strategies that incorporate basic science research to improve patient outcomes.

  2. [The "ideal" mesh--more than a mosquito net].

    PubMed

    Klinge, U; Klink, C D; Klosterhalfen, B

    2010-04-01

    Modern meshes permit a radical treatment of hernias, an expectation that Billroth articulated already more than 100 years ago. Because clinical trials are insufficient to evaluate the distinct effects of modified mesh materials in regard to tissue biocompatibility and functionality, a basic understanding of the physico-chemical properties is essential for a rational selection of the most appropriate device. Experimental data indicate that particularly the mesh's porosity is of outstanding importance, resulting from the demanded tensile strength as well as the employed fibre material. Considering that different operation techniques require different mesh materials, specific requirements are discussed using the example of intraabdominal meshes, of parastomal meshes, of meshes in areas with bacterial contamination and of meshes in the hiatus region. Considering the late manifestation of some complications even after many years, any thorough quality control should include an assessment of explanted implant failures in addition to clinical experience.

  3. Algebra for Everyone.

    ERIC Educational Resources Information Center

    Edwards, Edgar L., Jr., Ed.

    The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…

  4. On Exceptional Superconformal Algebras

    SciTech Connect

    Poletaeva, Elena

    2010-06-17

    We obtain realizations of superconformal algebras K(2), K'(4) and the exceptional N = 6 superconformal algebra in matrices over a Weyl algebra of size 2x2, 4x4 and 8x8, respectively. A general construction of these realizations is based on the spin representations of the orthogonal Lie algebras. We give explicit descriptions of these matrix realizations.

  5. A peeling mesh.

    PubMed

    Bohmer, R D; Byrne, P D; Maddern, G J

    2002-07-01

    A number of different materials are available for incisional hernia repair. Benefits of the various types are controversial and are partly dependent on the anatomical placement of the mesh. Composite mesh has been introduced to provide tissue ingrowth for strength and a non-adherent side to protect the bowel, these layers being laminated together. This report is on the separation of layers in an infected mesh and adherence of the expanded polytetrafluoroethylene layer to the small bowel.

  6. Automated hexahedral meshing of anatomic structures using deformable registration.

    PubMed

    Grosland, Nicole M; Bafna, Ritesh; Magnotta, Vincent A

    2009-02-01

    This work introduces a novel method of automating the process of patient-specific finite element (FE) model development using a mapped mesh technique. The objective is to map a predefined mesh (template) of high quality directly onto a new bony surface (target) definition, thereby yielding a similar mesh with minimal user interaction. To bring the template mesh into correspondence with the target surface, a deformable registration technique based on the FE method has been adopted. The procedure has been made hierarchical allowing several levels of mesh refinement to be used, thus reducing the time required to achieve a solution. Our initial efforts have focused on the phalanx bones of the human hand. Mesh quality metrics, such as element volume and distortion were evaluated. Furthermore, the distance between the target surface and the final mapped mesh were measured. The results have satisfactorily proven the applicability of the proposed method.

  7. Quality of life and hernia development 5 years after open abdomen treatment with vacuum-assisted wound closure and mesh-mediated fascial traction.

    PubMed

    Petersson, U; Bjarnason, T; Björck, M; Montgomery, A; Rogmark, P; Svensson, M; Sörelius, K; Acosta, S

    2016-10-01

    To report incisional hernia (IH) incidence, abdominal wall (AW) discomfort and quality of life (QoL) 5 years after open abdomen treatment with vacuum-assisted wound closure and mesh-mediated fascial traction (VAWCM). Five-year follow-up of patients included in a prospective study 2006-2009. The protocol included physical examination, patient interview, chart review, questionnaires on abdominal wall and stoma complaints and the SF-36 questionnaire. Fifty-five (12 women, 43 men; median age 70 years) of 111 included patients were alive. Follow-up rate was 91 %. Cumulative IH incidence during the whole study was 62 %. One-third of the IHs was repaired. At 5-year follow-up 59 % of IHs were clinically detectable. AW symptoms were equivalent in patients with (15/23) and without (11/21) IH (p = 0.541). SF-36 scores were lower than population mean for component scores and all subscales except bodily pain. Patients with major co-morbidity had lower physical component score [31.6 (95 %, CI 25.6-37.4)] compared to those without [48.9 (95 %, CI 46.2-51.4)]. Major co-morbidity was not associated with IH (p = 0.56), AW symptoms (p = 0.54) or stoma (p = 0.10). Patients with IH or other AW symptoms had similar SF-36 results compared to those without, whereas patients with a stoma had >5 point lower mean scores for general health, social function and physical component score compared to those without. VAWCM treatment results in high incidence of IH. However, at five years, there was no detectable difference in abdominal wall complaints and QoL in patients with IH compared to those without. Lower QoL appeared mainly to be associated with the presence of major co-morbidity.

  8. A finite-element mesh generator based on growing neural networks.

    PubMed

    Triantafyllidis, D G; Labridis, D P

    2002-01-01

    A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance.

  9. States and synaptic algebras

    NASA Astrophysics Data System (ADS)

    Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

    2017-02-01

    Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a generalization of the partially ordered Jordan algebra of all bounded self-adjoint operators on a Hilbert space. The paper culminates with a characterization of extremal states on a commutative generalized Hermitian algebra, a special kind of synaptic algebra.

  10. Mesh convergence study for hydraulic turbine draft-tube

    NASA Astrophysics Data System (ADS)

    Devals, C.; Vu, T. C.; Zhang, Y.; Dompierre, J.; Guibault, F.

    2016-11-01

    Computational flow analysis is an essential tool for hydraulic turbine designers. Grid generation is the first step in the flow analysis process. Grid quality and solution accuracy are strongly linked. Even though many studies have addressed the issue of mesh independence, there is still no definitive consensus on mesh best practices, and research on that topic is still needed. This paper presents a mesh convergence study for turbulence flow in hydraulic turbine draft- tubes which represents the most challenging turbine component for CFD predictions. The findings from this parametric study will be incorporated as mesh control rules in an in-house automatic mesh generator for turbine components.

  11. Analysis automation with paving: A new quadrilateral meshing technique

    SciTech Connect

    Blacker, T.D. ); Stephenson, M.B.; Canann, S. )

    1990-01-01

    This paper describes the impact of paving, a new automatic mesh generation algorithm, on the analysis portion of the design process. Paving generates an all-quadrilateral mesh in arbitrary 2D geometries. The paving technique significantly impacts the analysis process by drastically reducing the time and expertise requirements of traditional mesh generation. Paving produces a high quality mesh based on geometric boundary definitions and user specified element sizing constraints. In this paper we describe the paving algorithm, discuss varying aspects of the impact of the technique on design automation, and elaborate on current research into 3D all-hexahedral mesh generation. 11 refs., 10 figs.

  12. Parallel adaptive mesh refinement within the PUMAA3D Project

    NASA Technical Reports Server (NTRS)

    Freitag, Lori; Jones, Mark; Plassmann, Paul

    1995-01-01

    To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.

  13. Guaranteed-Quality Triangular Meshes

    DTIC Science & Technology

    1989-04-01

    grant E it-86-17355, ONR grant N0014-86-K-0281, and DA.RPA un ler ONR contract N00014-88-K-0591.. TIM views and cvonc-rIsionn. containe, in this document...point p and let e be the closest edge to p. Since e has length < (43)h, if point p is closer than h/2 to such an edge then it is also closer than h to...to be close to regular tetrahedra, would be of significant interest in Computer Aided Design. Tue. Apr 4. 1989 15 References [BGR88] B. S. Baker, E

  14. Quantum cluster algebras and quantum nilpotent algebras.

    PubMed

    Goodearl, Kenneth R; Yakimov, Milen T

    2014-07-08

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.

  15. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  16. 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

  17. An Adaptive Mesh Algorithm: Mapping the Mesh Variables

    SciTech Connect

    Scannapieco, Anthony J.

    2016-07-25

    Both thermodynamic and kinematic variables must be mapped. The kinematic variables are defined on a separate kinematic mesh; it is the duel mesh to the thermodynamic mesh. The map of the kinematic variables is done by calculating the contributions of kinematic variables on the old thermodynamic mesh, mapping the kinematic variable contributions onto the new thermodynamic mesh and then synthesizing the mapped kinematic variables on the new kinematic mesh. In this document the map of the thermodynamic variables will be described.

  18. Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

    NASA Astrophysics Data System (ADS)

    Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk

    2017-04-01

    We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a-priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.

  19. Deformed Virasoro Algebras from Elliptic Quantum Algebras

    NASA Astrophysics Data System (ADS)

    Avan, J.; Frappat, L.; Ragoucy, E.

    2017-09-01

    We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.

  20. Automatic polygon mesh repair and simplification for three-dimensional human modeling

    NASA Astrophysics Data System (ADS)

    Zhu, Yaolin; Tian, Li; Wan, Taoruan

    2017-07-01

    We present a new approach to repair degenerated and self-intersected mesh of digitized human models, which automatically transforms a raw digitized mesh into a single manifold and closed triangle mesh. The algorithm interactively removes growing neighborhoods of undesired elements and fills resulted surface gaps to yield meshes which subject to user-specified quality criteria. We demonstrate our experimental results by multiple sets of low-quality original models with qualitative measurements compared with a number of existing methods. The results show that the proposed method produces high visual quality meshes with minimal changes of the original mesh appearances.

  1. Array-based Hierarchical Mesh Generation in Parallel

    DOE PAGES

    Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

    2015-11-03

    In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less

  2. Array-based Hierarchical Mesh Generation in Parallel

    SciTech Connect

    Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; Mahadevan, Vijay; Jiao, Xiangmin

    2015-11-03

    In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. In conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.

  3. Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

    PubMed Central

    Bronson, Jonathan; Levine, Joshua A.; Whitaker, Ross

    2014-01-01

    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, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach. PMID:24356365

  4. Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

    DOE PAGES

    Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

    2016-08-18

    In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

  5. Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

    SciTech Connect

    Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; Mahadevan, Vijay; Jiao, Xiangmin

    2016-08-18

    In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.

  6. Optimized testing of meshes

    NASA Technical Reports Server (NTRS)

    Malek, Miroslaw; Ozden, Banu

    1990-01-01

    Efficient testing techniques for two-dimensional mesh interconnection networks are presented. The tests cover faults in the arbitration logic of the switches; this includes an examination of fault detection in the data paths, routing, and control circuitry, including the conflict resolution capabilities of mesh interconnection networks using topological test methods. The proposed methods are not implementation specific and can be applied to any design with a mesh topology. The topology and behavior of the network are described and definitions are presented. The fault model is defined and parallel testing methods for the entire network are given.

  7. Prolene mesh mentoplasty.

    PubMed

    Ilhan, A Emre; Kayabasoglu, Gurkan; Kazikdas, K Cagdas; Goksel, Abdulkadir

    2011-04-01

    Augmentation mentoplasty is a cosmetic surgical procedure to correct chin retrusion or microgenia which usually requires placement of an alloplastic material over the pogonion, and which results in increased chin projection and a more aesthetically balanced facial profile. Polypropylene mesh is easy to purchase, widely available in a general hospital and most commonly used by general surgeons. In this series of 192 patients, we wanted to demonstrate our simple mentoplasty technique using prolene mesh that can easily be combined with a rhinoplasty procedure, with possible causes of infection and the rationale for using prolene mesh in such procedures.

  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…

  9. 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

  10. A meta-analysis comparing lightweight meshes with heavyweight meshes in Lichtenstein inguinal hernia repair.

    PubMed

    Zhong, Chunlin; Wu, Bo; Yang, Zhili; Deng, Xianzhao; Kang, Jie; Guo, Bomin; Fan, Youben

    2013-02-01

    To evaluate the influence of lightweight and heavyweight mesh on postoperative recovery in Lichtenstein inguinal hernia repair. PubMed, EMBASE, and the Cochrane library were used to search for published clinical randomized controlled trials (RCTs), which compared lightweight meshes with heavyweight meshes in Lichtenstein inguinal hernia repair. Two independent reviewers assessed the trials for eligibility and quality, and all the related data matching our standards were abstracted for meta-analysis by RevMan 5.0 software. The evaluation criteria included recurrence, pain, seroma, hematoma, the sensation of a foreign body, wound infection, urine retention, and testicular atrophy. A total of 2231 hernias from 11 RCTs were included. Compared with a heavyweight polypropylene mesh, the lightweight mesh led to less postoperative chronic pain (odds ratio [OR] = 0.64, 95% confidence interval (CI) = 0.51-0.82; P < .05) and less sensation of a foreign body (OR = 0.56; 95% CI = 0.40-0.78; P < .05), regardless of whether the mesh was made of partially absorbable or nonabsorbable material. There was no significant difference in postoperative recurrence, seroma, hematoma, wound infection, urine retention, and testicular atrophy. Current evidence suggests that the use of a lightweight mesh is associated with less postoperative pain and less sensation of a foreign body, without increasing the incidence of recurrence. Further high-quality, long-term follow-up RCTs are needed to provide more reliable evidence.

  11. Urogynecologic Surgical Mesh Implants

    MedlinePlus

    ... urogynecologic repair. Absorbable mesh will degrade and lose strength over time. It is not intended to provide long-term reinforcement to the repair site. As the material degrades, new tissue growth is intended to provide ...

  12. Hernia Surgical Mesh Implants

    MedlinePlus

    ... The surgeon makes several small incisions in the abdomen that allow surgical tools into the openings to repair the hernia. Laparoscopic surgery can be performed with or without surgical mesh. Open Repair - The surgeon makes an incision near the ...

  13. 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…

  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. Writing to Learn Algebra.

    ERIC Educational Resources Information Center

    Miller, L. Diane; England, David A.

    1989-01-01

    Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)

  16. 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…

  17. Arithmetic: Prerequisite to Algebra?

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…

  18. Year 7 Algebra

    ERIC Educational Resources Information Center

    Mitchell, Sarah

    2006-01-01

    Many students find the leap from arithmetic to algebra a difficult one to make, and current literature suggests that a number of the common misconceptions held by students arise as a result of the methods which teachers use to present algebra. The abstract nature of algebra makes it difficult for students to grasp; students also struggle with the…

  19. 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,…

  20. 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.

  1. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  2. Wireless Mesh Networks

    NASA Astrophysics Data System (ADS)

    Ishmael, Johnathan; Race, Nicholas

    Wireless Mesh Networks have emerged as an important technology in building next-generation networks. They are seen to have a range of benefits over traditional wired and wireless networks including low deployment costs, high scalability and resiliency to faults. Moreover, Wireless Mesh Networks (WMNs) are often described as being autonomic with self-* (healing and configuration) properties and their popularity has grown both as a research platform and as a commercially exploitable technology.

  3. 2D Mesh Manipulation

    DTIC Science & Technology

    2011-11-01

    PLATE A two-dimensional flat plate mesh was created using the Gridgen software package (Ref. 13). This mesh (shown in Fig. 10) closely resembled a...desired tolerance of the projection onto the surface. The geometry file on which the geometry surface is based can be easily generated using Gridgen ...by exporting a curve (or number of curves) under the INPUT/OUTPUT commands in the Gridgen interface (Ref. 13). Initially, the floating boundary

  4. Gear mesh stiffness and load sharing in planetary gearing

    NASA Technical Reports Server (NTRS)

    Kasuba, R.; August, R.

    1984-01-01

    An interactive computerized analysis was developed for determining load sharing among planetary gears. The load sharing is established as a function of transmitted torque, degree of sun gear fixity, component flexibility, gear tooth quality, and phasing of individual planet gears. A nonlinear variable gear tooth mesh stiffness model was used to simulate the sun/plant and planet/ring gear meshes. The determined load sharing and gear mesh stiffness parameters then can be used for the subsequent assessment of dynamic load factors.

  5. A comparison of mesh morphing methods for shape optimization.

    SciTech Connect

    Staten, Matthew L.; Owen, Steven James

    2010-08-01

    The ability to automatically morph an existing mesh to conform to geometry modifications is a necessary capability to enable rapid prototyping of design variations. This paper compares six methods for morphing hexahedral and tetrahedral meshes, including the previously published FEMWARP and LBWARP methods as well as four new methods. Element quality and performance results show that different methods are superior on different models. We recommend that designers of applications that use mesh morphing consider both the FEMWARP and a linear simplex based method.

  6. Fiber-mesh photonic molecule

    NASA Astrophysics Data System (ADS)

    Mishra, Subodha; Satpathy, Sashi

    2008-03-01

    Analogous to the photonic crystal, we introduce the concept of a fiber-mesh photonic molecule made up of optical fibers and study its transmission characteristics. We consider a specific example of a photonic molecule, inspired by the well-known C60 molecule, with the arms of the molecule formed out of single-moded optical fibers. The transmittance consists of sharp peaks determined by the pole structure of the scattering matrix in the complex energy plane. A molecule can be designed to control the positions and the widths of the transmission peaks, opening up the possibility of building new photonic devices such as high quality band-pass filters.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. Unstructured and Adaptive Mesh Generation for High Reynolds Number Viscous Flows

    DTIC Science & Technology

    1991-02-01

    smoothness of the mesh. This solution has been computed using a previously described finite-element Navier-Stokes solver in conjunction with an algebraic ...Computational Geometry, An introducion , Texts and Monographs in Computer Science, Springer-Verlag, 1985. 13. Dyn, N., Levin, D., and Rippa, S., "Data Dependent...F. Thompson, !"ineridge Press 1:1., 1988, pp. 05.1-03. - 12 - 16(. Nlavrip! is, D). J., " Algebraic Turbulence Modeling for- UnstrUiciured and

  12. On Derivations Of Genetic Algebras

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh; Qaralleh, Izzat

    2014-11-01

    A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two.

  13. 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.

  14. Algebraic grid generation with corner singularities

    NASA Technical Reports Server (NTRS)

    Vinokur, M.; Lombard, C. K.

    1983-01-01

    A simple noniterative algebraic procedure is presented for generating smooth computational meshes on a quadrilateral topology. Coordinate distribution and normal derivative are provided on all boundaries, one of which may include a slope discontinuity. The boundary conditions are sufficient to guarantee continuity of global meshes formed of joined patches generated by the procedure. The method extends to 3-D. The procedure involves a synthesis of prior techniques stretching functions, cubic blending functions, and transfinite interpolation - to which is added the functional form of the corner solution. The procedure introduces the concept of generalized blending, which is implemented as an automatic scaling of the boundary derivatives for effective interpolation. Some implications of the treatment at boundaries for techniques solving elliptic PDE's are discussed in an Appendix.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. Prediction of Algebraic Instabilities

    NASA Astrophysics Data System (ADS)

    Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael

    2016-11-01

    A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.

  20. 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)

  1. Infinite dimensional matrix algebras

    NASA Astrophysics Data System (ADS)

    Bordemann, M.; Hoppe, J.; Schaller, P.

    1989-11-01

    To each (finite dimensional) Lie algebra g we associate a class L λ(g) of infinite dimensional Lie algebras, induced by representations D λ(g). We show that in the case of sl(2, C) one obtains a series of pairwise non-isomorphic infinite dimensional Lie algebras depending continuously on a complex parameter λ. We connect this method with previous results on the relation between Diff AS 2 and su( N), and comment on a recent conjecture concerning higher spin algebras, and (2 + 1)-dimensional gravity.

  2. 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.

  3. 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.

  4. MeshLab: 3D triangular meshes processing and editing

    NASA Astrophysics Data System (ADS)

    Cignoni, P.; Callieri, M.; Corsini, M.; Dellepiane, M.; Ganovelli, F.; Ranzuglia, G.

    2017-09-01

    MeshLab processes and edits 3D triangular meshes. It includes tools for editing, cleaning, healing, inspecting, rendering, texturing and converting meshes, and offers features for processing raw data produced by 3D digitization tools and devices and for preparing models for 3D printing.

  5. 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.

  6. The Virasoro vertex algebra and factorization algebras on Riemann surfaces

    NASA Astrophysics Data System (ADS)

    Williams, Brian

    2017-08-01

    This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello-Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta-gamma system using the method of effective BV quantization.

  7. Language Approaches to Beginning Algebra.

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    1990-01-01

    Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)

  8. Multigrid Methods for Mesh Relaxation

    SciTech Connect

    O'Brien, M J

    2006-06-12

    When generating a mesh for the initial conditions for a computer simulation, you want the mesh to be as smooth as possible. A common practice is to use equipotential mesh relaxation to smooth out a distorted computational mesh. Typically a Laplace-like equation is set up for the mesh coordinates and then one or more Jacobi iterations are performed to relax the mesh. As the zone count gets really large, the Jacobi iteration becomes less and less effective and we are stuck with our original unrelaxed mesh. This type of iteration can only damp high frequency errors and the smooth errors remain. When the zone count is large, almost everything looks smooth so relaxation cannot solve the problem. In this paper we examine a multigrid technique which effectively smooths out the mesh, independent of the number of zones.

  9. Toward An Unstructured Mesh Database

    NASA Astrophysics Data System (ADS)

    Rezaei Mahdiraji, Alireza; Baumann, Peter Peter

    2014-05-01

    Unstructured meshes are used in several application domains such as earth sciences (e.g., seismology), medicine, oceanography, cli- mate modeling, GIS as approximate representations of physical objects. Meshes subdivide a domain into smaller geometric elements (called cells) which are glued together by incidence relationships. The subdivision of a domain allows computational manipulation of complicated physical structures. For instance, seismologists model earthquakes using elastic wave propagation solvers on hexahedral meshes. The hexahedral con- tains several hundred millions of grid points and millions of hexahedral cells. Each vertex node in the hexahedrals stores a multitude of data fields. To run simulation on such meshes, one needs to iterate over all the cells, iterate over incident cells to a given cell, retrieve coordinates of cells, assign data values to cells, etc. Although meshes are used in many application domains, to the best of our knowledge there is no database vendor that support unstructured mesh features. Currently, the main tool for querying and manipulating unstructured meshes are mesh libraries, e.g., CGAL and GRAL. Mesh li- braries are dedicated libraries which includes mesh algorithms and can be run on mesh representations. The libraries do not scale with dataset size, do not have declarative query language, and need deep C++ knowledge for query implementations. Furthermore, due to high coupling between the implementations and input file structure, the implementations are less reusable and costly to maintain. A dedicated mesh database offers the following advantages: 1) declarative querying, 2) ease of maintenance, 3) hiding mesh storage structure from applications, and 4) transparent query optimization. To design a mesh database, the first challenge is to define a suitable generic data model for unstructured meshes. We proposed ImG-Complexes data model as a generic topological mesh data model which extends incidence graph model to multi

  10. Fast Dynamic Meshing Method Based on Delaunay Graph and Inverse Distance Weighting Interpolation

    NASA Astrophysics Data System (ADS)

    Wang, Yibin; Qin, Ning; Zhao, Ning

    2016-06-01

    A novel mesh deformation technique is developed based on the Delaunay graph mapping method and the inverse distance weighting (IDW) interpolation. The algorithm maintains the advantages of the efficiency of Delaunay-graph-mapping mesh deformation while possess the ability for better controlling the near surface mesh quality. The Delaunay graph is used to divide the mesh domain into a number of sub-domains. On each of the sub-domains, the inverse distance weighting interpolation is applied to build a much smaller sized translation matrix between the original mesh and the deformed mesh, resulting a similar efficiency for the mesh deformation as compared to the fast Delaunay graph mapping method. The paper will show how the near-wall mesh quality is controlled and improved by the new method while the computational time is compared with the original Delaunay graph mapping method.

  11. 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.

  12. Algebraic-hyperbolic grid generation with precise control of intersection of angles

    NASA Astrophysics Data System (ADS)

    Brakhage, Karl-Heinz; Müller, Siegfried

    2000-05-01

    A new approach to construct high quality meshes for flow calculations is investigated in the context of algebraic grid generation, where the angle of intersection between two alternate co-ordinate lines can be specified by the user. From an initial grid, new co-ordinate lines in one parameter direction are determined by solving a set of ordinary differential equations (ODE). These trajectories intersect the alternate co-ordinate lines of the initial grid in a prescribed angle. The resulting grid function is proven to be folding-free. The advantages with respect to grid quality achieved by prescribing the angles are gained at the expense that the boundary distribution can only be prescribed on three of four boundaries. In view of a sparse representation of the grid function, the points of intersection are interpolated by a B-spline surface. Thus, the grid can be accessed evaluating the generated parametric representation of the computational domain. Investigations of several test configurations have shown that useful grids with high resolution can be computed from the B-spline representation only depending on a small number of locally chosen parameters. Therefore, only a small amount of computational memory is required for storing these parameters and evaluating the grid function can be efficiently performed at reduced computational costs. This is particularly promising when the mesh has to be frequently changed or updated in time. Copyright

  13. Bicovariant quantum algebras and quantum Lie algebras

    NASA Astrophysics Data System (ADS)

    Schupp, Peter; Watts, Paul; Zumino, Bruno

    1993-10-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).

  14. Analytic real algebras.

    PubMed

    Seo, Young Joo; Kim, Young Hee

    2016-01-01

    In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d-algebra.

  15. 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…

  16. 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 dissertation,…

  17. 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.

  18. 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…

  19. Learning Activity Package, Algebra.

    ERIC Educational Resources Information Center

    Evans, Diane

    A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

  20. 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.

  1. 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…

  2. 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 dissertation,…

  3. Parastatistics Algebras and Combinatorics

    NASA Astrophysics Data System (ADS)

    Popov, T.

    2005-03-01

    We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.

  4. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  5. Surgical mesh for ventral incisional hernia repairs: Understanding mesh design

    PubMed Central

    Rastegarpour, Ali; Cheung, Michael; Vardhan, Madhurima; Ibrahim, Mohamed M; Butler, Charles E; Levinson, Howard

    2016-01-01

    Surgical mesh has become an indispensable tool in hernia repair to improve outcomes and reduce costs; however, efforts are constantly being undertaken in mesh development to overcome postoperative complications. Common complications include infection, pain, adhesions, mesh extrusion and hernia recurrence. Reducing the complications of mesh implantation is of utmost importance given that hernias occur in hundreds of thousands of patients per year in the United States. In the present review, the authors present the different types of hernia meshes, discuss the key properties of mesh design, and demonstrate how each design element affects performance and complications. The present article will provide a basis for surgeons to understand which mesh to choose for patient care and why, and will explain the important technological aspects that will continue to evolve over the ensuing years. PMID:27054138

  6. 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

  7. Remarks on Effect Algebras

    NASA Astrophysics Data System (ADS)

    Majewski, Władysław A.; Tylec, Tomasz I.

    2010-12-01

    Erik M. Alfsen and Frederic W. Shultz had recently developed the characterisation of state spaces of operator algebras. It established full equivalence (in the mathematical sense) between the Heisenberg and the Schrödinger picture, i.e. given a physical system we are able to construct its state space out of its observables as well as to construct algebra of observables from its state space. As an underlying mathematical structure they used the theory of duality of ordered linear spaces and obtained results are valid for various types of operator algebras (namely C *, von Neumann, JB and JBW algebras). Here, we show that the language they developed also admits a representation of an effect algebra.

  8. 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.

  9. Student and Instructor Perceptions of a Flipped College Algebra Classroom

    ERIC Educational Resources Information Center

    Jaster, Robert W.

    2017-01-01

    Each year about half a million students fail to make planned academic progress due to college algebra, hence the need for researchers to find ways of improving the quality of instruction in the course. Recent research suggests that flipping college algebra to allow time for active learning in the classroom may improve student performance. Also,…

  10. Relational Knowledge and Successful Problem Solving in Algebra

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2004-01-01

    The quality of knowledge underlying students' algebraic thinking is a major concern of K-12 mathematics teaching and reform-driven curriculum documents. In this paper the author examines this issue by characterizing a group of high school students' algebraic knowledge and patterns of use of that knowledge during the solution of selected problems.…

  11. 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.

  12. 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

  13. On Optimal Bilinear Quadrilateral Meshes

    SciTech Connect

    D'Azevedo, E

    2000-03-17

    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 ''superconvergent'' 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 corner or point singularities.

  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. 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.

  16. 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

  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. 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.

  19. A Proposed Algebra Assessment for Use in a Problem-Analysis Framework

    ERIC Educational Resources Information Center

    Walick, Christopher M.; Burns, Matthew K.

    2017-01-01

    Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

  20. Algebraic Nonlinear Collective Motion

    NASA Astrophysics Data System (ADS)

    Troupe, J.; Rosensteel, G.

    1998-11-01

    Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).

  1. Algebraic invariants for homotopy types

    NASA Astrophysics Data System (ADS)

    Blanc, David

    1999-11-01

    We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.

  2. 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,…

  3. 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.

  4. 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.

  5. The lightweight and large porous mesh concept for hernia repair.

    PubMed

    Klosterhalfen, Bernd; Junge, Karsten; Klinge, Uwe

    2005-01-01

    In modern hernia surgery, there are two competing mesh concepts which often lead to controversial discussions, on the one hand the heavyweight small porous model and on the other, the lightweight large porous hypothesis. The present review illustrates the rationale of both mesh concepts and compares experimental data with the first clinical data available. In summary, the lightweight large porous mesh philosophy takes into consideration all of the recent data regarding physiology and mechanics of the abdominal wall and inguinal region. Furthermore, the new mesh concept reveals an optimized foreign body reaction based on reduced amounts of mesh material and, in particular, a significantly decreased surface area in contact with the recipient host tissues by the large porous model. Finally, recent data demonstrate that alterations in the extracellular matrix of hernia patients play a crucial role in the development of hernia recurrence. In particular, long-term recurrences months or years after surgery and implantation of mesh can be explained by the extracellular matrix hypothesis. However, if the altered extracellular matrix proves to be the weak area, the decisive question is whether the amount of material as well as mechanical and tensile strength of the surgical mesh are really of significant importance for the development of recurrent hernia. All experimental evidence and first clinical data indicate the superiority of the lightweight large porous mesh concept with regard to a reduced number of long-term complications and particularly, increased comfort and quality of life after hernia repair.

  6. Pseudo-Riemannian Novikov algebras

    NASA Astrophysics Data System (ADS)

    Chen, Zhiqi; Zhu, Fuhai

    2008-08-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

  7. 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.

  8. 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)

  9. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  10. Jordan Algebraic Quantum Categories

    NASA Astrophysics Data System (ADS)

    Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander

    2015-03-01

    State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.

  11. An Abstract Algebra Story.

    ERIC Educational Resources Information Center

    Leron, Uri; Dubinsky, Ed

    1995-01-01

    Describes a constructivist, interactive approach for teaching undergraduate mathematics, abstract algebra in particular, using computer constructions programmed in ISETL to induce students' mental constructions and collaborative learning to help students reflect on these constructions. (18 references) (MKR)

  12. Accounting Equals Applied Algebra.

    ERIC Educational Resources Information Center

    Roberts, Sondra

    1997-01-01

    Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)

  13. Weyl n-Algebras

    NASA Astrophysics Data System (ADS)

    Markarian, Nikita

    2017-03-01

    We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.

  14. 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.

  15. 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.

  16. Aprepro - Algebraic Preprocessor

    SciTech Connect

    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.

  17. 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.

  18. Aprepro - Algebraic Preprocessor

    SciTech Connect

    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.

  19. Constrained CVT Meshes and a Comparison of Triangular Mesh Generators

    SciTech Connect

    Nguyen, Hoa; Burkardt, John; Gunzburger, Max; Ju, Lili; Saka, Yuki

    2009-01-01

    Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. We focus on the uniform Delaunay triangulation of planar regions and, in particular, on how one selects the positions of the vertices of the triangulation. We discuss a recently developed method, based on the centroidal Voronoi tessellation (CVT) concept, for effecting such triangulations and present two algorithms, including one new one, for CVT-based grid generation. We also compare several methods, including CVT-based methods, for triangulating planar domains. To this end, we define several quantitative measures of the quality of uniform grids. We then generate triangulations of several planar regions, including some having complexities that are representative of what one may encounter in practice. We subject the resulting grids to visual and quantitative comparisons and conclude that all the methods considered produce high-quality uniform grids and that the CVT-based grids are at least as good as any of the others.

  20. Global Geometric Deformations of the Virasoro Algebra, Current and Affine Algebras by Krichever Novikov Type Algebras

    NASA Astrophysics Data System (ADS)

    Fialowski, A.; Schlichenmaier, M.

    2007-11-01

    In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever Novikov type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra, the Virasoro algebra, the classical current, and the affine Kac Moody Lie algebras respectively. The constructed families are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid. This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The algebras are of relevance in the global operator approach to the Wess Zumino Witten Novikov models appearing in the quantization of Conformal Field Theory.

  1. An Adaptive Mesh Algorithm: Mesh Structure and Generation

    SciTech Connect

    Scannapieco, Anthony J.

    2016-06-21

    The purpose of Adaptive Mesh Refinement is to minimize spatial errors over the computational space not to minimize the number of computational elements. The additional result of the technique is that it may reduce the number of computational elements needed to retain a given level of spatial accuracy. Adaptive mesh refinement is a computational technique used to dynamically select, over a region of space, a set of computational elements designed to minimize spatial error in the computational model of a physical process. The fundamental idea is to increase the mesh resolution in regions where the physical variables are represented by a broad spectrum of modes in k-space, hence increasing the effective global spectral coverage of those physical variables. In addition, the selection of the spatially distributed elements is done dynamically by cyclically adjusting the mesh to follow the spectral evolution of the system. Over the years three types of AMR schemes have evolved; block, patch and locally refined AMR. In block and patch AMR logical blocks of various grid sizes are overlaid to span the physical space of interest, whereas in locally refined AMR no logical blocks are employed but locally nested mesh levels are used to span the physical space. The distinction between block and patch AMR is that in block AMR the original blocks refine and coarsen entirely in time, whereas in patch AMR the patches change location and zone size with time. The type of AMR described herein is a locally refi ned AMR. In the algorithm described, at any point in physical space only one zone exists at whatever level of mesh that is appropriate for that physical location. The dynamic creation of a locally refi ned computational mesh is made practical by a judicious selection of mesh rules. With these rules the mesh is evolved via a mesh potential designed to concentrate the nest mesh in regions where the physics is modally dense, and coarsen zones in regions where the physics is modally

  2. 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.

  3. 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.

  4. Host response to synthetic mesh in women with mesh complications

    PubMed Central

    Nolfi, Alexis L.; Brown, Bryan N.; Liang, Rui; Palcsey, Stacy L.; Bonidie, Michael J.; Abramowitch, Steven D.; Moalli, Pamela A.

    2016-01-01

    BACKGROUND Despite good anatomic and functional outcomes, urogynecologic polypropylene meshes that are used to treat pelvic organ prolapse and stress urinary incontinence are associated with significant complications, most commonly mesh exposure and pain. Few studies have been performed that specifically focus on the host response to urogynecologic meshes. The macrophage has long been known to be the key cell type that mediates the foreign body response. Conceptually, macrophages that respond to a foreign body can be dichotomized broadly into M1 proinflammatory and M2 proremodeling subtypes. A prolonged M1 response is thought to result in chronic inflammation and the formation of foreign body giant cells with potential for ongoing tissue damage and destruction. Although a limited M2 predominant response is favorable for tissue integration and ingrowth, excessive M2 activity can lead to accelerated fibrillar matrix deposition and result in fibrosis and encapsulation of the mesh. OBJECTIVE The purpose of this study was to define and compare the macrophage response in patients who undergo mesh excision surgery for the indication of pain vs a mesh exposure. STUDY DESIGN Patients who were scheduled to undergo a surgical excision of mesh for pain or exposure at Magee-Womens Hospital were offered enrollment. Twenty-seven mesh-vagina complexes that were removed for the primary complaint of a mesh exposure (n = 15) vs pain in the absence of an exposure (n = 12) were compared with 30 full-thickness vaginal biopsy specimens from women who underwent benign gynecologic surgery without mesh. Macrophage M1 proinflammatory vs M2 proremodeling phenotypes were examined via immunofluorescent labeling for cell surface markers CD86 (M1) vs CD206 (M2) and M1 vs M2 cytokines via enzyme-linked immunosorbent assay. The amount of matrix metalloproteinase-2 (MMP-2) and matrix metalloproteinase-9 (MMP-9) proteolytic enzymes were quantified by zymography and substrate degradation assays, as an

  5. Prevention of Adhesion to Prosthetic Mesh

    PubMed Central

    van ’t Riet, Martijne; de Vos van Steenwijk, Peggy J.; Bonthuis, Fred; Marquet, Richard L.; Steyerberg, Ewout W.; Jeekel, Johannes; Bonjer, H. Jaap

    2003-01-01

    Objective To assess whether use of antiadhesive liquids or coatings could prevent adhesion formation to prosthetic mesh. Summary Background Data Incisional hernia repair frequently involves the use of prosthetic mesh. However, concern exists about development of adhesions between viscera and the mesh, predisposing to intestinal obstruction or enterocutaneous fistulas. Methods In 91 rats, a defect in the muscular abdominal wall was created, and mesh was fixed intraperitoneally to cover the defect. Rats were divided in five groups: polypropylene mesh only (control group), addition of Sepracoat or Icodextrin solution to polypropylene mesh, Sepramesh (polypropylene mesh with Seprafilm coating), and Parietex composite mesh (polyester mesh with collagen coating). Seven and 30 days postoperatively, adhesions were assessed and wound healing was studied by microscopy. Results Intraperitoneal placement of polypropylene mesh was followed by bowel adhesions to the mesh in 50% of the cases. A mean of 74% of the mesh surface was covered by adhesions after 7 days, and 48% after 30 days. Administration of Sepracoat or Icodextrin solution had no influence on adhesion formation. Coated meshes (Sepramesh and Parietex composite mesh) had no bowel adhesions. Sepramesh was associated with a significant reduction of the mesh surface covered by adhesions after 7 and 30 days. Infection was more prevalent with Parietex composite mesh, with concurrent increased mesh surface covered by adhesions after 30 days (78%). Conclusions Sepramesh significantly reduced mesh surface covered by adhesions and prevented bowel adhesion to the mesh. Parietex composite mesh prevented bowel adhesions as well but increased infection rates in the current model. PMID:12496539

  6. 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

  7. 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

  8. Invisible metallic mesh.

    PubMed

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

    2016-03-08

    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.

  9. 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.

  10. Quadrilateral finite element mesh coarsening

    SciTech Connect

    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.

  11. 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.

  12. 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.

  13. 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

  14. Composite structured mesh generation with automatic domain decomposition in complex geometries

    USDA-ARS?s Scientific Manuscript database

    This paper presents a novel automatic domain decomposition method to generate quality composite structured meshes in complex domains with arbitrary shapes, in which quality structured mesh generation still remains a challenge. The proposed decomposition algorithm is based on the analysis of an initi...

  15. Analysis of adhesion formation of a new elastic thermoplastic polyurethane (TPU) mesh in comparison to polypropylene (PP) meshes in IPOM position.

    PubMed

    Lambertz, A; van den Hil, L C L; Schöb, D S; Binnebösel, M; Kroh, A; Klinge, U; Neumann, U P; Klink, C D

    2016-01-01

    Postsurgical adhesions severely affect the patients' quality of life causing various complications like bowel obstruction or chronic pain. Especially the implantation of alloplastic prostheses in IPOM position for hernia repair carries a high risk of adhesion formation due to the close contact between mesh and viscera. The extent of adhesions mainly depends on the type and textile characteristics of the implanted mesh. The aim of this study was to examine the degree of adhesion formation of a newly developed, elastic thermoplastic polyurethane (TPU) mesh in comparison to polypropylene (PP) meshes in IPOM position in a rabbit model. Sixteen female chinchilla rabbits were laparoscopically operated. Two different meshes were placed to the left and the right lower abdominal wall in IPOM position in each rabbit. After 7 or 21 days, midline laparotomy was performed, the degree of adhesion formation was examined by the Diamond score and mesh elongation was measured under a force of 3N. Finally, the abdominal walls were explanted for immunohistochemical and histopathological investigations. TPU meshes showed significantly lower Diamond scores than PP meshes. After explantation, mesh elongation of the TPU mesh was significantly larger than expansion of PP under a force of 3N. Thus, the TPU mesh preserved its elastic properties after 7 and 21 days. The amount of CD68 positive, Ki67 positive and apoptotic cells within the granuloma around the fibers did not show significant differences between the study groups. The newly developed TPU mesh seems to reduce peritoneal adhesion formation in IPOM position in a rabbit model compared to PP meshes after 7 and 21 days. Immunohistochemistry did not reveal differences in biocompatibility of the two meshes used. Copyright © 2015 Elsevier Ltd. All rights reserved.

  16. 50 CFR 300.110 - Mesh size.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... material and capable of retaining their shape. They may have either a series of parallel-edged sides... the resistance of the mesh. (3) Selection of meshes to be measured. (i) Meshes to be measured will...

  17. 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…

  18. 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…

  19. 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.

  20. Resonant algebras and gravity

    NASA Astrophysics Data System (ADS)

    Durka, R.

    2017-04-01

    The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.

  1. Quantum algebra of superspace

    SciTech Connect

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

    2006-02-15

    We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.

  2. On weak Lie 2-algebras

    NASA Astrophysics Data System (ADS)

    Roytenberg, Dmitry

    2007-11-01

    A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.

  3. A Holistic Approach to Algebra.

    ERIC Educational Resources Information Center

    Barbeau, Edward J.

    1991-01-01

    Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

  4. 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.

  5. 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.

  6. 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)

  7. Algebra of Neuron Matrices,

    DTIC Science & Technology

    1985-03-13

    AD-Ri55 296 ALGEBRA OF NEURON MATRICES(U) FOREIGN TECHNOLOGY DIV i/i WRIGHT-PATTERSON RF8 ON K~ G RGRBRBYRN 13 MAR 85 FTD-ID(RS)T-8@4i-85...ANCLASSIFIED F/G6/6 NL I. 1j.2 U .611111 ’’ K1*10 Vl( PIH OPY Pl (iLUTION TL T CHART I-" FTD-ID(RS )T-0041-85 FOREIGN TECHNOLOGY DIVISION In ALGEBRA OF NEURON ... NEURON MATRICES DTIC TAB Unannounced Q By: K.G. Agababyan JustLficatlon English pages: 10 By Distribution/ Source: Doklady Akademii Nauk SSSR, Vol. 199

  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. Report on FY11 Extensions to MeshKit and RGG

    SciTech Connect

    Jain, Rajeev

    2014-01-01

    One of the barriers to performing high-fidelity computational simulation of reactor core phenomena is the production of good-quality geometry and mesh models required by these simulations. Although a variety of geometry and meshing tools are available, they suffer from shortcomings in usability, robustness, or generality which makes them difficult to apply to reactor applications. The SHARP frameworks project is addressing these deficiencies by developing a library of mesh generation algorithms, and tools based on that library. The library is known as MeshKit, and one of the tools being developed is named RGG, for Reactor Geometry (and mesh) Generator. Over the past year, our meshing-related work was split between general design improvements in MeshKit, enhancing RGG to run in parallel, and the application of RGG to several specific reactor designs. These activities are described in this report.

  10. 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....

  11. 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....

  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, 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. ...

  14. 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. ...

  15. Are patient specific meshes required for EIT head imaging?

    PubMed

    Jehl, Markus; Aristovich, Kirill; Faulkner, Mayo; Holder, David

    2016-06-01

    Head imaging with electrical impedance tomography (EIT) is usually done with time-differential measurements, to reduce time-invariant modelling errors. Previous research suggested that more accurate head models improved image quality, but no thorough analysis has been done on the required accuracy. We propose a novel pipeline for creation of precise head meshes from magnetic resonance imaging and computed tomography scans, which was applied to four different heads. Voltages were simulated on all four heads for perturbations of different magnitude, haemorrhage and ischaemia, in five different positions and for three levels of instrumentation noise. Statistical analysis showed that reconstructions on the correct mesh were on average 25% better than on the other meshes. However, the stroke detection rates were not improved. We conclude that a generic head mesh is sufficient for monitoring patients for secondary strokes following head trauma.

  16. 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.

  17. An algebra of reversible computation.

    PubMed

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  18. On Weak-BCC-Algebras

    PubMed Central

    Thomys, Janus; Zhang, Xiaohong

    2013-01-01

    We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

  19. Visual Salience of Algebraic Transformations

    ERIC Educational Resources Information Center

    Kirshner, David; Awtry, Thomas

    2004-01-01

    Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

  20. 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.

  1. Parallel adaptive mesh-refining scheme on a three-dimensional unstructured tetrahedral mesh and its applications

    NASA Astrophysics Data System (ADS)

    Lian, Y.-Y.; Hsu, K.-H.; Shao, Y.-L.; Lee, Y.-M.; Jeng, Y.-W.; Wu, J.-S.

    2006-12-01

    The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N for N⩽32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson-Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.

  2. A Cost-Utility Assessment of Mesh Selection in Clean-Contaminated Ventral Hernia Repair.

    PubMed

    Fischer, John P; Basta, Marten N; Krishnan, Naveen M; Wink, Jason D; Kovach, Stephen J

    2016-02-01

    Mesh reinforcement can reduce hernia recurrence, but mesh selection is poorly understood, particularly in contaminated defects. Acellular dermal matrix has enabled single-stage ventral hernia repair in clean-contaminated wounds but can be associated with higher complications and cost compared with synthetic mesh. This study evaluated the cost-utility of synthetic mesh and acellular dermal matrix for clean-contaminated ventral hernia repairs. A systematic review of articles comparing outcomes for synthetic and acellular dermal matrix repairs identified 14 ventral hernia repair-specific health states. Quality-adjusted life years were determined through Web-based visual analog scale survey of 300 nationally representative individuals. Overall expected cost and quality-adjusted life-years for ventral hernia repair were assessed using a Monte Carlo simulation with sensitivity analyses. Synthetic mesh reinforcement had an expected cost of $15,776 and quality-adjusted life-year value gained of 21.03. Biological mesh had an expected cost of $23,844 and quality-adjusted life-year value gained of 20.94. When referencing a common baseline (do nothing), acellular dermal matrix (incremental cost-effectiveness ratio, 3378 ($/quality-adjusted life years)) and synthetic mesh (incremental cost-effectiveness ratio, 2208 ($/quality-adjusted life years)) were judged cost-effective, although synthetic mesh was more strongly favored. Monte Carlo sensitivity analysis demonstrated that synthetic mesh was the preferred and most cost-effective strategy in 94 percent of simulations, supporting its overall greater cost-utility. Despite varying the willingness-to-pay threshold from $0 to $100,000 per quality-adjusted life-year, synthetic mesh remained the optimal strategy across all thresholds in sensitivity analysis. This cost-utility analysis suggests that synthetic mesh repair of clean-contaminated hernia defects is more cost-effective than acellular dermal matrix.

  3. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  4. Algebraic Thinking through Origami.

    ERIC Educational Resources Information Center

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  5. Pre-Algebra.

    ERIC Educational Resources Information Center

    Kennedy, John

    This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

  6. 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,…

  7. Algebraic Thinking through Origami.

    ERIC Educational Resources Information Center

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  8. 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…

  9. 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…

  10. 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…

  11. 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…

  12. 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

  13. 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.

  14. Mersiline mesh in premaxillary augmentation.

    PubMed

    Foda, Hossam M T

    2005-01-01

    Premaxillary retrusion may distort the aesthetic appearance of the columella, lip, and nasal tip. This defect is characteristically seen in, but not limited to, patients with cleft lip nasal deformity. This study investigated 60 patients presenting with premaxillary deficiencies in which Mersiline mesh was used to augment the premaxilla. All the cases had surgery using the external rhinoplasty technique. Two methods of augmentation with Mersiline mesh were used: the Mersiline roll technique, for the cases with central symmetric deficiencies, and the Mersiline packing technique, for the cases with asymmetric deficiencies. Premaxillary augmentation with Mersiline mesh proved to be simple technically, easy to perform, and not associated with any complications. Periodic follow-up evaluation for a mean period of 32 months (range, 12-98 months) showed that an adequate degree of premaxillary augmentation was maintained with no clinically detectable resorption of the mesh implant.

  15. Mesh Convergence Requirements for Composite Damage Models

    NASA Technical Reports Server (NTRS)

    Davila, Carlos G.

    2016-01-01

    The ability of the finite element method to accurately represent the response of objects with intricate geometry and loading renders the finite element method as an extremely versatile analysis technique for structural analysis. Finite element analysis is routinely used in industry to calculate deflections, stress concentrations, natural frequencies, buckling loads, and much more. The method works by discretizing complex problems into smaller, simpler approximations that are valid over small uniform domains. For common analyses, the maximum size of the elements that can be used is often be determined by experience. However, to verify the quality of a solution, analyses with several levels of mesh refinement should be performed to ensure that the solution has converged. In recent years, the finite element method has been used to calculate the resistance of structures, and in particular that of composite structures. A number of techniques such as cohesive zone modeling, the virtual crack closure technique, and continuum damage modeling have emerged that can be used to predict cracking, delaminations, fiber failure, and other composite damage modes that lead to structural collapse. However, damage models present mesh refinement requirements that are not well understood. In this presentation, we examine different mesh refinement issues related to the representation of damage in composite materials. Damage process zone sizes and their corresponding mesh requirements will be discussed. The difficulties of modeling discontinuities and the associated need for regularization techniques will be illustrated, and some unexpected element size constraints will be presented. Finally, some of the difficulties in constructing models of composite structures capable of predicting transverse matrix cracking will be discussed. It will be shown that to predict the initiation and propagation of transverse matrix cracks, their density, and their saturation may require models that are

  16. Planar Para Algebras, Reflection Positivity

    NASA Astrophysics Data System (ADS)

    Jaffe, Arthur; Liu, Zhengwei

    2017-05-01

    We define a planar para algebra, which arises naturally from combining planar algebras with the idea of ZN para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects that are invariant under para isotopy. For each ZN, we construct a family of subfactor planar para algebras that play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras, which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), which we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity by relating the two reflections through the string Fourier transform.

  17. Unstructured mesh methods for CFD

    NASA Technical Reports Server (NTRS)

    Peraire, J.; Morgan, K.; Peiro, J.

    1990-01-01

    Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.

  18. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  19. On extensions of Leibniz algebras

    NASA Astrophysics Data System (ADS)

    Rakhimov, I. S.; Said Husain, Sh. K.; Mohammed, M. A.

    2017-09-01

    This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it to classify four-dimensional Leibniz algebras over a field K. We obtain complete classification of four-dimensional nilpotent Leibniz algebras. The main idea of the method is to transfer the “base change” action to an action of automorphism group of the algebras of smaller dimension on cocycles constructed by the annihilator extensions. The method can be used to classify low-dimensional Leibniz algebras over other finite fields as well.

  20. 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.

  1. 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.

  2. 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.

  3. An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh

    DTIC Science & Technology

    2011-01-01

    1980; Ferziger and Peric, 1995; Wu, 2007), etc. The algebraic equations resulting from the classic, structured FDM and FVM usually have banded...computational fluid dynamics (CFD) (Muzaferija, 1994; Ferziger and Peric, 1995; Greaves, 2004; Liang et al., 2008; Nabi, 2008). On the quadtree mesh...Proceedings 17th Coastal Engineering Conference, ASCE, 2,726–2,744. Ferziger , J.H. and Peric, M., 1995. Computational Methods for Fluid Dynamics. Springer

  4. 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.

  5. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  6. 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.

  7. Coarse mesh transport theory model for heterogeneous systems

    NASA Astrophysics Data System (ADS)

    Ilas, Danut

    To improve fuel utilization, recent reactor cores have become substantially more heterogeneous. In these cores, use of variable fuel enrichments and strong absorbers lead to high neutron flux gradients, which may limit the accuracy (validity) of diffusion theory based methods. In fact, the diffusion equation itself may become a poor approximation of the Boltzmann equation, the exact equation that describes the neutron flux. Therefore, numerical methods to solve the transport equation efficiently over a large heterogeneous region (such as a reactor core) are very desirable in case where the diffusion approximation breaks down. Presently, the only methods capable of computing the power (flux) distributions very accurately throughout a large system such as a nuclear reactor core are the Monte-Carlo or the fine-mesh transport theory methods. Both these methods suffer from the long computational time which makes them useless for routine core calculations. Starting from a variational principle that admits trial functions that can be discontinuous at coarse mesh (assembly) interfaces, we propose a method to solve the transport equation on a spatial grid made up of meshes as large as the size of a fuel assembly. The variational principle is derived for the most general case, but further methods are developed for one-dimensional geometry with the angular variable treated by discrete ordinates. The method uses the finite element approach for the space variable with basis functions precomputed for each element to obtain an algebraic linear system of equations. The eigenvalue of this system is the multiplication constant and the eigenvector represents the incoming angular fluxes for each coarse mesh. The latter allows the reconstruction of the fine mesh solution (angular flux) throughout the domain of interest when used with the basis functions (surface Green's function) for each coarse mesh. The method requires no homogenization procedure that can be a serious source of

  8. 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

  9. 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®,…

  10. 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®,…

  11. 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.

  12. 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.

  13. The tensor hierarchy algebra

    SciTech Connect

    Palmkvist, Jakob

    2014-01-15

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  14. 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.

  15. 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).

  16. 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

  17. Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation ☆

    PubMed Central

    Gao, Zhanheng; Yu, Zeyun; Holst, Michael

    2012-01-01

    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. PMID:23580890

  18. Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

    NASA Astrophysics Data System (ADS)

    Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.

    2016-10-01

    We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.

  19. 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…

  20. 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.

  1. 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.

  2. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  3. 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…

  4. 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.

  5. Applications of algebraic grid generation

    NASA Technical Reports Server (NTRS)

    Eiseman, Peter R.; Smith, Robert E.

    1990-01-01

    Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.

  6. Almost isometric mesh parameterization through abstract domains.

    PubMed

    Pietroni, Nico; Tarini, Marco; Cignoni, Paolo

    2010-01-01

    In this paper, we propose a robust, automatic technique to build a global hi-quality parameterization of a two-manifold triangular mesh. An adaptively chosen 2D domain of the parameterization is built as part of the process. The produced parameterization exhibits very low isometric distortion, because it is globally optimized to preserve both areas and angles. The domain is a collection of equilateral triangular 2D regions enriched with explicit adjacency relationships (it is abstract in the sense that no 3D embedding is necessary). It is tailored to minimize isometric distortion, resulting in excellent parameterization qualities, even when meshes with complex shape and topology are mapped into domains composed of a small number of large continuous regions. Moreover, this domain is, in turn, remapped into a collection of 2D square regions, unlocking many advantages found in quad-based domains (e.g., ease of packing). The technique is tested on a variety of cases, including challenging ones, and compares very favorably with known approaches. An open-source implementation is made available.

  7. Higher level twisted Zhu algebras

    NASA Astrophysics Data System (ADS)

    van Ekeren, Jethro

    2011-05-01

    The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by Γ /{Z} for some subgroup Γ of {R} containing {Z}, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras operatorname{Zhu}_{p, Γ }(V), and we prove the following theorems: For each p, there is a bijection between the irreducible operatorname{Zhu}_{p, Γ }(V)-modules and the irreducible Γ-twisted positive energy V-modules, and V is (Γ, H)-rational if and only if all its Zhu algebras operatorname{Zhu}_{p, Γ }(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra operatorname{Vir}^c and the universal affine Kac-Moody vertex algebra V^k({g}) at non-critical level. We also compute the inverse limits of these directed systems of algebras.

  8. Epetra Linear Algebra Services Package

    SciTech Connect

    2011-09-09

    Epetra provides the fundamental construction routines and service functions that are required for serial and paraliellinear algebra libraries using double precision scalar values and int ordinal values.

  9. An electrostatic Particle-In-Cell code on multi-block structured meshes

    DOE PAGES

    Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca; ...

    2017-09-14

    We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. In spite of the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where anmore » arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma–material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. And compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.« less

  10. Omental Lipid-Coated Mesh

    DTIC Science & Technology

    2011-06-16

    infection. If benefit is proven, this method will be a cost- effective way to prepare biologic and possibly synthetic meshes for use in hernia repair...omental coating is encouraging. 10. ::’UD./CI.I I CI’IIVI::’ Omentum, Mesh , Hernia 𔃺. ::.CI.Utill , I.LA::’::’II"II.A IIUN UI": I-­ a -.-I’I-c­...-u...abdominal wall hernia repair. If cheap and effective promotion of neovascularization could be initiated, we might be able to improve upon current

  11. Imaging of slings and meshes

    PubMed Central

    Dietz, Hans Peter

    2015-01-01

    Abstract The popularity of imaging in pelvic floor medicine continues to increase. Among the various modalities, ultrasound is superior as it is cheap, safe, easily accesible and simple, resulting in high patient compliance. It is the only technique that allows imaging of modern wide‐weave polypropylene sling or mesh implants, and imaging of such implants is commonly required due to the popularity of surgical techniques that involve the placement of slings and meshes. This review article will discuss the role of translabial ultrasound in the evaluation of synthetic implants used in the treatment of urinary incontinence and pelvic organ prolapse. PMID:28191210

  12. 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.

  13. 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.

  14. 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

  15. Multiscale mesh generation on the sphere

    NASA Astrophysics Data System (ADS)

    Lambrechts, Jonathan; Comblen, Richard; Legat, Vincent; Geuzaine, Christophe; Remacle, Jean-François

    2008-12-01

    A method for generating computational meshes for applications in ocean modeling is presented. The method uses a standard engineering approach for describing the geometry of the domain that requires meshing. The underlying sphere is parametrized using stereographic coordinates. Then, coastlines are described with cubic splines drawn in the stereographic parametric space. The mesh generation algorithm builds the mesh in the parametric plane using available techniques. The method enables to import coastlines from different data sets and, consequently, to build meshes of domains with highly variable length scales. The results include meshes together with numerical simulations of various kinds.

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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.

  1. Adaptive Algebraic Smoothers

    SciTech Connect

    Philip, Bobby; Chartier, Dr Timothy

    2012-01-01

    methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

  2. 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

  3. 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.

  4. 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

  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. Semi-automatic surface and volume mesh generation for subject-specific biomedical geometries.

    PubMed

    Sazonov, Igor; Nithiarasu, Perumal

    2012-01-01

    An overview of surface and volume mesh generation techniques for creating valid meshes to carry out biomedical flows is provided. The methods presented are designed for robust numerical modelling of biofluid flow through subject-specific geometries. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. The methods described are designed to minimize distortion to a given domain boundary. They are also designed to generate a triangular surface mesh first and then volume mesh (tetrahedrons) with high quality surface and volume elements. For blood flow applications, a simple procedure to generate a boundary layer mesh is also described. The methods described here are semi-automatic in nature because of the fact that the geometries are complex, and automation of the procedures may be possible if high quality scans are used.

  8. 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.

  9. Design of a wire-mesh collimator for gamma cameras.

    PubMed

    Saripan, M Iqbal; Petrou, Maria; Wells, Kevin

    2007-09-01

    This paper presents a model of a wire-mesh collimator for a gamma camera that produces images of comparable quality as those produced with the conventional multihole collimator, but has about half the weight of the multihole collimator. The gamma camera and the collimator are simulated using the MCNPX code. Two final configurations of the wire-mesh collimator are proposed, and their performance is compared with other wire-mesh collimators and with the multihole collimator, using a point source, a planar square source, and two point sources, all in water. In all cases, photons with energy 140 keV are simulated. In addition, we use the simulation of a realistic phantom of a hot tumor in a warm background to assess the performance of our collimator in conjunction with an extended source.

  10. 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…

  11. Viterbi/algebraic hybrid decoder

    NASA Technical Reports Server (NTRS)

    Boyd, R. W.; Ingels, F. M.; Mo, C.

    1980-01-01

    Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.

  12. Teaching Algebra Conceptually: Student Achievement

    ERIC Educational Resources Information Center

    Linsell, Chris; Tozer, Lynn; Anakin, Megan; Cox, Anna; Jones, Rachel; McAuslan, Eric; Smith, Donna; Turner, Garry

    2012-01-01

    This paper reports findings from the second year of a two-year study designed to develop approaches to teaching algebra in years 9 and 10. The aim of the research was to explore and develop teaching approaches to assist students to acquire a conceptual understanding of algebra, and to document the impact of these approaches on student outcomes.…

  13. SICs and Algebraic Number Theory

    NASA Astrophysics Data System (ADS)

    Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon

    2017-08-01

    We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.

  14. 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…

  15. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

  16. 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.)

  17. 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.

  18. Multiplier operator algebras and applications.

    PubMed

    Blecher, David P; Zarikian, Vrej

    2004-01-20

    The one-sided multipliers of an operator space X are a key to "latent operator algebraic structure" in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals.

  19. 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…

  20. 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.

  1. 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…

  2. 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.)

  3. 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.)

  4. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  5. 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.

  6. Prosthetic mesh materials used in hernia surgery.

    PubMed

    Sanders, David L; Kingsnorth, Andrew N

    2012-03-01

    It is estimated that 20 million prosthetic meshes are implanted each year worldwide. It is clear that the evolution of meshes is not yet complete and the ideal mesh is yet to be found. There is a vast array of prosthetics available for hernia repair. This review outlines the properties of available meshes and the evidence to be considered when choosing a prosthetic for hernia repair.

  7. [Late vaginal mesh exposure after prolapse repair].

    PubMed

    Chanelles, O; Poncelet, C

    2010-12-01

    Mesh exposure is the major complication of vaginal prolapse repair. Incidence rates are variable according to the series. Mesh exposure usually occurs during the year following the intervention. We report here the first case of a patient with a late exposure of an anterior vaginal mesh 4 years after a surgical cystocele repair. The mesh has been easily removed at the operative theatre by vaginal approach.

  8. Symplectic Clifford Algebraic Field Theory.

    NASA Astrophysics Data System (ADS)

    Dixon, Geoffrey Moore

    We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.

  9. 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.

  10. Hybrid mesh generation using advancing reduction technique

    USDA-ARS?s Scientific Manuscript database

    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. Vaginal repair with mesh versus colporrhaphy for prolapse: a randomised controlled trial

    PubMed Central

    Carey, M; Higgs, P; Goh, J; Lim, J; Leong, A; Krause, H; Cornish, A

    2009-01-01

    Objective To compare vaginal repair augmented by mesh with traditional colporrhaphy for the treatment of pelvic organ prolapse. Design Prospective randomised controlled trial. Setting Tertiary teaching hospital. Population One hundred and thirty-nine women with stage ≥2 prolapse according to the pelvic organ prolapse quantification (POP-Q) system requiring both anterior and posterior compartment repair. Methods Subjects were randomised to anterior and posterior vaginal repair with mesh augmentation (mesh group, n= 69) or traditional anterior and posterior colporrhaphy (no mesh group, n= 70). Main outcome measures The primary outcome was the absence of POP-Q stage ≥2 prolapse at 12 months. Secondary outcomes were symptoms, quality-of-life outcomes and satisfaction with surgery. Complications were also reported. Results For subjects attending the 12-month review, success in the mesh group was 81.0% (51 of 63 subjects) compared with 65.6% (40/61) in the no mesh group and was not significantly different (P-value = 0.07). A high level of satisfaction with surgery and improvements in symptoms and quality-of-life data were observed at 12 months compared to baseline in both groups, but there was no significant difference in these outcomes between the two groups. Vaginal mesh exposure occurred in four women in the mesh group (5.6%). De novo dyspareunia was reported by five of 30 (16.7%) sexually active women in the mesh group and five of 33 (15.2%) in the no mesh group at 12 months. Conclusion In this study, vaginal surgery augmented by mesh did not result in significantly less recurrent prolapse than traditional colporrhaphy 12 months following surgery. PMID:19583714

  12. Three-year outcomes of vaginal mesh for prolapse: a randomized controlled trial.

    PubMed

    Gutman, Robert E; Nosti, Patrick A; Sokol, Andrew I; Sokol, Eric R; Peterson, Joanna L; Wang, Hong; Iglesia, Cheryl B

    2013-10-01

    To present the 3-year outcomes of a double-blind, multicenter, randomized trial comparing vaginal prolapse repair with and without mesh. This was a planned final analysis of women with Pelvic Organ Prolapse Quantification (POP-Q) stage 2-4 prolapse randomized to traditional vaginal prolapse surgery without mesh and vaginal colpopexy repair with mesh. We evaluated anatomic, symptomatic, and combined cure rates for those with at least 3-year validated quality-of-life questionnaires and 2- or 3-year postoperative blinded POP-Q examination. Participants undergoing reoperation for recurrent prolapse were removed for anatomic and subjective outcomes analysis and considered failures for combined outcomes analysis. Sixty-five women were enrolled (33 mesh, 32 no mesh) before the study was prematurely halted as a result of a 15.6% mesh exposure rate. At 3 years, 51 of 65 (78%) had quality-of-life questionnaires (25 mesh, 26 no mesh) and 41 (63%) had examinations. Three participants died, three required reoperation for recurrent prolapse (all in mesh group), and eight were lost to follow-up. No differences were observed between groups at 3 years for prolapse stage or individual prolapse points. Stage improved for each group (90% and 86%) from baseline to 3 years (P<.01). Symptomatic improvement was observed with no differences in scores between groups. Cure rates did not differ between groups using a variety of definitions, and anatomic cure was lowest for the anterior compartment. There was no difference in 3-year cure rates when comparing patients undergoing traditional vaginal prolapse surgery without mesh with those undergoing vaginal colpopexy repair with mesh. Clinicaltrials.gov, www.clinicaltrials.gov, NCT00475540. : I.

  13. User Manual for the PROTEUS Mesh Tools

    SciTech Connect

    Smith, Micheal A.; Shemon, Emily R

    2016-09-19

    PROTEUS is built around a finite element representation of the geometry for visualization. In addition, the PROTEUS-SN solver was built to solve the even-parity transport equation on a finite element mesh provided as input. Similarly, PROTEUS-MOC and PROTEUS-NEMO were built to apply the method of characteristics on unstructured finite element meshes. Given the complexity of real world problems, experience has shown that using commercial mesh generator to create rather simple input geometries is overly complex and slow. As a consequence, significant effort has been put into place to create multiple codes that help assist in the mesh generation and manipulation. There are three input means to create a mesh in PROTEUS: UFMESH, GRID, and NEMESH. At present, the UFMESH is a simple way to generate two-dimensional Cartesian and hexagonal fuel assembly geometries. The UFmesh input allows for simple assembly mesh generation while the GRID input allows the generation of Cartesian, hexagonal, and regular triangular structured grid geometry options. The NEMESH is a way for the user to create their own mesh or convert another mesh file format into a PROTEUS input format. Given that one has an input mesh format acceptable for PROTEUS, we have constructed several tools which allow further mesh and geometry construction (i.e. mesh extrusion and merging). 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

  14. 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)

  15. 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)

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

    PubMed Central

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

    2009-01-01

    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

  17. Macdonald index and chiral algebra

    NASA Astrophysics Data System (ADS)

    Song, Jaewon

    2017-08-01

    For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

  18. 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.

  19. 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.

  20. 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.

  1. The algebraic method

    NASA Astrophysics Data System (ADS)

    Grassi, P. A.; Hurth, T.; Steinhauser, M.

    2001-09-01

    Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process b→ sγ.

  2. 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.

  3. 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.

  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. Mesh materials and hernia repair

    PubMed Central

    Elango, Santhini; Perumalsamy, Sakthivel; Ramachandran, Krishnakumar; Vadodaria, Ketankumar

    2017-01-01

    Hernia incidence has been observed since ancient time. Advancement in the medical textile industry came up with the variety of mesh materials to repair hernia, but none of them are without complications including recurrence of hernia. Therefore individuals once developed with the hernia could not lead a healthy and comfortable life. This drawn attention of surgeons, patients, researchers and industry to know the exact mechanism behind its development, complications and recurrence. Recent investigations highlighted the role of genetic factors and connective tissue disorders being the reason for the development of hernia apart from the abnormal pressure that is known to develop during other disease conditions. This review discusses different mesh materials, their advantages and disadvantages and their biological response after its implantation. PMID:28840830

  6. 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.

  7. Translating MeSH concepts.

    PubMed

    Soualmia, Lina F; Letord, Catherine; Merabti, Tayeb; Griffon, Nicolas; Manel, Jacques; Darmoni, Stéfan J

    2013-01-01

    The concept-oriented structure of the MeSH® thesaurus is not yet in common use. Nevertheless, it has been shown that a concept-based querying of PubMed may be of interest. To take full advantage of the concept-oriented structure of MeSH in the information retrieval tool associated with the CISMeF catalogue, it was necessary to translate such concepts into French.

  8. 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.

  9. Particle-like structure of Lie algebras

    NASA Astrophysics Data System (ADS)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  10. Investigating Teacher Noticing of Student Algebraic Thinking

    ERIC Educational Resources Information Center

    Walkoe, Janet Dawn Kim

    2013-01-01

    Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…

  11. Investigating Teacher Noticing of Student Algebraic Thinking

    ERIC Educational Resources Information Center

    Walkoe, Janet Dawn Kim

    2013-01-01

    Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…

  12. Generalized Lie algebras of type An

    NASA Astrophysics Data System (ADS)

    Lyubashenko, Volodymyr; Sudbery, Anthony

    1998-06-01

    It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz's. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré-Birkhoff-Witt basis.

  13. 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…

  14. All-quad meshing without cleanup

    SciTech Connect

    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 we 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.

  15. All-quad meshing without cleanup

    DOE PAGES

    Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.; ...

    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

  16. Mesh segmentation with concavity-aware fields.

    PubMed

    Au, Oscar Kin-Chung; Zheng, Youyi; Chen, Menglin; Xu, Pengfei; Tai, Chiew-Lan

    2012-07-01

    This paper presents a simple and efficient automatic mesh segmentation algorithm that solely exploits the shape concavity information. The method locates concave creases and seams using a set of concavity-sensitive scalar fields. These fields are computed by solving a Laplacian system with a novel concavity-sensitive weighting scheme. Isolines sampled from the concavity-aware fields naturally gather at concave seams, serving as good cutting boundary candidates. In addition, the fields provide sufficient information allowing efficient evaluation of the candidate cuts. We perform a summarization of all field gradient magnitudes to define a score for each isoline and employ a score-based greedy algorithm to select the best cuts. Extensive experiments and quantitative analysis have shown that the quality of our segmentations are better than or comparable with existing state-of-the-art more complex approaches.

  17. All-quad meshing without cleanup

    SciTech Connect

    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 we 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.

  18. Loop Virasoro Lie conformal algebra

    SciTech Connect

    Wu, Henan Chen, Qiufan; Yue, Xiaoqing

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  19. Grating droplets with a mesh

    NASA Astrophysics Data System (ADS)

    Soto, Dan; Le Helloco, Antoine; Clanet, Cristophe; Quere, David; Varanasi, Kripa

    2016-11-01

    A drop thrown against a mesh can pass through its holes if impacting with enough inertia. As a result, although part of the droplet may remain on one side of the sieve, the rest will end up grated through the other side. This inexpensive method to break up millimetric droplets into micrometric ones may be of particular interest in a wide variety of applications: enhancing evaporation of droplets launched from the top of an evaporative cooling tower or preventing drift of pesticides sprayed above crops by increasing their initial size and atomizing them at the very last moment with a mesh. In order to understand how much liquid will be grated we propose in this presentation to start first by studying a simpler situation: a drop impacting a plate pierced with a single off centered hole. The study of the role of natural parameters such as the radius drop and speed or the hole position, size and thickness allows us to discuss then the more general situation of a plate pierced with multiple holes: the mesh.

  20. 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.

  1. 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.

  2. Central extensions of Lax operator algebras

    NASA Astrophysics Data System (ADS)

    Schlichenmaier, M.; Sheinman, O. K.

    2008-08-01

    Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.

  3. Prospective randomized controlled study using polyethylene mesh for inguinal hernia meshplasty as a safe and cost-effective alternative to polypropylene mesh.

    PubMed

    Gundre, Nitin P; Iyer, Sandhya P; Subramaniyan, Prabhakar

    2012-03-01

    Most patients who come to a general hospital in a developing country are poor. The most important prohibiting factor for use of polypropylene mesh in hernia repair is its exorbitant cost. Hence, research workers have been on the lookout for an equally effective but economically affordable mesh. Worldwide, surgical repair of inguinal hernia is the most common general surgery procedure performed at the present. Lifetime risk of groin hernia is 15% in males and 5% in females. Most of the patients who visit a general hospital are from either lower middle class or poor socioeconomic strata. The most important prohibiting factor for use of polypropylene mesh in hernia repair for the common man is its exorbitant cost. The aim of this study is to document the feasibility, safety and cost-effectiveness of the use of polyethylene mesh. A single blind, prospective, randomized controlled study, comparing 35 patients of two groups was conducted in a tertiary teaching hospital over a period of 5 years. The patients in both groups underwent inguinal hernioplasty, and were administered similar antibiotics and analgesics. The postoperative course with regard to pain, seroma formation, infection, hospital stay, recurrence and scar quality was evaluated and compared. Statistical analysis was performed with Chi square test. The properties of both meshes were the same with respect to ease of handling, pain score, seroma formation, infection rate, resumption of daily activities, scar quality and mesh rejection. Recurrence rate was zero for both groups. Polyethylene mesh was 2,808 times cheaper than the commercially available polypropylene mesh. This study proved the safety, simplicity, efficacy and cost-effectiveness of polyethylene mesh for inguinal hernia meshplasty, insuring economical, accessible health care for the financially weak section of the population.

  4. Efficient and exact mesh deformation using multiscale RBF interpolation

    NASA Astrophysics Data System (ADS)

    Kedward, L.; Allen, C. B.; Rendall, T. C. S.

    2017-09-01

    Radial basis function (RBF) interpolation is popular for mesh deformation due to robustness and generality, but the cost scales with the number of surface points sourcing the deformation as O (Ns3). Hence, there have been numerous works investigating efficient methods using reduced datasets. However, although reduced-data methods are efficient, they require a secondary method to treat an error vector field to ensure surface points not included in the primary deformation are moved to the correct location, and the volume mesh moved accordingly. A new method is presented which captures global and local motions at multiple scales using all the surface points, and so no correction stage is required; all surface points are used and a single interpolation built, but the cost and conditioning issues associated with RBF methods are eliminated. Moreover, the sparsity introduced is exploited using a wall distance function, to further reduce the cost. The method is compared to an efficient greedy method, and it is shown mesh quality is always comparable with or better than with the greedy method, and cost is comparable or cheaper at all stages. Surface mesh preprocessing is the dominant cost for reduced-data methods and this cost is reduced significantly here: greedy methods select points to minimise interpolation error, requiring repeated system solution and cost O (Nred4) to select Nred points; the multiscale method has no error, and the problem is transferred to a geometric search, with cost O (Ns log (Ns)), resulting in an eight orders of magnitude cost reduction for three-dimensional meshes. Furthermore, since the method is dependent on geometry, not deformation, it only needs to be applied once, prior to simulation, as the mesh deformation is decoupled from the point selection process.

  5. Asymptotic aspect of derivations in Banach algebras.

    PubMed

    Roh, Jaiok; Chang, Ick-Soon

    2017-01-01

    We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  6. Computing Matrix Representations of Filiform Lie Algebras

    NASA Astrophysics Data System (ADS)

    Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.

    In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.

  7. 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.

  8. Recent progress on fully analytic mesh based computer-generated holography

    NASA Astrophysics Data System (ADS)

    Park, Jae-Hyeung

    2016-10-01

    Computer generated holography plays a main role in the contents generation for holographic displays and digital archiving of three-dimensional objects. The fully analytic mesh based computer generated holography finds exact complex optical field for each triangular mesh of the three-dimensional objects for given sampling interval in the hologram plane without any approximation, enhancing the quality of the reconstruction. The mesh based processing rather than conventional point based one makes it compatible with most computer graphics techniques and efficient especially for large objects. In this paper, we present a few recent progress on fully analytic mesh based computer generated holography techniques including the dark line artifact removal, continuous shading of each mesh surface, the implementation of the angular reflectance distribution of the object surface and application of the texture map.

  9. 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.

  10. 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.

  11. Transvaginal single-incision mesh reconstruction for recurrent or advanced anterior vaginal wall prolapse.

    PubMed

    Marschke, J; Hengst, L; Schwertner-Tiepelmann, N; Beilecke, K; Tunn, R

    2015-05-01

    Single-incision transvaginal mesh for reconstruction of Level I and II prolapses in women with recurrent or advanced prolapse. We evaluated functional, anatomical, sonomorphological and quality-of-life outcome. Data were collected retrospectively for preoperative parameters and at follow-up visits. Anatomical cure was assessed with vaginal examination using the ICS-POP-Q system; introital-ultrasound scan for postvoidal residual and description of mesh characteristics was performed. We applied a visual analogue scale (VAS) and the German Pelvic Floor Questionnaire to assess quality-of-life. Seventy women with cystocele (III: 61.3%/IV: 16%), all post-hysterectomy and in majority (81.4%) after previous cystocele repair, were operated using a single-incision transvaginal technique. Overall anatomical success rate was 95.7% with significant improvement in quality-of-life (p < 0.0001). Mesh erosion occurred in 5.7%, one patient presented symptomatic vaginal vault prolapse. Postvoidal residual declined significantly (58 vs. 2.9%). Sonographic mesh length was 55.7% of implanted mesh with a wide range of mesh position, but no signs of mesh dislocation. There was no de novo dyspareunia reported, one case of preoperative existing dyspareunia worsened. No severe adverse event was observed. We hereby present a trial of a high-risk group of patients requiring reconstruction of anterior and apical vaginal wall in mostly recurrent prolapse situation. Our data support the hypothesis of improved anatomical and functional results and less mesh shrinkage caused by the single-incision technique with fixation in sacrospinous ligament in combination with modification in mesh quality compared to former multi-incision techniques.

  12. 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.

  13. 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.

  14. 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.

  15. Semiclassical states on Lie algebras

    SciTech Connect

    Tsobanjan, Artur

    2015-03-15

    The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.

  16. An "Arithmetic" Thinker Tackles Algebra

    ERIC Educational Resources Information Center

    Armstrong, Alayne C.

    2006-01-01

    Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.

  17. 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.

  18. Synthetic Versus Biological Mesh-Related Erosion After Laparoscopic Ventral Mesh Rectopexy: A Systematic Review.

    PubMed

    Balla, Andrea; Quaresima, Silvia; Smolarek, Sebastian; Shalaby, Mostafa; Missori, Giulia; Sileri, Pierpaolo

    2017-04-01

    This review reports the incidence of mesh-related erosion after ventral mesh rectopexy to determine whether any difference exists in the erosion rate between synthetic and biological mesh. A systematic search of the MEDLINE and the Ovid databases was conducted to identify suitable articles published between 2004 and 2015. The search strategy capture terms were laparoscopic ventral mesh rectopexy, laparoscopic anterior rectopexy, robotic ventral rectopexy, and robotic anterior rectopexy. Eight studies (3,956 patients) were included in this review. Of those patients, 3,517 patients underwent laparoscopic ventral rectopexy (LVR) using synthetic mesh and 439 using biological mesh. Sixty-six erosions were observed with synthetic mesh (26 rectal, 32 vaginal, 8 recto-vaginal fistulae) and one (perineal erosion) with biological mesh. The synthetic and the biological mesh-related erosion rates were 1.87% and 0.22%, respectively. The time between rectopexy and diagnosis of mesh erosion ranged from 1.7 to 124 months. No mesh-related mortalities were reported. The incidence of mesh-related erosion after LVR is low and is more common after the placement of synthetic mesh. The use of biological mesh for LVR seems to be a safer option; however, large, multicenter, randomized, control trials with long follow-ups are required if a definitive answer is to be obtained.

  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. Quantum Process Algebra with Priorities

    NASA Astrophysics Data System (ADS)

    Ren, Xingtian; Wang, Yong; Dai, Guiping

    2017-08-01

    One of the most fascinating characteristics is the modularity of ACP (Algebra of Communicating Processes), that is, ACP can be extended easily. qACP also inherents the modularity characteristics of ACP. By introducing new operators or new constants, qACP can have more properties. In this paper, we extend the quantum process algebra qACP with priorities support in an elegant way. And we obtain the soundness and completeness of the extension.

  1. Coherent States for Hopf Algebras

    NASA Astrophysics Data System (ADS)

    Škoda, Zoran

    2007-07-01

    Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.

  2. Multiplier operator algebras and applications

    PubMed Central

    Blecher, David P.; Zarikian, Vrej

    2004-01-01

    The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990

  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. Practical implementation of tetrahedral mesh reconstruction in emission tomography

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

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

    2013-05-07

    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. Comparing the Effects of Mesh Size on Benthic Macroinvertebrate Performance Characteristics in Montana streams

    NASA Astrophysics Data System (ADS)

    Laidlaw, T. L.; Jessup, B.; Stagliano, D.; Stribling, J.; Feldman, D. L.; Bollman, W.

    2005-05-01

    Montana's Department of Environmental Quality (DEQ) has collected macroinvertebrate data for twenty years. During this time, sampling methods and mesh sizes have been modified, though the effects of the modifications on the samples collected have not been studied. DEQ has used and continues to use both 500 and 1200 ìm mesh sizes. The purpose of this study is to evaluate the effects of the different mesh sizes on taxonomic diversity and metric values. Field crews followed DEQ's traveling kick sampling methods and collected samples at each site using both mesh sizes. Sixteen sampling locations were distributed throughout two ecoregions (the Mountains and the Mountain and Valley Foothills) with replicate samples collected at seven locations. We developed a suite of both quantitative and qualitative performance characteristics (precision, accuracy, bias) and directly compared them for each mesh size. Preliminary ordination results showed no significant differences between the community level performance measures. Preliminary metric analysis showed that the 1200 ìm mesh captured a greater abundance and diversity of caddisflies (Trichoptera) than the 500 ìm mesh. This study will determine if data collected using different mesh sizes can be aggregated for development of bioassessment tools and will help DEQ implement consistent statewide sampling protocols.

  7. Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.

    ERIC Educational Resources Information Center

    Stoutemyer, David R.

    1983-01-01

    Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)

  8. 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.

  9. Novikov algebras with associative bilinear forms

    NASA Astrophysics Data System (ADS)

    Zhu, Fuhai; Chen, Zhiqi

    2007-11-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  10. 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

  11. 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

  12. 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.

  13. 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.

  14. Bluetooth Low Energy Mesh Networks: A Survey.

    PubMed

    Darroudi, Seyed Mahdi; Gomez, Carles

    2017-06-22

    Bluetooth Low Energy (BLE) has gained significant momentum. However, the original design of BLE focused on star topology networking, which limits network coverage range and precludes end-to-end path diversity. In contrast, other competing technologies overcome such constraints by supporting the mesh network topology. For these reasons, academia, industry, and standards development organizations have been designing solutions to enable BLE mesh networks. Nevertheless, the literature lacks a consolidated view on this emerging area. This paper comprehensively surveys state of the art BLE mesh networking. We first provide a taxonomy of BLE mesh network solutions. We then review the solutions, describing the variety of approaches that leverage existing BLE functionality to enable BLE mesh networks. We identify crucial aspects of BLE mesh network solutions and discuss their advantages and drawbacks. Finally, we highlight currently open issues.

  15. Bluetooth Low Energy Mesh Networks: A Survey

    PubMed Central

    Darroudi, Seyed Mahdi; Gomez, Carles

    2017-01-01

    Bluetooth Low Energy (BLE) has gained significant momentum. However, the original design of BLE focused on star topology networking, which limits network coverage range and precludes end-to-end path diversity. In contrast, other competing technologies overcome such constraints by supporting the mesh network topology. For these reasons, academia, industry, and standards development organizations have been designing solutions to enable BLE mesh networks. Nevertheless, the literature lacks a consolidated view on this emerging area. This paper comprehensively surveys state of the art BLE mesh networking. We first provide a taxonomy of BLE mesh network solutions. We then review the solutions, describing the variety of approaches that leverage existing BLE functionality to enable BLE mesh networks. We identify crucial aspects of BLE mesh network solutions and discuss their advantages and drawbacks. Finally, we highlight currently open issues. PMID:28640183

  16. MPDATA error estimator for mesh adaptivity

    NASA Astrophysics Data System (ADS)

    Szmelter, Joanna; Smolarkiewicz, Piotr K.

    2006-04-01

    In multidimensional positive definite advection transport algorithm (MPDATA) the leading error as well as the first- and second-order solutions are known explicitly by design. This property is employed to construct refinement indicators for mesh adaptivity. Recent progress with the edge-based formulation of MPDATA facilitates the use of the method in an unstructured-mesh environment. In particular, the edge-based data structure allows for flow solvers to operate on arbitrary hybrid meshes, thereby lending itself to implementations of various mesh adaptivity techniques. A novel unstructured-mesh nonoscillatory forward-in-time (NFT) solver for compressible Euler equations is used to illustrate the benefits of adaptive remeshing as well as mesh movement and enrichment for the efficacy of MPDATA-based flow solvers. Validation against benchmark test cases demonstrates robustness and accuracy of the approach.

  17. Improved ALE mesh velocities for complex flows

    DOE PAGES

    Bakosi, Jozsef; Waltz, Jacob I.; Morgan, Nathaniel Ray

    2017-05-31

    A key choice in the development of arbitrary Lagrangian-Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring-force model. This approach allows distinct and separate control over rotational and translational modes. In conclusion, the utility of the new mesh motion algorithmmore » is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.« less

  18. Mesh networking optimized for robotic teleoperation

    NASA Astrophysics Data System (ADS)

    Hart, Abraham; Pezeshkian, Narek; Nguyen, Hoa

    2012-06-01

    Mesh networks for robot teleoperation pose different challenges than those associated with traditional mesh networks. Unmanned ground vehicles (UGVs) are mobile and operate in constantly changing and uncontrollable environments. Building a mesh network to work well under these harsh conditions presents a unique challenge. The Manually Deployed Communication Relay (MDCR) mesh networking system extends the range of and provides non-line-of-sight (NLOS) communications for tactical and explosive ordnance disposal (EOD) robots currently in theater. It supports multiple mesh nodes, robots acting as nodes, and works with all Internet Protocol (IP)-based robotic systems. Under MDCR, the performance of different routing protocols and route selection metrics were compared resulting in a modified version of the Babel mesh networking protocol. This paper discusses this and other topics encountered during development and testing of the MDCR system.

  19. On the application of hybrid meshes in hydraulic machinery CFD simulations

    NASA Astrophysics Data System (ADS)

    Schlipf, M.; Tismer, A.; Riedelbauch, S.

    2016-11-01

    The application of two different hybrid mesh types for the simulation of a Francis runner for automated optimization processes without user input is investigated. Those mesh types are applied to simplified test cases such as flow around NACA airfoils to identify the special mesh resolution effects with reduced complexity, like rotating cascade flows, as they occur in a turbomachine runner channel. The analysis includes the application of those different meshes on the geometries by keeping defined quality criteria and exploring the influences on the simulation results. All results are compared with reference values gained by simulations with blockstructured hexahedron meshes and the same numerical scheme. This avoids additional inaccuracies caused by further numerical and experimental measurement methods. The results show that a simulation with hybrid meshes built up by a blockstructured domain with hexahedrons around the blade in combination with a tetrahedral far field in the channel is sufficient to get results which are almost as accurate as the results gained by the reference simulation. Furthermore this method is robust enough for automated processes without user input and enables comparable meshes in size, distribution and quality for different similar geometries as occurring in optimization processes.

  20. Applications of quadrilateral and quadrilateral-prism mesh generation in overland and subsurface simulations

    NASA Astrophysics Data System (ADS)

    Sun, Lu; Yeh, Gour-Tsyh; Zhao, Guoqun

    2017-05-01

    This paper developed an automatic mesh generator used for simulating real-world problems of hydrological cycles, fluid flow, salinity and thermal transport, sediment and water quality transport, etc. The 2-D overland area was discretized with quadrilaterals based on conformal mapping technique. A position-percent interpolation equation was established to determine nodal vertical-coordinates and match boundaries. For 3-D simulations of subsurface zones, an additional mesh generation method was proposed to create quadrilaterals for filling the empty regions along river reaches and around junctions with storage, ponds or lakes. In order to deal with special storage region with an odd number of boundary nodes, an additional triangle was inserted. Five topological optimization templates were proposed to improve the quality of degenerated elements. This paper proposed the basic algorithms to generate quadrilateral-prism meshes through stretching the quadrilateral mesh along vertical directions based on material domains. Aiming at four types of fractures, corresponding extraction methods were presented to preserve geometric features. In order to accommodate the need for overland and subsurface simulations, 1-D/2-D/3-D correspondence was established between rivers, junctions, ponds, lakes, control structures and finite element meshes. Finally, several realistic hydrologic and geologic examples for meshing multi-domain areas were provided to demonstrate the accuracy and effectiveness of the mesh generator developed in this paper.

  1. Quantum Q systems: from cluster algebras to quantum current algebras

    NASA Astrophysics Data System (ADS)

    Di Francesco, Philippe; Kedem, Rinat

    2017-02-01

    This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.

  2. Floating shock fitting via Lagrangian adaptive meshes

    NASA Technical Reports Server (NTRS)

    Vanrosendale, John

    1995-01-01

    In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.

  3. [Treatment of paracolostomic hernias using polypropylene mesh].

    PubMed

    Grigoriuk, A A; Ishchenko, V N; Matveev, A V; Kovalev, V A; Krasnobaev, A E; Stuzhin, S A

    2015-01-01

    It was analyzed the results of treatment of 23 patients with large paracolostomic hernias. Twenty patients underwent colostomy suturing and hernial ring Onlay-plasty with polypropylene mesh without tension. Onlay-plasty of hernial ring with own tissues and polypropylene mesh and colostomy reconstruction outside of implant were performed in 3 patients. Onlay-alloplasty with polypropylene mesh "PROLENE" is effective method of treatment of postoperative paracolostomic ventral hernias with colostomy closing as well as with its reconstruction outside of implant.

  4. 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.

  5. 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.

  6. Are meshes with lightweight construction strong enough?

    PubMed

    Holste, Joerg L

    2005-01-01

    The use of mesh has become essential in the repair of abdominal wall incisional hernias. Suture techniques, reapplied after failure of a primary repair, are characterized by recurrence rates of up to 50 percent, whereas the reinforcement of the abdominal wall with surgical mesh has significantly decreased these rates to <10 percent. This article describes the background for the development of mesh with lightweight construction and physiological biomechanical performance.

  7. 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.

  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. Mesh infrastructure for coupled multiprocess geophysical simulations

    DOE PAGES

    Garimella, Rao V.; Perkins, William A.; Buksas, Mike W.; ...

    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

  10. 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.

  11. Method of generating a surface mesh

    SciTech Connect

    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.

  12. Transrectal Mesh Erosion Requiring Bowel Resection.

    PubMed

    Kemp, Marta Maria; Slim, Karem; Rabischong, Benoît; Bourdel, Nicolas; Canis, Michel; Botchorishvili, Revaz

    To report a case of a transrectal mesh erosion as complication of laparoscopic promontofixation with mesh repair, necessitating bowel resection and subsequent surgical interventions. Sacrocolpopexy has become a standard procedure for vaginal vault prolapse [1], and the laparoscopic approach has gained popularity owing to more rapid recovery and less morbidity [2,3]. Mesh erosion is a well-known complication of surgical treatment for prolapse as reported in several negative evaluations, including a report from the US Food and Drug Administration in 2011 [4]. Mesh complications are more common after surgeries via the vaginal approach [5]; nonetheless, the incidence of vaginal mesh erosion after laparoscopic procedures is as high as 9% [6]. The incidence of transrectal mesh exposure after laparoscopic ventral rectopexy is roughly 1% [7]. The diagnosis may be delayed because of its rarity and variable presentation. In addition, polyester meshes, such as the mesh used in this case, carry a higher risk of exposure [8]. A 57-year-old woman experiencing genital prolapse, with the cervix classified as +3 according to the Pelvic Organ Prolapse Quantification system, underwent laparoscopic standard sacrocolpopexy using polyester mesh. Subtotal hysterectomy and bilateral adnexectomy were performed concomitantly. A 3-year follow-up consultation demonstrated no signs or symptoms of erosion of any type. At 7 years after the surgery, however, the patient presented with rectal discharge, diagnosed as infectious rectocolitis with the isolation of Clostridium difficile. She underwent a total of 5 repair surgeries in a period of 4 months, including transrectal resection of exposed mesh, laparoscopic ablation of mesh with digestive resection, exploratory laparoscopy with abscess drainage, and exploratory laparoscopy with ablation of residual mesh and transverse colostomy. She recovered well after the last intervention, exhibiting no signs of vaginal or rectal fistula and no recurrence

  13. 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

  14. (Fuzzy) Ideals of BN-Algebras.

    PubMed

    Dymek, Grzegorz; 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.

  15. Antibiotic Coating of Hernia Meshes: The Next Step Toward Preventing Mesh Infection.

    PubMed

    Majumder, Arnab; Neupane, Ruel; Novitsky, Yuri W

    2015-11-01

    Mesh bacterial colonization/infection remains a critical issue in complex ventral hernia repair. Despite the recent emergence of biologic meshes, current strategies to prevent and treat mesh infection are largely ineffective, often leading to device failure and subsequent explantation along with the associated costs and effect on patient welfare. Unacceptably high rates of morbidity and hernia recurrence following mesh infection highlight the need for innovation in the area of hernia repair for the complex patient. One recent strategy to address such shortcomings is local antibiosis in the form of polymer coatings applied to the mesh itself. Current literature regarding the use of antibiotic-coated hernia mesh is limited but does illustrate the ability of these devices to inhibit bacterial growth and prevent mesh infection in both in vitro and in vivo studies. Although there is a paucity of literature regarding long-term clinical efficacy, this provides opportunity for further inquiry into a promising new development to combat mesh infective complications.

  16. 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

  17. 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

  18. Development and Verification of Unstructured Adaptive Mesh Technique with Edge Compatibility

    NASA Astrophysics Data System (ADS)

    Ito, Kei; Kunugi, Tomoaki; Ohshima, Hiroyuki

    In the design study of the large-sized sodium-cooled fast reactor (JSFR), one key issue is suppression of gas entrainment (GE) phenomena at a gas-liquid interface. Therefore, the authors have been developed a high-precision CFD algorithm to evaluate the GE phenomena accurately. The CFD algorithm has been developed on unstructured meshes to establish an accurate modeling of JSFR system. For two-phase interfacial flow simulations, a high-precision volume-of-fluid algorithm is employed. It was confirmed that the developed CFD algorithm could reproduce the GE phenomena in a simple GE experiment. Recently, the authors have been developed an important technique for the simulation of the GE phenomena in JSFR. That is an unstructured adaptive mesh technique which can apply fine cells dynamically to the region where the GE occurs in JSFR. In this paper, as a part of the development, a two-dimensional unstructured adaptive mesh technique is discussed. In the two-dimensional adaptive mesh technique, each cell is refined isotropically to reduce distortions of the mesh. In addition, connection cells are formed to eliminate the edge incompatibility between refined and non-refined cells. The two-dimensional unstructured adaptive mesh technique is verified by solving well-known lid-driven cavity flow problem. As a result, the two-dimensional unstructured adaptive mesh technique succeeds in providing a high-precision solution, even though poor-quality distorted initial mesh is employed. In addition, the simulation error on the two-dimensional unstructured adaptive mesh is much less than the error on the structured mesh with a larger number of cells.

  19. Early Wound Morbidity after Open Ventral Hernia Repair with Biosynthetic or Polypropylene Mesh.

    PubMed

    Sahoo, Sambit; Haskins, Ivy N; Huang, Li-Ching; Krpata, David M; Derwin, Kathleen A; Poulose, Benjamin K; Rosen, Michael J

    2017-10-01

    Recently introduced slow-resorbing biosynthetic and non-resorbing macroporous polypropylene meshes are being used in hernias with clean-contaminated and contaminated wounds. However, information about the use of biosynthetic meshes and their outcomes compared with polypropylene meshes in clean-contaminated and contaminated cases is lacking. Here we evaluate the use of biosynthetic mesh and polypropylene mesh in elective open ventral hernia repair (OVHR) and investigate differences in early wound morbidity after OVHR within clean-contaminated and contaminated cases. All elective, OVHR with biosynthetic mesh or uncoated polypropylene mesh from January 2013 through October 2016 were identified within the Americas Hernia Society Quality Collaborative. Association of mesh type with 30-day wound events in clean-contaminated or contaminated wounds was investigated using a 1:3 propensity-matched analysis. Biosynthetic meshes were used in 8.5% (175 of 2,051) of elective OVHR, with the majority (57.1%) used in low-risk or comorbid clean cases. Propensity-matched analysis in clean-contaminated and contaminated cases showed no significant difference between biosynthetic mesh and polypropylene mesh groups for 30-day surgical site occurrences (20.7% vs 16.7%; p = 0.49) or unplanned readmission (13.8% vs 9.8%; p = 0.4). However, surgical site infections (22.4% vs 10.9%; p = 0.03), surgical site occurrences requiring procedural intervention (24.1% vs 13.2%; p = 0.049), and reoperation rates (13.8% vs 4.0%; p = 0.009) were significantly higher in the biosynthetic group. Biosynthetic mesh appears to have higher rates of 30-day wound morbidity compared with polypropylene mesh in elective OVHR with clean-contaminated or contaminated wounds. Additional post-market analysis is needed to provide evidence defining best mesh choices, location, and surgical technique for repairing contaminated ventral hernias. Copyright © 2017 American College of Surgeons. Published by Elsevier Inc

  20. Tensile Behaviour of Welded Wire Mesh and Hexagonal Metal Mesh for Ferrocement Application

    NASA Astrophysics Data System (ADS)

    Tanawade, A. G.; Modhera, C. D.

    2017-08-01

    Tension tests were conducted on welded mesh and hexagonal Metal mesh. Welded Mesh is available in the market in different sizes. The two types are analysed viz. Ø 2.3 mm and Ø 2.7 mm welded mesh, having opening size 31.75 mm × 31.75 mm and 25.4 mm × 25.4 mm respectively. Tensile strength test was performed on samples of welded mesh in three different orientations namely 0°, 30° and 45° degrees with the loading axis and hexagonal Metal mesh of Ø 0.7 mm, having opening 19.05 × 19.05 mm. Experimental tests were conducted on samples of these meshes. The objective of this study was to investigate the behaviour of the welded mesh and hexagonal Metal mesh. The result shows that the tension load carrying capacity of welded mesh of Ø 2.7 mm of 0° orientation is good as compared to Ø2.3 mm mesh and ductility of hexagonal Metal mesh is good in behaviour.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. Using Number Theory to Reinforce Elementary Algebra.

    ERIC Educational Resources Information Center

    Covillion, Jane D.

    1995-01-01

    Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)

  6. 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.

  7. Comments on /N=4 superconformal algebras

    NASA Astrophysics Data System (ADS)

    Rasmussen, Jørgen

    2001-01-01

    We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)⊗U(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2|2) current superalgebra. Replacing SL(2|2) with the coset SL(2|2)/U(1), results directly in the small N=4 superconformal algebra.

  8. Tensor models and 3-ary algebras

    NASA Astrophysics Data System (ADS)

    Sasakura, Naoki

    2011-10-01

    Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.

  9. 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.

  10. Deployable modular mesh antenna - Concept and feasibility

    NASA Astrophysics Data System (ADS)

    Mitsugi, Jin; Yasaka, Tetsuo

    The feasibility of a 10m aperture deployable modular mesh antenna is evaluated by integrating the results of a statistical surface accuracy estimation and of surface shape adjustment experiments. It has been clarified that by combining seven 4m aperture modules, a 10m aperture deployable modular mesh antenna can be constructed, preserving the surface accuracy that is applicable to C band mission.

  11. 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.

  12. Structured mesh generation with smoothness controls

    USDA-ARS?s Scientific Manuscript database

    In geometrically complex domains, the RL (Ryskin and Leal) orthogonal mesh generation system may cause mesh distortion and overlapping problems when using the “weak constraint” method with specified boundary point distribution for all boundaries. To resolve these problems, an improved RL system with...

  13. Stretchable Mesh for Cavity Noise Reduction

    NASA Technical Reports Server (NTRS)

    Khorrami, Mehdi R. (Inventor)

    2017-01-01

    A stretchable mesh material extends across the opening of a cavity of the landing gear of an aircraft when the landing gear is in the deployed position. The mesh material alters the flow of air across the opening of the landing gear cavity and significantly reduces the amount of noise produced by the wheel well at low-to-mid frequencies.

  14. Mesh refinement strategy for optimal control problems

    NASA Astrophysics Data System (ADS)

    Paiva, L. T.; Fontes, F. A. C. C.

    2013-10-01

    Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

  15. Robust diamond meshes with unique wettability properties.

    PubMed

    Yang, Yizhou; Li, Hongdong; Cheng, Shaoheng; Zou, Guangtian; Wang, Chuanxi; Lin, Quan

    2014-03-18

    Robust diamond meshes with excellent superhydrophobic and superoleophilic properties have been fabricated. Superhydrophobicity is observed for water with varying pH from 1 to 14 with good recyclability. Reversible superhydrophobicity and hydrophilicity can be easily controlled. The diamond meshes show highly efficient water-oil separation and water pH droplet transference.

  16. 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

  17. 50 CFR 300.110 - Mesh size.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... either with a manual force or using a weight or dynamometer, until it is stopped at the tapering edges by... without using a weight or dynamometer. The mesh size of the net will then be determined in accordance with... for the determination of the mesh size and the net will be remeasured. (A) A weight or dynamometer...

  18. Matrix computations on mesh arrays

    SciTech Connect

    Moreno, J.H.

    1989-01-01

    This dissertation addresses the systematic derivation of mesh arrays for matrix computations, in particular realizing the algorithm-specific arrays and mapping algorithms onto class-specific arrays. A data-dependency graph-based transformational method is proposed in a design frame work consisting of two stages, namely algorithm regularization and derivation of arrays. The first stage derives the fully-parallel data-dependency graph (FPG) of an algorithm and transforms this graph into a three-dimensional one with unidirectional nearest-neighbor dependencies (a multi-mesh graph MMG). The second stage transforms the MMG into a two-dimensional G-graph, which is realized as an algorithm-specific array or mapped onto a class-specific array. This stage allows the incorporation of implementation restrictions and the evaluation of tradeoffs in properties of cells, as well as the derivation of arrays for fixed-size data and partitioned problems, while performing optimization of specific performance/cost measures. The proposed method is formalized by presenting a sufficient set of transformations and demonstrating the equivalence of graphs obtained from those transformations. Moreover, it is demonstrated that the MMG representation is always possible, due to the characteristics of the operators. The method has been applied to a collection of matrix algorithms, including matrix multiplication, convolution, matrix decompositions, transitive closure, the Faddeev algorithm, and BBA{sup {minus}1}. The examples show that, in addition to the features listed earlier, this method is easy to apply. Moreover, the method is compared with other techniques, concluding that it is advantageous because it meets evaluation criteria and produces more efficient arrays.

  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. Algebraic orbifold conformal field theories

    PubMed Central

    Xu, Feng

    2000-01-01

    The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383

  1. Entropic Forms and Related Algebras

    NASA Astrophysics Data System (ADS)

    Scarfone, Antonio

    2013-02-01

    Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.

  2. 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.

  3. Symmetry algebras of linear differential equations

    NASA Astrophysics Data System (ADS)

    Shapovalov, A. V.; Shirokov, I. V.

    1992-07-01

    The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

  4. Discrimination in a General Algebraic Setting

    PubMed Central

    Fine, Benjamin; 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

  5. Post-Lie algebras and factorization theorems

    NASA Astrophysics Data System (ADS)

    Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

    2017-09-01

    In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

  6. 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.

  7. 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.

  8. Applications of Algebraic Logic and Universal Algebra to Computer Science

    DTIC Science & Technology

    1989-06-21

    conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords

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

    PubMed Central

    Kuprat, Andrew P.; Einstein, Daniel R.

    2009-01-01

    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 Lmin and a maximum scale size Lmax. 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

  10. 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…

  11. 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…

  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. 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…

  14. Teacher Actions to Facilitate Early Algebraic Reasoning

    ERIC Educational Resources Information Center

    Hunter, Jodie

    2015-01-01

    In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

  15. 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…

  16. 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…

  17. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  18. Cyclic homology for Hom-associative algebras

    NASA Astrophysics Data System (ADS)

    Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan

    2015-12-01

    In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.

  19. 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…

  20. Embedding Algebraic Thinking throughout the Mathematics Curriculum

    ERIC Educational Resources Information Center

    Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph

    2005-01-01

    This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

  1. Constraint-Referenced Analytics of Algebra Learning

    ERIC Educational Resources Information Center

    Sutherland, Scot M.; White, Tobin F.

    2016-01-01

    The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

  2. 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…

  3. 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"…

  4. 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…

  5. 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…

  6. 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…

  7. Laparoscopic sacrocolpopexy: a comparison of Prolene and Tutoplast mesh.

    PubMed

    Loffeld, Cora J W; Thijs, Susanne; Mol, Ben W; Bongers, Marlies Y; Roovers, Jan-Paul W R

    2009-01-01

    A retrospective study was carried out to evaluate which mesh (cadaveric fascia lata (Tutoplast or Prolene mesh) is associated with the best outcome of laparoscopic sacrocolpopexy for vaginal vault prolapse. Nineteen women who had surgery with Tutoplast and 20 who underwent surgery with Prolene were followed and asked to complete the Urogenital Distress Inventory and Defecation Distress Inventory to measure disease-specific quality of life. The women were invited for a follow-up visit for pelvic examination at a mean time of 45 months. There were no significant differences in operating time, blood loss or hospital stay between the groups. The risk of re-intervention because of recurrent prolapse was higher in the Tutoplast group than in the Prolene group (relative risk 2.9 (95% Confidence interval 0.9-9.5)). Women in the Prolene group were significantly more satisfied with the operative result.

  8. 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.

  9. Quadratic Dynamical Systems and Algebras

    NASA Astrophysics Data System (ADS)

    Kinyon, M. K.; Sagle, A. A.

    1995-03-01

    Quadratic dynamical systems come from differential or discrete systems of the form Ẋ = Q(X) or X(k+1)=Q(X(k)), where Q:Rn→Rn is homogeneous of degree 2; i.e., Q(αX) = α2Q(X) for all α∈R, X∈Rn. Defining a bilinear mapping β:Rn × Rn→Rn by β(X, Y) ≔ {1}/{2}[Q(X+Y)-Q(X)-Q(Y)], we view XY≡β(X, Y) as a multiplication, and thus consider A=(Rn, β) to be a commutative, nonassociative algebra. The quadratic systems are then studied with the general theme that the structure of the algebras helps determine the behavior of the solutions. For example, semisimple algebras give a decoupling of the original system into systems occurring in simple algebras, and solvable algebras give solutions to differential systems via linear differential equations; the general three-dimensional example of the latter phenomenon is described. There are many classical examples and the scope of quadratic systems is large; every polynomial system can be embedded into a higher dimensional quadratic system such that solutions of the original system are obtained from the quadratic system. For differential systems, nilpotents of index 2 (N2=0) are equilibria and idempotents (E2=E) give ray solutions. The origin is never asymptotically stable, and the existence of nonzero idempotents implies that the origin is actually unstable. Nonzero equilibria are not hyperbolic, but can be studied by standard algebra techniques using nondegenerate bilinear forms as Lyapunov functions. Periodic orbits lie on "cones." They cannot occur in dimension 2 or in power-associative algebras. No periodic orbit can be an attractor but "limit cycles" (invariant cones) can exist. Automorphisms of the algebra A leave equilibria, periodic orbits, and domains of attraction invariant. Also, explicit solutions can be given by the action of automorphisms on an initial point; the general three-dimensional example of this is described. Thus if there are sufficient automorphisms, Hilbert‧s sixteenth problem in R3 has

  10. NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement

    PubMed Central

    Garcia-Cantero, Juan J.; Brito, Juan P.; Mata, Susana; Bayona, Sofia; Pastor, Luis

    2017-01-01

    Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells’ overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma’s morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh

  11. 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.

  12. Sonomorphological evaluation of polypropylene mesh implants after vaginal mesh repair in women with cystocele or rectocele.

    PubMed

    Tunn, R; Picot, A; Marschke, J; Gauruder-Burmester, A

    2007-04-01

    To investigate whether the sonographically measured size of the mesh implant in women who had undergone vaginal polypropylene mesh repair 6 weeks previously correlates with the original size of the mesh and whether the mesh ensures complete support of the anterior or posterior compartment. Forty postmenopausal women with anterior or posterior vaginal wall prolapse and sonographically proven cystocele (n = 20) or rectocele (n = 20) were evaluated preoperatively and 6 weeks after vaginal mesh repair. Introital ultrasound was performed to identify the polypropylene mesh and measure its distal to proximal length and configuration as well as its thickness. The initial mesh length was compared with that measured by ultrasound 6 weeks postoperatively. Vaginal length was measured pre- and postoperatively. The mean +/- SD age of the women was 68 +/- 7 years. The 20 women with cystocele underwent repair by means of anterior transobturator mesh implantation; the initial mesh length was 6.8 +/- 1.1 cm versus 2.9 +/- 0.6 cm postoperatively. The 20 women with rectocele underwent repair by posterior transischioanal mesh implantation; the initial mesh length was 9.9 +/- 0.8 cm versus 3.3 +/- 0.5 cm postoperatively. The mesh supported 43.4% of the length of the anterior vaginal wall and this value was 53.7% for the posterior wall (P = 0.016). Sonography is recommended for postoperative evaluation of the anterior and posterior mesh positions after prolapse surgery. There is a considerable discrepancy between the implanted mesh size and the length measured 6 weeks later by postoperative ultrasound. Published by John Wiley & Sons, Ltd. Copyright (c) 2007 ISUOG.

  13. 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.

  14. 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…

  15. 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…

  16. 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…

  17. Dimension independence in exterior algebra.

    PubMed

    Hawrylycz, M

    1995-03-14

    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.

  18. 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 contemporary…

  19. Experts Question California's Algebra Edict

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…

  20. 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.